2018 Problems

.gitattributes

@@ -72,3 +72,5 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 2017/finals/poles.in filter=lfs diff=lfs merge=lfs -text
 2017/finals/strolls.in filter=lfs diff=lfs merge=lfs -text
 2017/finals/tolls.in filter=lfs diff=lfs merge=lfs -text
+2018/finals/claw.in filter=lfs diff=lfs merge=lfs -text
+2018/finals/personal.in filter=lfs diff=lfs merge=lfs -text

2018/finals/citylights.cpp

@@ -0,0 +1,243 @@
+// City Lights
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+#define LIM 135
+#define MOD 1000000007
+
+int W,S,K,NH;
+PR PW[LIM],PS[LIM];
+int H[LIM];
+vector<int> ch[LIM],wh[LIM];
+LL dyn[LIM][LIM][LIM]; // dyn[i][h][b] = # of combinations in i's subtree requiring b buildings, with height h still required
+LL dynS[LIM][LIM][LIM]; // dynS[i][h][b] = sum of dyn[i][0..(h-1)][b]
+LL tmp[LIM][LIM];
+
+void CompSums(int i)
+{
+	int h,b;
+		Fox(h,NH)
+			Fox(b,W+1)
+				dynS[i][h+1][b]=(dynS[i][h][b]+dyn[i][h][b])%MOD;
+}
+
+void Add(LL &a,LL b)
+{
+	a=(a+b)%MOD;
+}
+
+void rec(int i)
+{
+	int j,c,h,b,h2,b2,nw;
+	LL pw;
+	// iterate over children
+	dyn[i][0][0]=1;
+		Fox(j,Sz(ch[i]))
+		{
+			rec(c=ch[i][j]);
+			// combine DP values
+			CompSums(i),CompSums(c);
+			Fill(tmp,0);
+				Fox(h,NH)
+					Fox(b,W+1)
+						Fox(b2,W-b+1)
+							Add(tmp[h][b+b2],dyn[i][h][b]*dynS[c][h+1][b2] + dynS[i][h][b]*dyn[c][h][b2]);
+			memcpy(dyn[i],tmp,sizeof(tmp));
+		}
+	// consider all possible subsets of windows coming into play here
+	nw=Sz(wh[i]);
+	sort(All(wh[i]));
+	reverse(All(wh[i]));
+	Fill(tmp,0);
+		Fox(j,nw+1)
+		{
+			h2=(j==nw ? 0 : wh[i][j]);
+			pw=(1LL<<(nw-min(nw,j+1)))%MOD;
+				Fox(h,NH)
+					Fox(b,W+1)
+						Add(tmp[max(h,h2)][b],pw*dyn[i][h][b]);
+		}
+	memcpy(dyn[i],tmp,sizeof(tmp));
+	// place a building here when necessary
+		FoxI(h,H[i],NH-1)
+			Fox(b,W+1)
+			{
+				Add(dyn[i][0][b+1],dyn[i][h][b]);
+				dyn[i][h][b]=0;
+			}
+	CompSums(i);
+}
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	int i,x,y,z,a,b,c;
+	LL ans;
+	vector<int> cy;
+	set<pair<PR,int> > SI;
+	set<pair<PR,int> >::iterator I;
+	map<int,int> MS;
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// input, and compress y-coordinates
+			Read(W),Read(S);
+			cy.clear(),cy.pb(0);
+				Fox(i,W)
+					Read(PW[i].y),Read(PW[i].x),cy.pb(PW[i].x);
+				Fox(i,S)
+					Read(PS[i].y),Read(PS[i].x),cy.pb(PS[i].x);
+			sort(All(cy));
+			cy.resize(unique(All(cy))-cy.begin());
+			NH=Sz(cy);
+				Fox(i,W)
+					PW[i].x=lower_bound(All(cy),PW[i].x)-cy.begin();
+				Fox(i,S)
+					PS[i].x=lower_bound(All(cy),PS[i].x)-cy.begin();
+			// init tree
+			Fill(H,60);
+				Fox(i,K)
+					ch[i].clear(),wh[i].clear();
+			K=0;
+			// iterate over stars in non-decreasing order of Y
+			sort(PS,PS+S);
+			SI.clear();
+			H[0]=1,SI.insert(mp(mp(0,INF+1),K++));
+			MS.clear();
+				Fox(i,S)
+				{
+					x=PS[i].y;
+					y=PS[i].x;
+					// find containing interval (if any)
+					I=SI.lower_bound(mp(mp(x,INF+2),0)),I--;
+					a=I->x.x;
+					b=I->x.y;
+					c=I->y;
+						if ((a<=x) && (b>=x))
+						{
+							// split interval at this X-coordinate
+								if (a<x)
+								{
+									ch[c].pb(K);
+									H[K]=y,SI.insert(mp(mp(a,x-1),K++));
+								}
+								if (b>x)
+								{
+									ch[c].pb(K);
+									H[K]=y,SI.insert(mp(mp(x+1,b),K++));
+								}
+							SI.erase(I);
+							MS[x]=c;
+						}
+				}
+			// associate windows with nodes
+				Fox(i,W)
+				{
+					x=PW[i].y;
+						if (MS.count(x))
+							c=MS[x];
+						else
+						{
+							I=SI.lower_bound(mp(mp(x,INF+2),0)),I--;
+							c=I->y;
+						}
+					wh[c].pb(PW[i].x);
+				}
+			// DP
+			Fill(dyn,0);
+			rec(0);
+			ans=0;
+				Fox1(i,W)
+					Add(ans,i*dyn[0][0][i]);
+			// output
+			printf("Case #%d: %lld\n",t,ans);
+		}
+	return(0);
+}

2018/finals/citylights.html

@@ -0,0 +1,76 @@
+<p>
+Dahlia is taking a roadtrip across all of Canada! Along the way, she's spending a night in one of the country's hallmark cities, Toronto.
+</p>
+
+<p>
+Toronto's nighttime skyline can be represented as a 2D plane, with the ground forming a horizontal line with y-coordinate 0. 
+There are <strong>W</strong> building windows, with the <em>i</em>th one at coordinates (<strong>XW<sub>i</sub></strong>, <strong>YW<sub>i</sub></strong>). 
+There are also <strong>S</strong> visible stars, with the <em>i</em>th one at coordinates (<strong>XS<sub>i</sub></strong>, <strong>YS<sub>i</sub></strong>). 
+It's guaranteed that all <strong>W</strong> + <strong>S</strong> of these points are distinct, and that no star is directly below a window (having the same x-coordinate but a smaller y-coordinate).
+</p>
+
+<p>
+At night, it's impossible to see any given window unless there's light coming from it. On any given night, each window is independently either lit up or not with equal probability. 
+As such, there are 2<sup><strong>W</strong></sup> equally-likely subsets of windows which might be visible. Dahlia finds herself looking at Toronto's skyline on one such random night.
+</p>
+
+<p>
+Dahlia knows that Toronto consists of 0 or more buildings, each of which covers a rectangular portion of the sky with some bottom-left corner (<strong>x<sub>1</sub></strong>, 0) 
+and some top-right corner (<strong>x<sub>2</sub></strong>, <strong>h</strong>), 
+for some real values of <strong>x<sub>1</sub></strong>, <strong>x<sub>2</sub></strong>, and <strong>h</strong> 
+(such that <strong>x<sub>1</sub></strong> &lt; <strong>x<sub>2</sub></strong> and <strong>h</strong> &gt; 0). 
+The buildings might overlap with one another. Based on Dahlia's view of the stars and lit-up windows, she can infer some things about the set of buildings present. 
+In particular, for each lit-up window <em>i</em>, Dahlia realizes that there must be at least one building whose rectangle inclusively covers the point 
+(<strong>XW<sub>i</sub></strong>, <strong>YW<sub>i</sub></strong>). Furthermore, for each star <em>i</em>, 
+Dahlia realizes that there must be no buildings whose rectangles inclusively cover the point (<strong>XS<sub>i</sub></strong>, <strong>YS<sub>i</sub></strong>).
+</p>
+
+<p>
+Dahlia is going to assume that Toronto consists of as few buildings as possible which are consistent with her observations on that night. 
+What's the expected number of buildings which she'll assume exist? 
+In order to avoid floating-point arithmetic and large integers, output this expected number multiplied by 2<sup><strong>W</strong></sup> (which is guaranteed to result in an integer) and then taken modulo 1,000,000,007.
+</p>
+
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of skylines.
+For each skyline, there is first a line containing the space-separated integers <strong>W</strong> and <strong>S</strong>.
+Then, <strong>W</strong> lines follow, the <em>i</em>th of which contains the space-separated integers <strong>XW<sub>i</sub></strong> and <strong>YW<sub>i</sub></strong>.
+Then, <strong>S</strong> lines follow, the <em>i</em>th of which contains the space-separated integers <strong>XS<sub>i</sub></strong> and <strong>YS<sub>i</sub></strong>.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th universe, output a line containing "Case #<em>i</em>: " the expected number of buildings which Dahlia will assume exist, multiplied by 2<sup><strong>W</strong></sup> and then taken modulo 1,000,000,007.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 150 <br />
+1 &le; <strong>W</strong> &le; 80 <br />
+1 &le; <strong>S</strong> &le; 50 <br />
+1 &le; <strong>XW<sub>i</sub></strong>, <strong>YW<sub>i</sub></strong>, <strong>XS<sub>i</sub></strong>, <strong>YS<sub>i</sub></strong> &le; 1,000,000,000 <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+  
+<p>
+In the first case, there's a 50% chance that the single window will be visible, in which case Dahlia will assume that Toronto has 1 building. 
+There's also a 50% chance that it won't be visible, in which case she'll assume that there are 0 buildings. As such, the expected number of buildings which she'll assume exist is (1 + 0) / 2 = 1/2.
+This should then be multiplied by 2<sup>1</sup> and taken modulo 1,000,000,007 to produce a final answer of 1.
+</p>
+
+<p>
+In the second case, however many windows are visible, Dahlia will assume Toronto has that many buildings. For example, if both windows are visible, then there must be at least 2 buildings, as a single building can't account for both windows without also covering the single visible star. This results in a final answer of ((0 + 1 + 1 + 2) / 4 * 2<sup>2</sup>) modulo 1,000,000,007 = 4.
+</p>
+
+<p>
+In the third case, the final answer is ((0 + 1 + 1 + 1 + 1 + 1 + 2 + 2) / 8 * 2<sup>3</sup>) modulo 1,000,000,007 = 9.
+</p>

2018/finals/citylights.md

@@ -0,0 +1,74 @@
+Dahlia is taking a roadtrip across all of Canada! Along the way, she's
+spending a night in one of the country's hallmark cities, Toronto.
+
+Toronto's nighttime skyline can be represented as a 2D plane, with the ground
+forming a horizontal line with y-coordinate 0. There are **W** building
+windows, with the _i_th one at coordinates (**XWi**, **YWi**). There are also
+**S** visible stars, with the _i_th one at coordinates (**XSi**, **YSi**).
+It's guaranteed that all **W** \+ **S** of these points are distinct, and that
+no star is directly below a window (having the same x-coordinate but a smaller
+y-coordinate).
+
+At night, it's impossible to see any given window unless there's light coming
+from it. On any given night, each window is independently either lit up or not
+with equal probability. As such, there are 2**W** equally-likely subsets of
+windows which might be visible. Dahlia finds herself looking at Toronto's
+skyline on one such random night.
+
+Dahlia knows that Toronto consists of 0 or more buildings, each of which
+covers a rectangular portion of the sky with some bottom-left corner (**x1**,
+0) and some top-right corner (**x2**, **h**), for some real values of **x1**,
+**x2**, and **h** (such that **x1** < **x2** and **h** > 0). The buildings
+might overlap with one another. Based on Dahlia's view of the stars and lit-up
+windows, she can infer some things about the set of buildings present. In
+particular, for each lit-up window _i_, Dahlia realizes that there must be at
+least one building whose rectangle inclusively covers the point (**XWi**,
+**YWi**). Furthermore, for each star _i_, Dahlia realizes that there must be
+no buildings whose rectangles inclusively cover the point (**XSi**, **YSi**).
+
+Dahlia is going to assume that Toronto consists of as few buildings as
+possible which are consistent with her observations on that night. What's the
+expected number of buildings which she'll assume exist? In order to avoid
+floating-point arithmetic and large integers, output this expected number
+multiplied by 2**W** (which is guaranteed to result in an integer) and then
+taken modulo 1,000,000,007.
+
+### Input
+
+Input begins with an integer **T**, the number of skylines. For each skyline,
+there is first a line containing the space-separated integers **W** and **S**.
+Then, **W** lines follow, the _i_th of which contains the space-separated
+integers **XWi** and **YWi**. Then, **S** lines follow, the _i_th of which
+contains the space-separated integers **XSi** and **YSi**.
+
+### Output
+
+For the _i_th universe, output a line containing "Case #_i_: " the expected
+number of buildings which Dahlia will assume exist, multiplied by 2**W** and
+then taken modulo 1,000,000,007.
+
+### Constraints
+
+1 ≤ **T** ≤ 150  
+1 ≤ **W** ≤ 80  
+1 ≤ **S** ≤ 50  
+1 ≤ **XWi**, **YWi**, **XSi**, **YSi** ≤ 1,000,000,000  
+
+### Explanation of Sample
+
+In the first case, there's a 50% chance that the single window will be
+visible, in which case Dahlia will assume that Toronto has 1 building. There's
+also a 50% chance that it won't be visible, in which case she'll assume that
+there are 0 buildings. As such, the expected number of buildings which she'll
+assume exist is (1 + 0) / 2 = 1/2. This should then be multiplied by 21 and
+taken modulo 1,000,000,007 to produce a final answer of 1.
+
+In the second case, however many windows are visible, Dahlia will assume
+Toronto has that many buildings. For example, if both windows are visible,
+then there must be at least 2 buildings, as a single building can't account
+for both windows without also covering the single visible star. This results
+in a final answer of ((0 + 1 + 1 + 2) / 4 * 22) modulo 1,000,000,007 = 4.
+
+In the third case, the final answer is ((0 + 1 + 1 + 1 + 1 + 1 + 2 + 2) / 8 *
+23) modulo 1,000,000,007 = 9.
+

2018/finals/citylights.out

@@ -0,0 +1,150 @@
+Case #1: 1
+Case #2: 4
+Case #3: 9
+Case #4: 684
+Case #5: 6602752
+Case #6: 1183
+Case #7: 395395372
+Case #8: 476192687
+Case #9: 307412416
+Case #10: 208183264
+Case #11: 179460552
+Case #12: 123720748
+Case #13: 2176
+Case #14: 251187805
+Case #15: 1
+Case #16: 24814920
+Case #17: 12
+Case #18: 950052158
+Case #19: 476192687
+Case #20: 37251179
+Case #21: 524338575
+Case #22: 84436692
+Case #23: 522842261
+Case #24: 960
+Case #25: 149016192
+Case #26: 401766512
+Case #27: 740220421
+Case #28: 806643165
+Case #29: 410108367
+Case #30: 476192687
+Case #31: 346263277
+Case #32: 511828703
+Case #33: 352768
+Case #34: 754620958
+Case #35: 24189841
+Case #36: 150357497
+Case #37: 27957735
+Case #38: 138609019
+Case #39: 938380288
+Case #40: 591
+Case #41: 476192687
+Case #42: 10327963
+Case #43: 1585152
+Case #44: 942892176
+Case #45: 733184
+Case #46: 963717906
+Case #47: 999149394
+Case #48: 336
+Case #49: 648770070
+Case #50: 41107
+Case #51: 358323
+Case #52: 476192687
+Case #53: 920603109
+Case #54: 583365539
+Case #55: 923455993
+Case #56: 32
+Case #57: 570359644
+Case #58: 576939345
+Case #59: 185078453
+Case #60: 87826432
+Case #61: 220714433
+Case #62: 779380393
+Case #63: 476192687
+Case #64: 454912501
+Case #65: 36175872
+Case #66: 61920862
+Case #67: 739035260
+Case #68: 241408
+Case #69: 72
+Case #70: 181137826
+Case #71: 12
+Case #72: 790528
+Case #73: 568
+Case #74: 476192687
+Case #75: 209894768
+Case #76: 409600
+Case #77: 9660075
+Case #78: 729659780
+Case #79: 987366468
+Case #80: 783255800
+Case #81: 150336261
+Case #82: 217745735
+Case #83: 14493184
+Case #84: 552983984
+Case #85: 476192687
+Case #86: 357205618
+Case #87: 650
+Case #88: 951990308
+Case #89: 51203491
+Case #90: 12525492
+Case #91: 203097080
+Case #92: 668435283
+Case #93: 285106003
+Case #94: 725943043
+Case #95: 311477996
+Case #96: 476192687
+Case #97: 808401215
+Case #98: 740898081
+Case #99: 723241603
+Case #100: 138936320
+Case #101: 9472
+Case #102: 80
+Case #103: 973081087
+Case #104: 3981312
+Case #105: 8196096
+Case #106: 232
+Case #107: 476192687
+Case #108: 451694354
+Case #109: 665349106
+Case #110: 939116400
+Case #111: 779208225
+Case #112: 665406988
+Case #113: 3
+Case #114: 7487488
+Case #115: 2048
+Case #116: 32
+Case #117: 386899298
+Case #118: 476192687
+Case #119: 426894991
+Case #120: 1616
+Case #121: 334418389
+Case #122: 882072248
+Case #123: 535159372
+Case #124: 1488
+Case #125: 878057472
+Case #126: 1555456
+Case #127: 487568093
+Case #128: 235337205
+Case #129: 476192687
+Case #130: 711001842
+Case #131: 895412998
+Case #132: 995550330
+Case #133: 442754895
+Case #134: 1
+Case #135: 3968
+Case #136: 192308626
+Case #137: 379881151
+Case #138: 569768760
+Case #139: 736443811
+Case #140: 476192687
+Case #141: 963356576
+Case #142: 874170611
+Case #143: 761856
+Case #144: 966256023
+Case #145: 14439824
+Case #146: 518979345
+Case #147: 574630397
+Case #148: 433417305
+Case #149: 902458354
+Case #150: 727041482

2018/finals/claw.cpp

@@ -0,0 +1,202 @@
+// The Claw
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+#define LIM 2100000
+
+PR P[LIM],R[LIM],S[LIM];
+vector<int> YP[LIM];
+vector<PR> YR[LIM];
+int sz;
+int tree[LIM],lazy[LIM];
+
+void Prop(int i)
+{
+	tree[i]+=lazy[i];
+		if (i<sz)
+		{
+			lazy[i<<1]+=lazy[i];
+			lazy[(i<<1)+1]+=lazy[i];
+		}
+	lazy[i]=0;
+}
+
+void Update(int i,int r1,int r2,int a,int b,int v)
+{
+	Prop(i);
+		if ((a<=r1) && (r2<=b))
+		{
+			lazy[i]+=v;
+			Prop(i);
+			return;
+		}
+	int c=i<<1,m=(r1+r2)>>1;
+		if (a<=m)
+			Update(c,r1,m,a,b,v);
+		if (b>m)
+			Update(c+1,m+1,r2,a,b,v);
+	Prop(c),Prop(c+1);
+	tree[i]=max(tree[c],tree[c+1]);
+}
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	int N,M,K;
+	int i,j,k,s,y,a,b,p,d;
+	LL ans;
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// init
+				Fox(i,LIM)
+					YP[i].clear(),YR[i].clear();
+			// input
+			Read(N),Read(M);
+			ans=M;
+				Fox(i,N)
+				{
+					Read(P[i].x),Read(P[i].y);
+					ans-=P[i].y;
+					YP[P[i].y].pb(P[i].x);
+						if (i)
+							R[i-1]=mp(max(P[i-1].x,P[i].x),min(P[i-1].x,P[i].x));
+				}
+			// associate intervals with their max contained heights
+			sort(P,P+N);
+			sort(R,R+N-1);
+			j=s=0;
+				Fox(i,N-1)
+				{
+					a=R[i].y,b=R[i].x;
+					// maintain convex hull of max heights so far
+						while ((j<N) && (P[j].x<=b))
+						{
+								while ((s) && (S[s-1].y<=P[j].y))
+									s--;
+							S[s++]=P[j++];
+						}
+					// binary search for max height no earlier than the start of this interval
+					k=lower_bound(S,S+s,mp(a,0))-S;
+					ans+=(y=S[k].y)+1;
+					YR[y].pb(R[i]);
+				}
+			// process set of targets at each height
+				Fox(i,LIM)
+					if (K=Sz(YP[i]))
+					{
+						// sort targets/intervals at this height
+						sort(All(YP[i]));
+						sort(All(YR[i]));
+						// segment-tree-assisted DP
+							for(sz=1;sz<K+1;sz<<=1);
+						memset(tree,0,sizeof(int)*sz*2);
+						memset(lazy,0,sizeof(int)*sz*2);
+						k=0,d=-1;
+							Fox(j,K+1)
+							{
+								// update prior DP values for intervals ending at this target
+								p=j==K ? INF : YP[i][j];
+									while ((k<Sz(YR[i])) && (YR[i][k].x<p))
+									{
+										a=lower_bound(All(YP[i]),YR[i][k++].y)-YP[i].begin();
+										Update(1,0,sz-1,0,a,1);
+									}
+								// compute DP value
+								d=max(d+1,tree[1]);
+								Update(1,0,sz-1,j,j,d);
+							}
+						ans-=d;
+					}
+			// output
+			printf("Case #%d: %lld\n",t,ans*2);
+		}
+	return(0);
+}

2018/finals/claw.html

@@ -0,0 +1,74 @@
+<p>
+Oh boy, Sid's family has taken him to Pizza Planet today! Pizza Planet is a fun family restaurant with lots of arcade games, but the highlight for Sid is Space Crane, 
+a crane game with cool toy prizes. He'd love to win some to add to his collection!
+</p>
+
+<p>
+Looking at Space Crane from the front, it can be represented as a 2D plane. 
+At the top, there's a horizontal crane track, a line segment running from (0, <strong>M</strong>) to (1,000,000, <strong>M</strong>). 
+There's a claw attached to this track by an extendible wire. The claw is initially located at coordinates (0, <strong>M</strong>) and may be moved anywhere within the inclusive range of 
+x-coordinates [0, 1,000,000] and the inclusive range of y-coordinates [0, <strong>M</strong>]. 
+At all points in time, the connecting wire runs vertically upwards from the claw's position to the track.
+That is, when the claw is at some point (<strong>x</strong>, <strong>y</strong>), the wire forms a line segment from 
+(<strong>x</strong>, <strong>y</strong>) to (<strong>x</strong>, <strong>M</strong>).
+</p>
+
+<p>
+Space Crane works differently than most crane games &mdash; rather than using the claw to directly pick up prizes, the player's objective is to navigate the claw to a series of targets. 
+There are <strong>N</strong> targets, all with distinct x-coordinates, with the <em>i</em>th target at coordinates (<strong>X<sub>i</sub></strong>, <strong>Y<sub>i</sub></strong>). 
+If Sid manages to move the claw to touch the <strong>N</strong> targets in order from 1 to <strong>N</strong>, and then return the claw to its original position at (0, <strong>M</strong>), 
+he'll win a prize! Targets are not collected along the way (they're only touched by the claw), meaning that all <strong>N</strong> targets will remain in place for the duration of the game.
+</p>
+
+<p>
+The claw may never be anywhere directly underneath a target (at the same x-coordinate but with a strictly smaller y-coordinate), as it would interfere with the crane's wire. 
+However, the claw may occupy exactly the same position as a target, including passing directly through targets which Sid is not currently trying to touch.
+</p>
+
+<p>
+Before the game starts, Sid is given an opportunity to adjust each of the <strong>N</strong> targets. 
+There are two possible choices for each target: it may either be left in its original position, or its y-coordinate may be increased by exactly 1 unit. 
+These adjustments may only be performed in advance, and the targets must then all remain in their chosen positions for the duration of the game.
+</p>
+
+<p>
+Completing the game normally isn't much of a challenge for Sid, but he's heard a rumour that Space Crane awards double prizes if completed as efficiently as possible! The game measures efficiency based on how much the claw's wire expands and contracts. As such, Sid would like to adjust the targets and then move the claw around such that the total amount of vertical movement (changes in y-coordinate) performed by the claw is minimized. Note that the claw's horizontal movement (changes in x-coordinate) is ignored. Help Sid determine the minimum total amount of vertical claw movement which might be required!
+</p>
+
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of times Sid plays Space Crane.
+For each game, there is first a line containing the space-separated integers <strong>N</strong> and <strong>M</strong>. 
+Then <strong>N</strong> lines follow, the <em>i</em>th of which contains the space-separated integers <strong>X<sub>i</sub></strong> and <strong>Y<sub>i</sub></strong>.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th game, output a line containing "Case #<em>i</em>: " followed by the the minimum total amount of vertical claw movement, in units.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 100 <br />
+1 &le; <strong>N</strong> &le; 1,000,000 <br />
+3 &le; <strong>M</strong> &le; 1,000,000 <br />
+0 &le; <strong>X<sub>i</sub></strong> &le; 1,000,000 <br />
+1 &le; <strong>Y<sub>i</sub></strong> &le; <strong>M</strong> - 2 <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+  
+<p>
+In the first case, the single target's height should be increased from 1 to 2. Then, aside from moving right and left by 1,000,000 units, the crane will need to move downwards by 8 units to reach the target and upwards by 8 units to return to its original position, for a total of 16 units of vertical movement.
+</p>
+
+<p>
+In the second case, if the targets are all left at their original heights, 10 units of vertical movement will be required. If their heights are all increased by 1, 8 units will be required. However, if just the first two targets are raised, then only 6 units will be required, which is the minimum achievable amount.
+</p>

2018/finals/claw.in

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ac5b14d1a848b20f48f7ab7a0779d108032bb5304399097d932fd447e44bc69f
+size 42254566

2018/finals/claw.md

@@ -0,0 +1,80 @@
+Oh boy, Sid's family has taken him to Pizza Planet today! Pizza Planet is a
+fun family restaurant with lots of arcade games, but the highlight for Sid is
+Space Crane, a crane game with cool toy prizes. He'd love to win some to add
+to his collection!
+
+Looking at Space Crane from the front, it can be represented as a 2D plane. At
+the top, there's a horizontal crane track, a line segment running from (0,
+**M**) to (1,000,000, **M**). There's a claw attached to this track by an
+extendible wire. The claw is initially located at coordinates (0, **M**) and
+may be moved anywhere within the inclusive range of x-coordinates [0,
+1,000,000] and the inclusive range of y-coordinates [0, **M**]. At all points
+in time, the connecting wire runs vertically upwards from the claw's position
+to the track. That is, when the claw is at some point (**x**, **y**), the wire
+forms a line segment from (**x**, **y**) to (**x**, **M**).
+
+Space Crane works differently than most crane games — rather than using the
+claw to directly pick up prizes, the player's objective is to navigate the
+claw to a series of targets. There are **N** targets, all with distinct
+x-coordinates, with the _i_th target at coordinates (**Xi**, **Yi**). If Sid
+manages to move the claw to touch the **N** targets in order from 1 to **N**,
+and then return the claw to its original position at (0, **M**), he'll win a
+prize! Targets are not collected along the way (they're only touched by the
+claw), meaning that all **N** targets will remain in place for the duration of
+the game.
+
+The claw may never be anywhere directly underneath a target (at the same
+x-coordinate but with a strictly smaller y-coordinate), as it would interfere
+with the crane's wire. However, the claw may occupy exactly the same position
+as a target, including passing directly through targets which Sid is not
+currently trying to touch.
+
+Before the game starts, Sid is given an opportunity to adjust each of the
+**N** targets. There are two possible choices for each target: it may either
+be left in its original position, or its y-coordinate may be increased by
+exactly 1 unit. These adjustments may only be performed in advance, and the
+targets must then all remain in their chosen positions for the duration of the
+game.
+
+Completing the game normally isn't much of a challenge for Sid, but he's heard
+a rumour that Space Crane awards double prizes if completed as efficiently as
+possible! The game measures efficiency based on how much the claw's wire
+expands and contracts. As such, Sid would like to adjust the targets and then
+move the claw around such that the total amount of vertical movement (changes
+in y-coordinate) performed by the claw is minimized. Note that the claw's
+horizontal movement (changes in x-coordinate) is ignored. Help Sid determine
+the minimum total amount of vertical claw movement which might be required!
+
+### Input
+
+Input begins with an integer **T**, the number of times Sid plays Space Crane.
+For each game, there is first a line containing the space-separated integers
+**N** and **M**. Then **N** lines follow, the _i_th of which contains the
+space-separated integers **Xi** and **Yi**.
+
+### Output
+
+For the _i_th game, output a line containing "Case #_i_: " followed by the the
+minimum total amount of vertical claw movement, in units.
+
+### Constraints
+
+1 ≤ **T** ≤ 100  
+1 ≤ **N** ≤ 1,000,000  
+3 ≤ **M** ≤ 1,000,000  
+0 ≤ **Xi** ≤ 1,000,000  
+1 ≤ **Yi** ≤ **M** \- 2  
+
+### Explanation of Sample
+
+In the first case, the single target's height should be increased from 1 to 2.
+Then, aside from moving right and left by 1,000,000 units, the crane will need
+to move downwards by 8 units to reach the target and upwards by 8 units to
+return to its original position, for a total of 16 units of vertical movement.
+
+In the second case, if the targets are all left at their original heights, 10
+units of vertical movement will be required. If their heights are all
+increased by 1, 8 units will be required. However, if just the first two
+targets are raised, then only 6 units will be required, which is the minimum
+achievable amount.
+

2018/finals/claw.out

@@ -0,0 +1,100 @@
+Case #1: 16
+Case #2: 6
+Case #3: 14
+Case #4: 260
+Case #5: 568
+Case #6: 1961626
+Case #7: 3358
+Case #8: 56024
+Case #9: 10
+Case #10: 178
+Case #11: 27323538
+Case #12: 8
+Case #13: 389736310
+Case #14: 591888518830
+Case #15: 60904108418
+Case #16: 220823790
+Case #17: 564095206
+Case #18: 37755430
+Case #19: 359556674
+Case #20: 185529394
+Case #21: 38921840
+Case #22: 685817766
+Case #23: 363038914
+Case #24: 352961076
+Case #25: 225139120
+Case #26: 117585226
+Case #27: 7278150
+Case #28: 104035988
+Case #29: 67748422
+Case #30: 844110702
+Case #31: 3523240
+Case #32: 343124806
+Case #33: 519026666
+Case #34: 320791480
+Case #35: 747964022
+Case #36: 466336844
+Case #37: 289981034
+Case #38: 15480402
+Case #39: 502793796
+Case #40: 1166910
+Case #41: 55345112
+Case #42: 110388890
+Case #43: 338556834
+Case #44: 435648088
+Case #45: 122741824
+Case #46: 297415336
+Case #47: 802859232
+Case #48: 28714256
+Case #49: 48366920
+Case #50: 107031646
+Case #51: 9686820
+Case #52: 237967738
+Case #53: 9088030
+Case #54: 372367388
+Case #55: 574725682
+Case #56: 76237660
+Case #57: 112384476
+Case #58: 58139852
+Case #59: 8805864
+Case #60: 171273912
+Case #61: 18464040
+Case #62: 320947738
+Case #63: 243050858
+Case #64: 501792574
+Case #65: 329135850
+Case #66: 216258438
+Case #67: 688019958
+Case #68: 239053688
+Case #69: 212823646
+Case #70: 117076682
+Case #71: 241045050
+Case #72: 90322022
+Case #73: 35474604
+Case #74: 528050404
+Case #75: 276667476
+Case #76: 466168544
+Case #77: 47753808
+Case #78: 10379782
+Case #79: 355000736
+Case #80: 288329662
+Case #81: 49497314
+Case #82: 121461146
+Case #83: 190014096
+Case #84: 33004856
+Case #85: 352105234
+Case #86: 43100142
+Case #87: 154193324
+Case #88: 430526288
+Case #89: 18058864
+Case #90: 309148716
+Case #91: 10742020
+Case #92: 17545340
+Case #93: 34545122
+Case #94: 76756074
+Case #95: 198464136
+Case #96: 157858174
+Case #97: 182626224
+Case #98: 585908516
+Case #99: 457182524
+Case #100: 7596382

2018/finals/contest.cpp

@@ -0,0 +1,134 @@
+// Contest Environment
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+#define LIM 2002
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	int N;
+	int i,b,c;
+	bool ans;
+	char A[LIM],B[LIM];
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			printf("Case #%d: ",t);
+			// input
+			scanf("%s%s",&A,&B);
+			N=strlen(A);
+			// bottom blocked?
+				Fox(i,N)
+					if (B[i]=='#')
+						goto Imp;
+			// count blanks
+			b=0;
+				Fox(i,N)
+					b+=(A[i]=='.')+(B[i]=='.');
+			// find sequences of blocked top-row cells
+			c=0;
+				Fox(i,N)
+					if (A[i]=='#')
+						c++;
+					else
+					{
+							if (b<c+3)
+								goto Imp;
+						c=0;
+					}
+			// output
+			printf("Possible\n");
+			continue;
+Imp:;
+			printf("Impossible\n");
+		}
+	return(0);
+}

2018/finals/contest.html

@@ -0,0 +1,78 @@
+<p>
+The 2018 Hacker Cup finals are underway! The contest is being held in a room with 2 rows of <strong>N</strong> desks each, with finalists sitting at some of them.
+</p>
+
+<p>
+One of the finalists, Alex, is sitting at the leftmost desk in the front row. Another finalist, Borys, is sitting at the rightmost desk in the front row. 
+Unfortunately, both of them find themselves distracted by the contest room's environment &mdash; Alex is a bit too hot on his side of the room, while Borys is a bit too cold. 
+If only they could switch places! Unfortunately, this would be against the rules, but if they work together with some other contestants, perhaps they can manage it without the 
+contest organizers noticing...
+</p>
+
+<p>
+The initial state of each row of desks can be represented by a string of <strong>N</strong> characters, with the <em>i</em>th character corresponding to the <em>i</em>th desk from 
+the left in that row. Each character is one of the following:
+</p>
+
+<ul>
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <code>A</code> - Alex's desk (guaranteed to appear exactly once, as the leftmost desk in the front row) </li>
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <code>B</code> - Borys's desk (guaranteed to appear exactly once, as the rightmost desk in the front row) </li>
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <code>*</code> - A cooperative finalist's desk </li>
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <code>#</code> - An uncooperative finalist's desk </li>
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <code>.</code> - An unoccupied desk </li>
+</ul>
+
+<p>
+At any point, a single finalist may move from their current desk to an adjacent, currently-unoccupied desk. 
+Two desks are considered adjacent if either they're in the same column, or they're directly side-by-side in the same row. 
+However, the finalists won't be foolish enough to move sideways between two desks in the front row, as that would surely attract the contest organizers' attention.
+</p>
+
+<p>
+Alex, Borys, and any cooperative finalists may all move between desks in this fashion. 
+On the other hand, uncooperative finalists are too busy actually competing, and will never move from their original desks.
+</p>
+
+<p>
+Assuming that Alex, Borys, and the cooperative finalists all work together, is it possible for Alex and Borys to switch seats (in other words, for Alex to occupy the front row's rightmost desk while Borys simultaneously occupies its leftmost desk) without the contest organizers noticing?
+</p>
+
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of parallel universes in which the 2018 Hacker Cup is occurring. 
+For each universe, there are two lines of <strong>N</strong> characters each, as described above. The first line is the front row of desks, and the second line is the back row of desks.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th universe, output a line containing "Case #<em>i</em>: " followed by the string "Possible" if Alex and Borys can successfully switch seats, 
+or "Impossible" otherwise.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 200 <br />
+2 &le; <strong>N</strong> &le; 2,000 <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+  
+<p>
+In the first case, the contest room looks as follows (with grey lines indicating adjacent desks which finalists may potentially move between).
+The blue circle denotes a cooperative finalist, and the gray square denotes an uncooperative finalist. A and B denote Alex and Borys respectively.
+</p>
+
+<p>
+One possible sequence of moves resulting in Alex and Borys switching places is as follows (with some moves omitted):
+</p>
+  
+<p>
+In the second case, Alex and Borys are unable to get past one another and switch seats.
+</p>

2018/finals/contest.md

@@ -0,0 +1,68 @@
+The 2018 Hacker Cup finals are underway! The contest is being held in a room
+with 2 rows of **N** desks each, with finalists sitting at some of them.
+
+One of the finalists, Alex, is sitting at the leftmost desk in the front row.
+Another finalist, Borys, is sitting at the rightmost desk in the front row.
+Unfortunately, both of them find themselves distracted by the contest room's
+environment — Alex is a bit too hot on his side of the room, while Borys is a
+bit too cold. If only they could switch places! Unfortunately, this would be
+against the rules, but if they work together with some other contestants,
+perhaps they can manage it without the contest organizers noticing...
+
+The initial state of each row of desks can be represented by a string of **N**
+characters, with the _i_th character corresponding to the _i_th desk from the
+left in that row. Each character is one of the following:
+
+  * `A` \- Alex's desk (guaranteed to appear exactly once, as the leftmost desk in the front row) 
+  * `B` \- Borys's desk (guaranteed to appear exactly once, as the rightmost desk in the front row) 
+  * `*` \- A cooperative finalist's desk 
+  * `#` \- An uncooperative finalist's desk 
+  * `.` \- An unoccupied desk 
+
+At any point, a single finalist may move from their current desk to an
+adjacent, currently-unoccupied desk. Two desks are considered adjacent if
+either they're in the same column, or they're directly side-by-side in the
+same row. However, the finalists won't be foolish enough to move sideways
+between two desks in the front row, as that would surely attract the contest
+organizers' attention.
+
+Alex, Borys, and any cooperative finalists may all move between desks in this
+fashion. On the other hand, uncooperative finalists are too busy actually
+competing, and will never move from their original desks.
+
+Assuming that Alex, Borys, and the cooperative finalists all work together, is
+it possible for Alex and Borys to switch seats (in other words, for Alex to
+occupy the front row's rightmost desk while Borys simultaneously occupies its
+leftmost desk) without the contest organizers noticing?
+
+### Input
+
+Input begins with an integer **T**, the number of parallel universes in which
+the 2018 Hacker Cup is occurring. For each universe, there are two lines of
+**N** characters each, as described above. The first line is the front row of
+desks, and the second line is the back row of desks.
+
+### Output
+
+For the _i_th universe, output a line containing "Case #_i_: " followed by the
+string "Possible" if Alex and Borys can successfully switch seats, or
+"Impossible" otherwise.
+
+### Constraints
+
+1 ≤ **T** ≤ 200  
+2 ≤ **N** ≤ 2,000  
+
+### Explanation of Sample
+
+In the first case, the contest room looks as follows (with grey lines
+indicating adjacent desks which finalists may potentially move between). The
+blue circle denotes a cooperative finalist, and the gray square denotes an
+uncooperative finalist. A and B denote Alex and Borys respectively.
+
+One possible sequence of moves resulting in Alex and Borys switching places is
+as follows (with some moves omitted):
+
+In the second case, Alex and Borys are unable to get past one another and
+switch seats.
+

2018/finals/contest.out

@@ -0,0 +1,200 @@
+Case #1: Possible
+Case #2: Impossible
+Case #3: Possible
+Case #4: Impossible
+Case #5: Possible
+Case #6: Impossible
+Case #7: Possible
+Case #8: Impossible
+Case #9: Possible
+Case #10: Impossible
+Case #11: Impossible
+Case #12: Possible
+Case #13: Impossible
+Case #14: Possible
+Case #15: Impossible
+Case #16: Possible
+Case #17: Impossible
+Case #18: Possible
+Case #19: Possible
+Case #20: Possible
+Case #21: Impossible
+Case #22: Impossible
+Case #23: Possible
+Case #24: Possible
+Case #25: Impossible
+Case #26: Possible
+Case #27: Possible
+Case #28: Possible
+Case #29: Impossible
+Case #30: Possible
+Case #31: Impossible
+Case #32: Possible
+Case #33: Impossible
+Case #34: Possible
+Case #35: Possible
+Case #36: Possible
+Case #37: Possible
+Case #38: Possible
+Case #39: Impossible
+Case #40: Possible
+Case #41: Impossible
+Case #42: Impossible
+Case #43: Impossible
+Case #44: Possible
+Case #45: Impossible
+Case #46: Possible
+Case #47: Possible
+Case #48: Possible
+Case #49: Impossible
+Case #50: Possible
+Case #51: Impossible
+Case #52: Possible
+Case #53: Impossible
+Case #54: Possible
+Case #55: Impossible
+Case #56: Possible
+Case #57: Impossible
+Case #58: Possible
+Case #59: Possible
+Case #60: Possible
+Case #61: Impossible
+Case #62: Possible
+Case #63: Possible
+Case #64: Possible
+Case #65: Impossible
+Case #66: Possible
+Case #67: Impossible
+Case #68: Possible
+Case #69: Impossible
+Case #70: Possible
+Case #71: Possible
+Case #72: Possible
+Case #73: Possible
+Case #74: Impossible
+Case #75: Impossible
+Case #76: Impossible
+Case #77: Possible
+Case #78: Impossible
+Case #79: Possible
+Case #80: Possible
+Case #81: Impossible
+Case #82: Possible
+Case #83: Impossible
+Case #84: Impossible
+Case #85: Possible
+Case #86: Possible
+Case #87: Possible
+Case #88: Impossible
+Case #89: Possible
+Case #90: Impossible
+Case #91: Possible
+Case #92: Possible
+Case #93: Impossible
+Case #94: Possible
+Case #95: Impossible
+Case #96: Possible
+Case #97: Possible
+Case #98: Possible
+Case #99: Possible
+Case #100: Possible
+Case #101: Possible
+Case #102: Possible
+Case #103: Possible
+Case #104: Possible
+Case #105: Possible
+Case #106: Possible
+Case #107: Impossible
+Case #108: Impossible
+Case #109: Impossible
+Case #110: Possible
+Case #111: Possible
+Case #112: Possible
+Case #113: Possible
+Case #114: Possible
+Case #115: Impossible
+Case #116: Possible
+Case #117: Impossible
+Case #118: Possible
+Case #119: Impossible
+Case #120: Impossible
+Case #121: Impossible
+Case #122: Possible
+Case #123: Impossible
+Case #124: Possible
+Case #125: Impossible
+Case #126: Possible
+Case #127: Possible
+Case #128: Impossible
+Case #129: Possible
+Case #130: Impossible
+Case #131: Impossible
+Case #132: Possible
+Case #133: Impossible
+Case #134: Impossible
+Case #135: Possible
+Case #136: Possible
+Case #137: Possible
+Case #138: Possible
+Case #139: Impossible
+Case #140: Possible
+Case #141: Possible
+Case #142: Possible
+Case #143: Impossible
+Case #144: Possible
+Case #145: Possible
+Case #146: Possible
+Case #147: Possible
+Case #148: Impossible
+Case #149: Impossible
+Case #150: Impossible
+Case #151: Impossible
+Case #152: Impossible
+Case #153: Impossible
+Case #154: Possible
+Case #155: Possible
+Case #156: Possible
+Case #157: Impossible
+Case #158: Possible
+Case #159: Possible
+Case #160: Impossible
+Case #161: Impossible
+Case #162: Impossible
+Case #163: Impossible
+Case #164: Impossible
+Case #165: Possible
+Case #166: Impossible
+Case #167: Impossible
+Case #168: Possible
+Case #169: Impossible
+Case #170: Possible
+Case #171: Possible
+Case #172: Possible
+Case #173: Possible
+Case #174: Possible
+Case #175: Impossible
+Case #176: Impossible
+Case #177: Impossible
+Case #178: Possible
+Case #179: Possible
+Case #180: Possible
+Case #181: Impossible
+Case #182: Impossible
+Case #183: Possible
+Case #184: Possible
+Case #185: Possible
+Case #186: Possible
+Case #187: Impossible
+Case #188: Possible
+Case #189: Impossible
+Case #190: Possible
+Case #191: Possible
+Case #192: Impossible
+Case #193: Possible
+Case #194: Possible
+Case #195: Impossible
+Case #196: Possible
+Case #197: Impossible
+Case #198: Impossible
+Case #199: Possible
+Case #200: Possible

2018/finals/ethan.cpp

@@ -0,0 +1,211 @@
+// Ethan Sums Shortest Distances
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+#define LIM 51
+
+int R[2][LIM],sum[2][LIM];
+LL dyn[LIM][3][LIM];
+// dyn[i][r][p] = min. cost such that:
+// - you're ending at a vertical edge in column i (its cost is exluded)
+// - you previously had a partial horizontal section in row r (r=2 indicates both rows)
+// - the partial horizontal section started in column p
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	int N;
+	LL S;
+	int i,i2,j,k,r,r2,p,p2,s;
+	LL ans,cur,cur2;
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// input, and compute each row's prefix sums
+			Read(N);
+				Fox(i,2)
+					Fox(j,N)
+					{
+						Read(R[i][j]);
+						sum[i][j+1]=sum[i][j]+R[i][j];
+					}
+			S=sum[0][N]+sum[1][N];
+			// initial DP step (before first vertical edge)
+			Fill(dyn,60);
+				Fox(i,N)
+				{
+					cur=0;
+					// compute horizontal section costs for both rows' prefixes
+						Fox(j,2)
+						{
+							s=0;
+								Fox(k,i)
+								{
+									s+=R[j][k];
+									cur+=s*(S-s);
+								}
+						}
+					dyn[i][2][0]=cur;
+				}
+			// main DP
+				Fox(i,N)
+					FoxI(i2,i+1,N-1)
+						Fox(r2,2)
+							FoxI(p2,i+1,i2)
+							{
+								cur=0;
+								// compute full horizontal section cost
+								s=sum[r2][p2]+sum[1-r2][i+1];
+									FoxI(j,i,i2-1)
+									{
+										cur+=s*(S-s);
+										s+=R[1-r2][j+1];
+									}
+								// compute left partial horizontal section cost
+								s=0;
+									FoxRI(j,i+1,p2-1)
+									{
+										s+=R[r2][j];
+										cur+=s*(S-s);
+									}
+								// compute right partial horizontal section cost
+								s=0;
+									FoxI(j,p2,i2-1)
+									{
+										s+=R[r2][j];
+										cur+=s*(S-s);
+									}
+								// consider all previous states
+									Fox(r,3)
+										Fox(p,i+1)
+										{
+											cur2=dyn[i][r][p]+cur;
+											// compute vertical edge cost
+												if (r==2)
+													s=sum[r2][p2];
+												else
+												if (r==r2)
+													s=sum[r2][p2]-sum[r2][p];
+												else
+													s=sum[r2][p2]+sum[1-r2][p];
+											cur2+=s*(S-s);
+											Min(dyn[i2][r2][p2],cur2);
+										}
+							}
+			// final DP step (after last vertical edge)
+			ans=(LL)INF*INF;
+				Fox(i,N)
+					Fox(r,3)
+						Fox(p,i+1)
+						{
+							cur=dyn[i][r][p];
+							// compute horizontal section costs for both rows' suffixes
+								Fox(j,2)
+								{
+									s=0;
+										FoxRI(k,i+1,N-1)
+										{
+											s+=R[j][k];
+											cur+=s*(S-s);
+										}
+								}
+							// compute vertical edge cost
+								if (r==2)
+									s=sum[0][N];
+								else
+									s=sum[r][N]-sum[r][p];
+							cur+=s*(S-s);
+							Min(ans,cur);
+						}
+			// output
+			printf("Case #%d: %lld\n",t,ans);
+		}
+	return(0);
+}

2018/finals/ethan.html

@@ -0,0 +1,109 @@
+<p>
+The final exam is here, and it's now or never for Ethan. 
+His current grade is abysmal so he needs a strong showing on this exam to have any chance of passing his introductory computer science class. 
+</p>
+
+<p>
+The exam has only one question: devise an algorithm to compute the compactness of a grid tree.
+</p>
+
+<p>
+Ethan recalls that a "grid tree" is simply an unweighted tree with 2<strong>N</strong> nodes that you can imagine being embedded within a 2x<strong>N</strong> grid. 
+The top row of the grid contains the nodes 1 ... <strong>N</strong> from left to right, 
+and the bottom row of the grid contains the nodes (<strong>N</strong> + 1) ... 2<strong>N</strong> from left to right.
+Every edge in a grid tree connects a pair of nodes which are adjacent in the 2x<strong>N</strong> grid.
+Two nodes are considered adjacent if either they're in the same column, or they're directly side-by-side in the same row. 
+There must be exactly 2<strong>N</strong>-1 edges that connect the 2<strong>N</strong> nodes to form a single tree.
+Additionally, the <em>i</em>th node in the grid tree is labelled with an integer <strong>A<sub>i</sub></strong>. 
+</p>
+
+<p>
+What was "compactness" again? After some intense thought, Ethan comes up with the following pseudocode to compute the compactness, <strong>c</strong>, of a grid tree:
+</p>
+
+<ul>
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1. Set <strong>c</strong> to be equal to 0.
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2. Iterate <em>i</em> upwards from 1 to 2<strong>N</strong> - 1:
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2a. Iterate <em>j</em> upwards from <em>i</em>+1 to 2<strong>N</strong>:
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2b. Increase <strong>c</strong> by <strong>A<sub>i</sub></strong> * <strong>A<sub>j</sub></strong> * <code>ShortestDistance(i, j)</code>
+<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3. Output <strong>c</strong>.
+</ul>
+
+<p>
+<code>ShortestDistance(i, j)</code> is a function which returns the number of edges on the shortest path from node <em>i</em> to node <em>j</em> in the tree, 
+which Ethan has implemented correctly. In fact, his whole algorithm is quite correct for once. This is exactly how you compute compactness!
+</p>
+
+<p>
+There's just one issue &mdash; in his code, Ethan has chosen to store <strong>c</strong> using a rather small integer type, 
+which is at risk of overflowing if <strong>c</strong> becomes too large! 
+</p>
+
+<p>
+Ethan is so close! Feeling sorry for him, you'd like to make some last-minute changes to the tree in order to minimize the final value of <strong>c</strong>, 
+and thus minimize the probability that it will overflow in Ethan's program and cost him much-needed marks.
+You can't change any of the node labels <strong>A<sub>1..2N</sub></strong>, 
+but you may choose your own set of 2<strong>N</strong> - 1 edges to connect them into a grid tree.
+</p>
+
+<p>
+For example, if <strong>A</strong> = [1, 3, 2, 2, 4, 5], then the grid of nodes looks like this:
+</p>
+
+<p>
+You'd like to determine the minimum possible compactness which Ethan's program can produce given a valid tree of your choice. 
+For example, one optimal tree for the above grid of nodes (which results in the minimum possible compactness of 198) is as follows:
+</p>
+  
+
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of trees. For each tree, there are three lines. The first line contains the single integer <strong>N</strong>. 
+The second line contains the <strong>N</strong> space-separated integers <strong>A<sub>1..N</sub></strong>.
+The third line contains the <strong>N</strong> space-separated integers <strong>A<sub>N+1..2N</sub></strong>.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th tree, output a line containing "Case #<em>i</em>: " followed by the minimum possible output of Ethan's program.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 80 <br />
+1 &le; <strong>N</strong> &le; 50 <br />
+1 &le; <strong>A<sub>i</sub></strong> &le; 1,000,000 <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+  
+<p>
+One optimal tree for the first case is given above. For that tree, Ethan's program would compute <strong>c</strong> as the sum of the following values (with some values omitted):
+</p>
+
+<ul>
+<li> <strong>A<sub>1</sub></strong> * <strong>A<sub>2</sub></strong> * <code>ShortestDistance(1, 2)</code> = 1 * 3 * 1 = 3
+<li> <strong>A<sub>1</sub></strong> * <strong>A<sub>3</sub></strong> * <code>ShortestDistance(1, 3)</code> = 1 * 2 * 4 = 8
+<li> ...
+<li> <strong>A<sub>1</sub></strong> * <strong>A<sub>6</sub></strong> * <code>ShortestDistance(1, 6)</code> = 1 * 5 * 3 = 15
+<li> <strong>A<sub>2</sub></strong> * <strong>A<sub>3</sub></strong> * <code>ShortestDistance(2, 3)</code> = 3 * 2 * 3 = 18
+<li> ...
+<li> <strong>A<sub>4</sub></strong> * <strong>A<sub>6</sub></strong> * <code>ShortestDistance(4, 6)</code> = 2 * 5 * 2 = 20
+<li> <strong>A<sub>5</sub></strong> * <strong>A<sub>6</sub></strong> * <code>ShortestDistance(5, 6)</code> = 4 * 5 * 1 = 20
+</ul>
+
+<p>
+In the second case, there's only one possible tree, for which <strong>c</strong> = 2 * 3 * 1 = 6.
+</p>
+
+<p>
+In the third case, two of the four possible trees are optimal (the ones omitting either the topmost or leftmost potential edge).
+</p>
+

2018/finals/ethan.in

@@ -0,0 +1,241 @@
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2018/finals/ethan.md

@@ -0,0 +1,89 @@
+The final exam is here, and it's now or never for Ethan. His current grade is
+abysmal so he needs a strong showing on this exam to have any chance of
+passing his introductory computer science class.
+
+The exam has only one question: devise an algorithm to compute the compactness
+of a grid tree.
+
+Ethan recalls that a "grid tree" is simply an unweighted tree with 2**N**
+nodes that you can imagine being embedded within a 2x**N** grid. The top row
+of the grid contains the nodes 1 ... **N** from left to right, and the bottom
+row of the grid contains the nodes (**N** \+ 1) ... 2**N** from left to right.
+Every edge in a grid tree connects a pair of nodes which are adjacent in the
+2x**N** grid. Two nodes are considered adjacent if either they're in the same
+column, or they're directly side-by-side in the same row. There must be
+exactly 2**N**-1 edges that connect the 2**N** nodes to form a single tree.
+Additionally, the _i_th node in the grid tree is labelled with an integer
+**Ai**.
+
+What was "compactness" again? After some intense thought, Ethan comes up with
+the following pseudocode to compute the compactness, **c**, of a grid tree:
+
+  * 1\. Set **c** to be equal to 0. 
+  * 2\. Iterate _i_ upwards from 1 to 2**N** \- 1: 
+  * 2a. Iterate _j_ upwards from _i_+1 to 2**N**: 
+  * 2b. Increase **c** by **Ai** * **Aj** * `ShortestDistance(i, j)`
+  * 3\. Output **c**. 
+
+`ShortestDistance(i, j)` is a function which returns the number of edges on
+the shortest path from node _i_ to node _j_ in the tree, which Ethan has
+implemented correctly. In fact, his whole algorithm is quite correct for once.
+This is exactly how you compute compactness!
+
+There's just one issue — in his code, Ethan has chosen to store **c** using a
+rather small integer type, which is at risk of overflowing if **c** becomes
+too large!
+
+Ethan is so close! Feeling sorry for him, you'd like to make some last-minute
+changes to the tree in order to minimize the final value of **c**, and thus
+minimize the probability that it will overflow in Ethan's program and cost him
+much-needed marks. You can't change any of the node labels **A1..2N**, but you
+may choose your own set of 2**N** \- 1 edges to connect them into a grid tree.
+
+For example, if **A** = [1, 3, 2, 2, 4, 5], then the grid of nodes looks like
+this:
+
+You'd like to determine the minimum possible compactness which Ethan's program
+can produce given a valid tree of your choice. For example, one optimal tree
+for the above grid of nodes (which results in the minimum possible compactness
+of 198) is as follows:
+
+### Input
+
+Input begins with an integer **T**, the number of trees. For each tree, there
+are three lines. The first line contains the single integer **N**. The second
+line contains the **N** space-separated integers **A1..N**. The third line
+contains the **N** space-separated integers **AN+1..2N**.
+
+### Output
+
+For the _i_th tree, output a line containing "Case #_i_: " followed by the
+minimum possible output of Ethan's program.
+
+### Constraints
+
+1 ≤ **T** ≤ 80  
+1 ≤ **N** ≤ 50  
+1 ≤ **Ai** ≤ 1,000,000  
+
+### Explanation of Sample
+
+One optimal tree for the first case is given above. For that tree, Ethan's
+program would compute **c** as the sum of the following values (with some
+values omitted):
+
+  * **A1** * **A2** * `ShortestDistance(1, 2)` = 1 * 3 * 1 = 3 
+  * **A1** * **A3** * `ShortestDistance(1, 3)` = 1 * 2 * 4 = 8 
+  * ... 
+  * **A1** * **A6** * `ShortestDistance(1, 6)` = 1 * 5 * 3 = 15 
+  * **A2** * **A3** * `ShortestDistance(2, 3)` = 3 * 2 * 3 = 18 
+  * ... 
+  * **A4** * **A6** * `ShortestDistance(4, 6)` = 2 * 5 * 2 = 20 
+  * **A5** * **A6** * `ShortestDistance(5, 6)` = 4 * 5 * 1 = 20 
+
+In the second case, there's only one possible tree, for which **c** = 2 * 3 *
+1 = 6.
+
+In the third case, two of the four possible trees are optimal (the ones
+omitting either the topmost or leftmost potential edge).
+

2018/finals/ethan.out

@@ -0,0 +1,80 @@
+Case #1: 198
+Case #2: 6
+Case #3: 14
+Case #4: 3226
+Case #5: 1019144
+Case #6: 1419999746000002
+Case #7: 158047445160
+Case #8: 716584960310
+Case #9: 9736953596494
+Case #10: 17523029121283
+Case #11: 25624979577048
+Case #12: 51879052453960
+Case #13: 44952771515198
+Case #14: 138921477249744
+Case #15: 154557212444750
+Case #16: 263813905787586
+Case #17: 265190693651962
+Case #18: 304235644843682
+Case #19: 288437821749958
+Case #20: 562183410188758
+Case #21: 730850210619340
+Case #22: 784962166425329
+Case #23: 994997514960940
+Case #24: 1319450452295692
+Case #25: 885545596906968
+Case #26: 1335512841639492
+Case #27: 1927337493116390
+Case #28: 2640681901892200
+Case #29: 2186376337606200
+Case #30: 2509006065539666
+Case #31: 2856785766675934
+Case #32: 2563828545385840
+Case #33: 4746997236964980
+Case #34: 3586716468471062
+Case #35: 4879373984024024
+Case #36: 4752078018709930
+Case #37: 6034532623161728
+Case #38: 6771827331269718
+Case #39: 5591295909858493
+Case #40: 7298784754791768
+Case #41: 5486666474630682
+Case #42: 9332642369782525
+Case #43: 8733013396037280
+Case #44: 12130181851078450
+Case #45: 11589165888666834
+Case #46: 14122677415946934
+Case #47: 12954763484697562
+Case #48: 15352025783178374
+Case #49: 14359370522693684
+Case #50: 15119666116137528
+Case #51: 16101306160199630
+Case #52: 15766082855660810
+Case #53: 21493653492400564
+Case #54: 19581131155672756
+Case #55: 19934745199996134
+Case #56: 20144645528868781
+Case #57: 740243073201006
+Case #58: 11092025848656242
+Case #59: 513652289219673
+Case #60: 1852667838189955
+Case #61: 10850691549893895
+Case #62: 13132395681767488
+Case #63: 358576712869924
+Case #64: 1076503999130657
+Case #65: 1622500695602593
+Case #66: 76228256147076
+Case #67: 8351115399776566
+Case #68: 130602948089283
+Case #69: 21480789947800
+Case #70: 924026532280304
+Case #71: 20915671700496984
+Case #72: 2907389607114549
+Case #73: 1905642433632046
+Case #74: 776641589472030
+Case #75: 5678227649489
+Case #76: 662315938181662
+Case #77: 6741975663260179
+Case #78: 11384965678113728
+Case #79: 2271400045654
+Case #80: 7256804525346519

2018/finals/personal.cpp

@@ -0,0 +1,202 @@
+// Personal Space
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+#define LIM 8000001
+
+int K1,K2;
+pair<PR,int> E1[LIM];
+pair<PR,PR> E2[LIM];
+int dyn[LIM];
+set<int> S1;
+set<PR> S2;
+set<int>::iterator I1;
+set<PR>::iterator I2,J2;
+
+void AddRect(int x1,int y1,int x2,int y2)
+{
+		if ((x2<0) || (y1>INF))
+			return;
+	int i=K2+1;
+	E2[K2++]=mp(mp(y1,1),mp(x1,i));
+	E2[K2++]=mp(mp(y2,0),mp(x2,i));
+}
+
+void AddRects(int x)
+{
+	int i;
+	int X[7];
+	I1=S1.lower_bound(x);
+		Fox(i,3)
+			I1--;
+		Fox(i,7)
+			X[i]=*I1,I1++;
+		Fox(i,4)
+			AddRect(X[i],X[i+1],X[i+2],X[i+3]);
+}
+
+int Query(int x)
+{
+	I2=S2.lower_bound(mp(x+1,0));
+	I2--;
+	return(I2->y);
+}
+
+void Update(int x,int v)
+{
+	I2=S2.lower_bound(mp(x+1,0));
+	I2--;
+		if (v<=I2->y)
+			return;
+		if (I2->x<x)
+			I2++;
+		while ((I2!=S2.end()) && (v>=I2->y))
+		{
+			J2=I2,I2++;
+			S2.erase(J2);
+		}
+	S2.insert(mp(x,v));
+}
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	int N;
+	int i,j,k,x,a,b,ans;
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// input
+			Read(N);
+			K1=0;
+				Fox(i,N)
+				{
+					Read(x),Read(a),Read(b);
+					E1[K1++]=mp(mp(a,x),1);
+					E1[K1++]=mp(mp(b+1,x),-1);
+				}
+			// bottom-up line sweep to generate all possible fish placement "rectangles"
+			sort(E1,E1+K1);
+			S1.clear();
+				Fox1(i,4)
+					S1.insert(-i),S1.insert(INF+i);
+			K2=0;
+				Fox(i,K1)
+				{
+					j=i;
+						while ((j+1<K1) && (E1[j+1].x.x==E1[i].x.x))
+							j++;
+						FoxI(k,i,j)
+							if (E1[k].y>0)
+								S1.insert(E1[k].x.y);
+							else
+								S1.erase(E1[k].x.y);
+						FoxI(k,i,j)
+							AddRects(E1[k].x.y);
+					i=j;
+				}
+			// bottom-up line sweep DP on rectangles
+			sort(E2,E2+K2);
+			S2.clear();
+			S2.insert(mp(-INF,0));
+			ans=0;
+				Fox(i,K2)
+				{
+					x=E2[i].y.x,j=E2[i].y.y;
+						if (E2[i].x.y)
+							Max(ans,dyn[j]=Query(x)+1);
+						else
+							Update(x,dyn[j]);
+				}
+			// output
+			printf("Case #%d: %d\n",t,ans);
+		}
+	return(0);
+}

2018/finals/personal.html

@@ -0,0 +1,82 @@
+<p>
+Phineas is the proud owner of an enormous new fish tank! Looking at the fish tank from the side, it can be represented as an infinite 2D plane. 
+Phineas has installed <strong>N</strong> vertical dividers into the tank, the <em>i</em>th of which is a line segment connecting points 
+(<strong>X<sub>i</sub></strong>, <strong>A<sub>i</sub></strong>) and (<strong>X<sub>i</sub></strong>, <strong>B<sub>i</sub></strong>). 
+No two dividers overlap at any point (including at their endpoints).
+</p>
+
+<p>
+Unfortunately, Phineas's fish tank is lacking in fish, but he'll soon rectify that! He's going to place one or more fish into the tank, with each one initially occupying any point of his choice 
+(each coordinate may be non-integral and arbitrarily small or large). No fish's location may overlap with any of the dividers (including their endpoints), but multiple fish may be placed at the same coordinates.
+</p>
+
+<p>
+After the fish have been placed, each one may swim left and right freely (continuously decreasing or increasing its x-coordinate), as long as it never touches a divider (including its endpoints). Fish do not block one another from swimming, so multiple fish are able to occupy the same coordinates. However, no fish is able to change its y-coordinate.
+</p>
+
+<p>
+At any given moment, each fish feels that its personal space is violated if any other fish is currently at the same x-coordinate as it 
+(either at its current y-coordinate, or arbitrarily far above or below it). As such, if two fish ever occupy the same x-coordinate as one another, they both become unhappy.
+</p>
+
+<p>
+Phineas suspects that someone's planning on stealing one of his dividers soon after he places fish into the tank!
+</p>
+
+<p>
+And he wants to ensure that none of his fish have any chance of becoming unhappy!
+</p>
+
+<p>
+But he still wants to have as many fish as possible!
+</p>
+
+<p>
+As such, he'd like to determine the maximum number of fish which he can place into the tank such that, no matter which single one of the <strong>N</strong> dividers is subsequently removed,
+and no matter how the fish then decide to swim around, none of the fish can ever become unhappy.
+</p>
+
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of fish tanks.
+For each fish tank, there is first a line containing the single integer <strong>N</strong>.
+Then, <strong>N</strong> lines follow, the <em>i</em>th of which contains the 3 space-separated integers 
+<strong>X<sub>i</sub></strong>, <strong>A<sub>i</sub></strong>, and <strong>B<sub>i</sub></strong>.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th fish tank, output a line containing "Case #<em>i</em>: " followed by the maximum number of fish which Phineas can place into the tank with no risk of unhappiness.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 90<br />
+1 &le; <strong>N</strong> &le; 500,000 <br />
+0 &le; <strong>X<sub>i</sub></strong> &le; 1,000,000,000 <br />
+0 &le; <strong>A<sub>i</sub></strong> &lt; <strong>B<sub>i</sub></strong> &le; 1,000,000,000 <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+  
+<p>
+In the first case, Phineas could, for example, place a fish at coordinates (5, 5). If he placed another fish anywhere else in the tank (for example at coordinates (-1, 2)), 
+then if the single divider were removed, both fish would be able to swim freely and might come to occupy the same x-coordinate as one another.
+</p>
+
+<p>
+In the second case, Phineas can place one fish at coordinates (-5, 5) and another at coordinates (15, 5).
+</p>
+
+<p>
+In the third case, no matter where Phineas might place two fish in the tank, at least one choice of removed divider would result in them potentially becoming unhappy.
+</p>
+
+

2018/finals/personal.in

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:02fe0e1530fd3d2688cf32df245f9976557d582ef811dfe918e22396b3fecd7c
+size 42711476

2018/finals/personal.md

@@ -0,0 +1,73 @@
+Phineas is the proud owner of an enormous new fish tank! Looking at the fish
+tank from the side, it can be represented as an infinite 2D plane. Phineas has
+installed **N** vertical dividers into the tank, the _i_th of which is a line
+segment connecting points (**Xi**, **Ai**) and (**Xi**, **Bi**). No two
+dividers overlap at any point (including at their endpoints).
+
+Unfortunately, Phineas's fish tank is lacking in fish, but he'll soon rectify
+that! He's going to place one or more fish into the tank, with each one
+initially occupying any point of his choice (each coordinate may be non-
+integral and arbitrarily small or large). No fish's location may overlap with
+any of the dividers (including their endpoints), but multiple fish may be
+placed at the same coordinates.
+
+After the fish have been placed, each one may swim left and right freely
+(continuously decreasing or increasing its x-coordinate), as long as it never
+touches a divider (including its endpoints). Fish do not block one another
+from swimming, so multiple fish are able to occupy the same coordinates.
+However, no fish is able to change its y-coordinate.
+
+At any given moment, each fish feels that its personal space is violated if
+any other fish is currently at the same x-coordinate as it (either at its
+current y-coordinate, or arbitrarily far above or below it). As such, if two
+fish ever occupy the same x-coordinate as one another, they both become
+unhappy.
+
+Phineas suspects that someone's planning on stealing one of his dividers soon
+after he places fish into the tank!
+
+And he wants to ensure that none of his fish have any chance of becoming
+unhappy!
+
+But he still wants to have as many fish as possible!
+
+As such, he'd like to determine the maximum number of fish which he can place
+into the tank such that, no matter which single one of the **N** dividers is
+subsequently removed, and no matter how the fish then decide to swim around,
+none of the fish can ever become unhappy.
+
+### Input
+
+Input begins with an integer **T**, the number of fish tanks. For each fish
+tank, there is first a line containing the single integer **N**. Then, **N**
+lines follow, the _i_th of which contains the 3 space-separated integers
+**Xi**, **Ai**, and **Bi**.
+
+### Output
+
+For the _i_th fish tank, output a line containing "Case #_i_: " followed by
+the maximum number of fish which Phineas can place into the tank with no risk
+of unhappiness.
+
+### Constraints
+
+1 ≤ **T** ≤ 90  
+1 ≤ **N** ≤ 500,000  
+0 ≤ **Xi** ≤ 1,000,000,000  
+0 ≤ **Ai** < **Bi** ≤ 1,000,000,000  
+
+### Explanation of Sample
+
+In the first case, Phineas could, for example, place a fish at coordinates (5,
+5). If he placed another fish anywhere else in the tank (for example at
+coordinates (-1, 2)), then if the single divider were removed, both fish would
+be able to swim freely and might come to occupy the same x-coordinate as one
+another.
+
+In the second case, Phineas can place one fish at coordinates (-5, 5) and
+another at coordinates (15, 5).
+
+In the third case, no matter where Phineas might place two fish in the tank,
+at least one choice of removed divider would result in them potentially
+becoming unhappy.
+

2018/finals/personal.out

@@ -0,0 +1,90 @@
+Case #1: 1
+Case #2: 2
+Case #3: 1
+Case #4: 3
+Case #5: 12
+Case #6: 250001
+Case #7: 163168
+Case #8: 166585
+Case #9: 164528
+Case #10: 1637
+Case #11: 38
+Case #12: 663
+Case #13: 945
+Case #14: 539
+Case #15: 427
+Case #16: 9
+Case #17: 197
+Case #18: 1371
+Case #19: 327
+Case #20: 8
+Case #21: 1063
+Case #22: 1079
+Case #23: 1549
+Case #24: 9
+Case #25: 18
+Case #26: 675
+Case #27: 507
+Case #28: 1067
+Case #29: 1248
+Case #30: 5
+Case #31: 769
+Case #32: 246
+Case #33: 310
+Case #34: 1350
+Case #35: 1702
+Case #36: 445
+Case #37: 610
+Case #38: 946
+Case #39: 1109
+Case #40: 1553
+Case #41: 6
+Case #42: 881
+Case #43: 653
+Case #44: 389
+Case #45: 5
+Case #46: 1689
+Case #47: 49
+Case #48: 1365
+Case #49: 8
+Case #50: 779
+Case #51: 8
+Case #52: 971
+Case #53: 779
+Case #54: 491
+Case #55: 59
+Case #56: 684
+Case #57: 561
+Case #58: 929
+Case #59: 1547
+Case #60: 21
+Case #61: 7
+Case #62: 608
+Case #63: 857
+Case #64: 6
+Case #65: 872
+Case #66: 570
+Case #67: 253
+Case #68: 782
+Case #69: 504
+Case #70: 6
+Case #71: 7
+Case #72: 611
+Case #73: 1634
+Case #74: 722
+Case #75: 7
+Case #76: 1487
+Case #77: 1179
+Case #78: 955
+Case #79: 1486
+Case #80: 735
+Case #81: 1355
+Case #82: 1090
+Case #83: 1481
+Case #84: 232
+Case #85: 8
+Case #86: 508
+Case #87: 63
+Case #88: 1368
+Case #89: 7
+Case #90: 391

2018/finals/stockholm.cpp

@@ -0,0 +1,146 @@
+// Stockholm
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+pair<int,bool> Cost(string s)
+{
+		if (!Sz(s))
+			return(mp(0,0));
+	int i=Sz(s)-1;
+	// delete equal digits from the end
+		while ((i) && (s[i]==s[i-1]))
+			i--;
+	// delete one more digit from the end
+		if (i)
+			i--;
+	// now empty?
+		if (!i)
+			return(mp(0,Sz(s)>=2 && s[0]==s[Sz(s)-1]));
+	pair<int,bool> c=Cost(s.substr(0,i));
+	c.x++;
+	return(c);
+}
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	LL A,B;
+	string X,Y;
+	int p,ans;
+	pair<int,bool> c1,c2;
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// input
+			scanf("%lld%lld",&A,&B);
+			// convert nodes to binary
+			A++,B++;
+			X=Y="";
+				while (A)
+					X=char(A%2+'0')+X,A/=2;
+				while (B)
+					Y=char(B%2+'0')+Y,B/=2;
+			// find LCA
+				Fox(p,min(Sz(X),Sz(Y)))
+					if (X[p]!=Y[p])
+						break;
+			// compute costs to LCA
+			X=X.substr(p);
+			Y=Y.substr(p);
+			c1=Cost(X),c2=Cost(Y);
+			ans=c1.x+c2.x;
+			// at least one node is coming from the outside, and neither is the LCA?
+				if ((Sz(X)) && (Sz(Y)) && (c1.y || c2.y))
+					ans++;
+			// output
+			printf("Case #%d: %d\n",t,ans);
+		}
+	return(0);
+}

2018/finals/stockholm.html

@@ -0,0 +1,76 @@
+<p>
+Melody is visiting the beautiful city of Stockholm, Sweden! Stockholm has a number of waterways flowing through it, dividing the city up into a number of islands. 
+Like most visitors, Melody was surprised to learn that there are in fact an infinite number of waterways and an infinite number of islands!
+</p>
+
+<p>
+The waterways flow between an infinite number of junctions, which are numbered with non-negative integers starting from 0. 
+There's an infinitely-long waterway flowing into junction 0, and then for each junction <em>j</em>, 
+there are two waterways flowing out of it into junctions 2<em>j</em>+1 and 2<em>j</em>+2. This results in each junction having exactly three incident waterways.
+</p>
+
+<p>
+An island is a connected region of land. Each waterway is adjacent to two different islands (one on each side of it), and has a bridge connecting those two islands together. 
+Each junction is adjacent to three different islands (the distinct islands adjacent to its incident waterways).
+</p>
+
+<p>
+A portion of Stockholm (including junctions 0 to 14) is illustrated below, with islands represented as contiguous regions filled with various shades of grey, and bridges between them represented as brown curves:
+</p>
+
+<img width="500px" src="{{PHOTO_ID:923060468192530}}" />
+  
+<p>
+Melody is currently aboard a friend's boat parked at some junction <strong>A</strong>, but she wants to visit another friend's boat which is parked at a different junction <strong>B</strong>. 
+She'll begin by getting out of the first boat onto any of the three islands of her choice which are adjacent to junction <strong>A</strong>. 
+She'll then walk on land until she arrives at any of the three islands which are adjacent to junction <strong>B</strong>, 
+potentially crossing some bridges between islands along the way. Finally, she'll board the second boat from that island.
+</p>
+
+<p>
+Melody's not a big fan of walking on Stockholm's rather unevenly cobbled bridges, so she'd like to cross as few of them as possible along the way. 
+Help her determine the minimum number of bridges which she must cross to walk from junction <strong>A</strong> to junction <strong>B</strong>!
+</p>
+
+<p>
+For example, the following illustration indicates the only optimal path from junction 8 to junction 5 in red (crossing only 1 bridge), 
+and one of the optimal paths from junction 12 to junction 3 in yellow (crossing only 2 bridges):
+</p>
+
+<img width="500px" src="{{PHOTO_ID:293195401822038}}" />
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of times Melody needs to travel between two junctions.
+For each trip, there is a single line containing the space-separated integers <strong>A</strong> and <strong>B</strong>.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th trip, output a line containing "Case #<em>i</em>: " followed by the minimum number of bridges which Melody must cross to walk from junction 
+<strong>A</strong> to junction <strong>B</strong>.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 2,000 <br />
+0 &le; <strong>A</strong>, <strong>B</strong> &le; 10<sup>18</sup> <br />
+<strong>A</strong> &ne; <strong>B</strong>
+</p>
+
+
+<h3>Explanation of Sample</h3>
+  
+<p>
+The first two cases are described above.
+</p>
+
+<p>
+In the third and fourth cases, it's unnecessary for Melody to cross any bridges.
+</p>
+

2018/finals/stockholm.in

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2018/finals/stockholm.md

@@ -0,0 +1,67 @@
+Melody is visiting the beautiful city of Stockholm, Sweden! Stockholm has a
+number of waterways flowing through it, dividing the city up into a number of
+islands. Like most visitors, Melody was surprised to learn that there are in
+fact an infinite number of waterways and an infinite number of islands!
+
+The waterways flow between an infinite number of junctions, which are numbered
+with non-negative integers starting from 0. There's an infinitely-long
+waterway flowing into junction 0, and then for each junction _j_, there are
+two waterways flowing out of it into junctions 2_j_+1 and 2_j_+2. This results
+in each junction having exactly three incident waterways.
+
+An island is a connected region of land. Each waterway is adjacent to two
+different islands (one on each side of it), and has a bridge connecting those
+two islands together. Each junction is adjacent to three different islands
+(the distinct islands adjacent to its incident waterways).
+
+A portion of Stockholm (including junctions 0 to 14) is illustrated below,
+with islands represented as contiguous regions filled with various shades of
+grey, and bridges between them represented as brown curves:
+
+![]({{PHOTO_ID:923060468192530}})
+
+Melody is currently aboard a friend's boat parked at some junction **A**, but
+she wants to visit another friend's boat which is parked at a different
+junction **B**. She'll begin by getting out of the first boat onto any of the
+three islands of her choice which are adjacent to junction **A**. She'll then
+walk on land until she arrives at any of the three islands which are adjacent
+to junction **B**, potentially crossing some bridges between islands along the
+way. Finally, she'll board the second boat from that island.
+
+Melody's not a big fan of walking on Stockholm's rather unevenly cobbled
+bridges, so she'd like to cross as few of them as possible along the way. Help
+her determine the minimum number of bridges which she must cross to walk from
+junction **A** to junction **B**!
+
+For example, the following illustration indicates the only optimal path from
+junction 8 to junction 5 in red (crossing only 1 bridge), and one of the
+optimal paths from junction 12 to junction 3 in yellow (crossing only 2
+bridges):
+
+![]({{PHOTO_ID:293195401822038}})
+
+### Input
+
+Input begins with an integer **T**, the number of times Melody needs to travel
+between two junctions. For each trip, there is a single line containing the
+space-separated integers **A** and **B**.
+
+### Output
+
+For the _i_th trip, output a line containing "Case #_i_: " followed by the
+minimum number of bridges which Melody must cross to walk from junction **A**
+to junction **B**.
+
+### Constraints
+
+1 ≤ **T** ≤ 2,000  
+0 ≤ **A**, **B** ≤ 1018  
+**A** ≠ **B**
+
+### Explanation of Sample
+
+The first two cases are described above.
+
+In the third and fourth cases, it's unnecessary for Melody to cross any
+bridges.
+

2018/finals/stockholm.out

@@ -0,0 +1,2000 @@
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+Case #1602: 28
+Case #1603: 39
+Case #1604: 33
+Case #1605: 39
+Case #1606: 42
+Case #1607: 38
+Case #1608: 38
+Case #1609: 37
+Case #1610: 36
+Case #1611: 37
+Case #1612: 33
+Case #1613: 39
+Case #1614: 38
+Case #1615: 39
+Case #1616: 37
+Case #1617: 35
+Case #1618: 39
+Case #1619: 34
+Case #1620: 38
+Case #1621: 38
+Case #1622: 37
+Case #1623: 31
+Case #1624: 36
+Case #1625: 36
+Case #1626: 37
+Case #1627: 33
+Case #1628: 34
+Case #1629: 28
+Case #1630: 41
+Case #1631: 39
+Case #1632: 37
+Case #1633: 36
+Case #1634: 34
+Case #1635: 37
+Case #1636: 32
+Case #1637: 41
+Case #1638: 40
+Case #1639: 36
+Case #1640: 41
+Case #1641: 36
+Case #1642: 36
+Case #1643: 36
+Case #1644: 37
+Case #1645: 40
+Case #1646: 42
+Case #1647: 37
+Case #1648: 35
+Case #1649: 40
+Case #1650: 40
+Case #1651: 42
+Case #1652: 40
+Case #1653: 41
+Case #1654: 40
+Case #1655: 36
+Case #1656: 37
+Case #1657: 41
+Case #1658: 34
+Case #1659: 36
+Case #1660: 30
+Case #1661: 36
+Case #1662: 36
+Case #1663: 38
+Case #1664: 34
+Case #1665: 42
+Case #1666: 36
+Case #1667: 36
+Case #1668: 39
+Case #1669: 40
+Case #1670: 36
+Case #1671: 43
+Case #1672: 36
+Case #1673: 31
+Case #1674: 36
+Case #1675: 36
+Case #1676: 35
+Case #1677: 38
+Case #1678: 35
+Case #1679: 35
+Case #1680: 38
+Case #1681: 38
+Case #1682: 38
+Case #1683: 30
+Case #1684: 39
+Case #1685: 34
+Case #1686: 39
+Case #1687: 35
+Case #1688: 36
+Case #1689: 43
+Case #1690: 40
+Case #1691: 28
+Case #1692: 42
+Case #1693: 41
+Case #1694: 38
+Case #1695: 42
+Case #1696: 39
+Case #1697: 38
+Case #1698: 40
+Case #1699: 33
+Case #1700: 42
+Case #1701: 42
+Case #1702: 38
+Case #1703: 31
+Case #1704: 40
+Case #1705: 38
+Case #1706: 34
+Case #1707: 34
+Case #1708: 42
+Case #1709: 35
+Case #1710: 42
+Case #1711: 37
+Case #1712: 39
+Case #1713: 36
+Case #1714: 33
+Case #1715: 39
+Case #1716: 36
+Case #1717: 30
+Case #1718: 36
+Case #1719: 38
+Case #1720: 37
+Case #1721: 33
+Case #1722: 40
+Case #1723: 36
+Case #1724: 37
+Case #1725: 36
+Case #1726: 42
+Case #1727: 42
+Case #1728: 34
+Case #1729: 35
+Case #1730: 42
+Case #1731: 36
+Case #1732: 38
+Case #1733: 41
+Case #1734: 36
+Case #1735: 43
+Case #1736: 40
+Case #1737: 37
+Case #1738: 40
+Case #1739: 39
+Case #1740: 37
+Case #1741: 36
+Case #1742: 33
+Case #1743: 32
+Case #1744: 38
+Case #1745: 36
+Case #1746: 32
+Case #1747: 42
+Case #1748: 40
+Case #1749: 35
+Case #1750: 39
+Case #1751: 41
+Case #1752: 37
+Case #1753: 37
+Case #1754: 32
+Case #1755: 34
+Case #1756: 40
+Case #1757: 39
+Case #1758: 36
+Case #1759: 45
+Case #1760: 42
+Case #1761: 40
+Case #1762: 37
+Case #1763: 40
+Case #1764: 35
+Case #1765: 36
+Case #1766: 36
+Case #1767: 40
+Case #1768: 40
+Case #1769: 43
+Case #1770: 37
+Case #1771: 36
+Case #1772: 32
+Case #1773: 36
+Case #1774: 34
+Case #1775: 32
+Case #1776: 32
+Case #1777: 38
+Case #1778: 42
+Case #1779: 40
+Case #1780: 39
+Case #1781: 39
+Case #1782: 39
+Case #1783: 44
+Case #1784: 43
+Case #1785: 36
+Case #1786: 38
+Case #1787: 39
+Case #1788: 40
+Case #1789: 36
+Case #1790: 38
+Case #1791: 40
+Case #1792: 37
+Case #1793: 39
+Case #1794: 35
+Case #1795: 31
+Case #1796: 40
+Case #1797: 40
+Case #1798: 40
+Case #1799: 40
+Case #1800: 37
+Case #1801: 36
+Case #1802: 34
+Case #1803: 33
+Case #1804: 37
+Case #1805: 42
+Case #1806: 40
+Case #1807: 40
+Case #1808: 34
+Case #1809: 41
+Case #1810: 35
+Case #1811: 38
+Case #1812: 41
+Case #1813: 34
+Case #1814: 40
+Case #1815: 36
+Case #1816: 42
+Case #1817: 37
+Case #1818: 31
+Case #1819: 35
+Case #1820: 34
+Case #1821: 37
+Case #1822: 40
+Case #1823: 36
+Case #1824: 37
+Case #1825: 37
+Case #1826: 44
+Case #1827: 41
+Case #1828: 36
+Case #1829: 38
+Case #1830: 35
+Case #1831: 39
+Case #1832: 37
+Case #1833: 35
+Case #1834: 42
+Case #1835: 34
+Case #1836: 38
+Case #1837: 33
+Case #1838: 40
+Case #1839: 38
+Case #1840: 37
+Case #1841: 38
+Case #1842: 36
+Case #1843: 41
+Case #1844: 35
+Case #1845: 35
+Case #1846: 41
+Case #1847: 37
+Case #1848: 37
+Case #1849: 40
+Case #1850: 32
+Case #1851: 35
+Case #1852: 39
+Case #1853: 37
+Case #1854: 38
+Case #1855: 37
+Case #1856: 38
+Case #1857: 37
+Case #1858: 35
+Case #1859: 35
+Case #1860: 37
+Case #1861: 38
+Case #1862: 35
+Case #1863: 38
+Case #1864: 36
+Case #1865: 37
+Case #1866: 36
+Case #1867: 31
+Case #1868: 39
+Case #1869: 40
+Case #1870: 35
+Case #1871: 34
+Case #1872: 37
+Case #1873: 37
+Case #1874: 37
+Case #1875: 42
+Case #1876: 34
+Case #1877: 36
+Case #1878: 41
+Case #1879: 38
+Case #1880: 38
+Case #1881: 34
+Case #1882: 41
+Case #1883: 33
+Case #1884: 37
+Case #1885: 37
+Case #1886: 32
+Case #1887: 36
+Case #1888: 33
+Case #1889: 37
+Case #1890: 41
+Case #1891: 38
+Case #1892: 39
+Case #1893: 40
+Case #1894: 32
+Case #1895: 42
+Case #1896: 30
+Case #1897: 35
+Case #1898: 37
+Case #1899: 36
+Case #1900: 36
+Case #1901: 38
+Case #1902: 35
+Case #1903: 37
+Case #1904: 36
+Case #1905: 42
+Case #1906: 38
+Case #1907: 43
+Case #1908: 35
+Case #1909: 36
+Case #1910: 34
+Case #1911: 36
+Case #1912: 42
+Case #1913: 34
+Case #1914: 40
+Case #1915: 39
+Case #1916: 32
+Case #1917: 32
+Case #1918: 30
+Case #1919: 36
+Case #1920: 39
+Case #1921: 39
+Case #1922: 37
+Case #1923: 44
+Case #1924: 36
+Case #1925: 34
+Case #1926: 37
+Case #1927: 36
+Case #1928: 35
+Case #1929: 39
+Case #1930: 40
+Case #1931: 33
+Case #1932: 39
+Case #1933: 32
+Case #1934: 39
+Case #1935: 32
+Case #1936: 38
+Case #1937: 32
+Case #1938: 44
+Case #1939: 36
+Case #1940: 37
+Case #1941: 37
+Case #1942: 38
+Case #1943: 46
+Case #1944: 36
+Case #1945: 38
+Case #1946: 36
+Case #1947: 37
+Case #1948: 33
+Case #1949: 39
+Case #1950: 40
+Case #1951: 37
+Case #1952: 39
+Case #1953: 40
+Case #1954: 35
+Case #1955: 36
+Case #1956: 39
+Case #1957: 35
+Case #1958: 41
+Case #1959: 37
+Case #1960: 36
+Case #1961: 37
+Case #1962: 37
+Case #1963: 39
+Case #1964: 41
+Case #1965: 38
+Case #1966: 36
+Case #1967: 37
+Case #1968: 40
+Case #1969: 37
+Case #1970: 34
+Case #1971: 37
+Case #1972: 38
+Case #1973: 38
+Case #1974: 39
+Case #1975: 37
+Case #1976: 32
+Case #1977: 33
+Case #1978: 40
+Case #1979: 41
+Case #1980: 33
+Case #1981: 38
+Case #1982: 41
+Case #1983: 41
+Case #1984: 37
+Case #1985: 38
+Case #1986: 35
+Case #1987: 37
+Case #1988: 32
+Case #1989: 41
+Case #1990: 38
+Case #1991: 42
+Case #1992: 39
+Case #1993: 38
+Case #1994: 41
+Case #1995: 44
+Case #1996: 40
+Case #1997: 40
+Case #1998: 35
+Case #1999: 33
+Case #2000: 37

2018/quals/ethanstring.cpp

@@ -0,0 +1,117 @@
+// Ethan Searches for a String
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	string A,B;
+	int i,j;
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// input
+			cin >> A;
+			// check for a valid prefix to repeat
+			B="Impossible";
+				Fox1(i,Sz(A)-1)
+					if (A[i]==A[0])
+					{
+							Fox(j,Sz(A))
+								if (A[j]!=A[j%i])
+									B=A.substr(0,i)+A;
+						break;
+					}
+			// output
+			printf("Case #%d: ",t);
+			cout << B << endl;
+		}
+	return(0);
+}

2018/quals/ethanstring.html

@@ -0,0 +1,79 @@
+<p>
+Ethan's doing his very first programming assignment: implementing a <code>contains()</code> function. This function takes two strings, <strong>A</strong> and <strong>B</strong>,
+and returns <code>true</code> if <strong>A</strong> is a substring of <strong>B</strong>, and <code>false</code> otherwise.
+</p>
+
+<p>
+Here's the algorithm that Ethan has come up with. Note that |<strong>A</strong>| denotes the length of <strong>A</strong>, and the individual characters of the strings are 1-indexed.
+</p>
+
+<ol>
+<li>Set <em>i</em> and <em>j</em> to each be equal to 1.</li>
+<li>If <em>i</em> &gt; |<strong>A</strong>|, return <code>true</code>.</li>
+<li>If <em>j</em> &gt; |<strong>B</strong>|, return <code>false</code>.</li>
+<li>If <strong>A<sub>i</sub></strong> = <strong>B<sub>j</sub></strong>, increment <em>i</em> and <em>j</em> by 1 each, and return to Step 2.</li>
+<li>If <em>i</em> = 1, increment <em>j</em> by 1, and return to Step 2.</li>
+<li>Set <em>i</em> to be equal to 1, and return to Step 2.</li>
+</ol>
+
+<p>
+As the TA in charge of grading Ethan's assignment, this doesn't look quite right to you. To make sure Ethan doesn't get any more credit than he deserves, you'd like to find some inputs
+for which his algorithm returns <code>false</code> even though it should return <code>true</code>.
+</p>
+
+<p>
+The professor teaching this class has provided you with a half-written list of test cases. In particular, it's a list of inputs for the <strong>A</strong> parameter, and you're free to come up with
+your own inputs for the <strong>B</strong> parameter. For each given string <strong>A</strong>, you want to find a string <strong>B</strong> that will cause Ethan's algorithm to return the
+wrong output (<code>false</code> instead of <code>true</code>), if possible. <strong>A</strong> will only contain uppercase alphabetic characters, and <strong>B</strong> must follow the same constraint. The test cases shouldn't be too
+large, so <strong>B</strong> must also contain at most 10,000 characters.
+</p>
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of given strings.
+Then, <strong>T</strong> lines follow. Each line contains a single string, <strong>A</strong>.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th given string, print a line containing "Case #<em>i</em>: "
+followed by any valid string <strong>B</strong> that will cause Ethan's algorithm to return the wrong value, or "Impossible" if no such string exists.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 100 <br />
+1 &le; |<strong>A</strong>| &le; 2,000 <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+
+<p>
+In the first case, <em>i</em> and <em>j</em> will have these values in order the first 10 times the algorithm is at Step 2:
+</p>
+
+<pre>
+i j
+---
+1 1
+2 2
+1 2
+1 3
+1 4
+1 5
+2 6
+3 7
+4 8
+1 8
+</pre>
+
+<p>
+Please note that other outputs for example cases 1 and 3 would also be accepted.
+</p>
+

2018/quals/ethanstring.md

@@ -0,0 +1,66 @@
+Ethan's doing his very first programming assignment: implementing a
+`contains()` function. This function takes two strings, **A** and **B**, and
+returns `true` if **A** is a substring of **B**, and `false` otherwise.
+
+Here's the algorithm that Ethan has come up with. Note that |**A**| denotes
+the length of **A**, and the individual characters of the strings are
+1-indexed.
+
+  1. Set _i_ and _j_ to each be equal to 1.
+  2. If _i_ > |**A**|, return `true`.
+  3. If _j_ > |**B**|, return `false`.
+  4. If **Ai** = **Bj**, increment _i_ and _j_ by 1 each, and return to Step 2.
+  5. If _i_ = 1, increment _j_ by 1, and return to Step 2.
+  6. Set _i_ to be equal to 1, and return to Step 2.
+
+As the TA in charge of grading Ethan's assignment, this doesn't look quite
+right to you. To make sure Ethan doesn't get any more credit than he deserves,
+you'd like to find some inputs for which his algorithm returns `false` even
+though it should return `true`.
+
+The professor teaching this class has provided you with a half-written list of
+test cases. In particular, it's a list of inputs for the **A** parameter, and
+you're free to come up with your own inputs for the **B** parameter. For each
+given string **A**, you want to find a string **B** that will cause Ethan's
+algorithm to return the wrong output (`false` instead of `true`), if possible.
+**A** will only contain uppercase alphabetic characters, and **B** must follow
+the same constraint. The test cases shouldn't be too large, so **B** must also
+contain at most 10,000 characters.
+
+### Input
+
+Input begins with an integer **T**, the number of given strings. Then, **T**
+lines follow. Each line contains a single string, **A**.
+
+### Output
+
+For the _i_th given string, print a line containing "Case #_i_: " followed by
+any valid string **B** that will cause Ethan's algorithm to return the wrong
+value, or "Impossible" if no such string exists.
+
+### Constraints
+
+1 ≤ **T** ≤ 100  
+1 ≤ |**A**| ≤ 2,000  
+
+### Explanation of Sample
+
+In the first case, _i_ and _j_ will have these values in order the first 10
+times the algorithm is at Step 2:
+
+    i j
+    ---
+    1 1
+    2 2
+    1 2
+    1 3
+    1 4
+    1 5
+    2 6
+    3 7
+    4 8
+    1 8
+
+Please note that other outputs for example cases 1 and 3 would also be
+accepted.
+

2018/quals/interception.cpp

@@ -0,0 +1,112 @@
+// Interception
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	int N;
+	int i,p;
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// input
+			Read(N);
+				Fox(i,N+1)
+					Read(p);
+			// output
+			printf("Case #%d: ",t);
+				if (N%2==0)
+					printf("0\n");
+				else
+					printf("1\n0\n");
+		}
+	return(0);
+}

2018/quals/interception.html

@@ -0,0 +1,61 @@
+<p>
+Consider an N-degree polynomial, expressed as follows:
+</p>
+
+<p>
+  <b>P</b><sub>N</sub> * x<sup>N</sup> + <b>P</b><sub>N-1</sub> * x<sup>N-1</sup> + ... + <b>P</b><sub>1</sub> * x<sup>1</sup> + <b>P</b><sub>0</sub> * x<sup>0</sup>
+</p>
+
+<p>
+You'd like to find all of the polynomial's x-intercepts &mdash; in other words, all distinct real values of x for which the expression evaluates to 0.
+</p>
+
+<p>
+Unfortunately, the order of operations has been reversed: 
+Addition (<strong>+</strong>) now has the highest precedence, followed by multiplication (<strong>*</strong>), followed by exponentiation (<strong>^</strong>). 
+In other words, an expression like a<sup>b</sup> + c * d should be evaluated as a<sup>((b+c)*d)</sup>. 
+For our purposes, exponentiation is right-associative (in other words, a<sup>b<sup>c</sup></sup> = a<sup>(b<sup>c</sup>)</sup>), 
+and 0<sup>0</sup> = 1.
+The unary negation operator still has the highest precedence, so the expression -2<sup>-3</sup> * -1 + -2 evaluates to -2<sup>(-3 * (-1 + -2))</sup> = -2<sup>9</sup> = -512.
+</p>
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of polynomials.
+For each polynomial, there is first a line containing the integer <strong>N</strong>, the degree of the polynomial.
+Then, <strong>N</strong>+1 lines follow. The <em>i</em>th of these lines contains the integer <strong>P<sub>i-1</sub></strong>.
+</p>
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th polynomial, print a line containing "Case #<em>i</em>: <strong>K</strong>", 
+where <strong>K</strong> is the number of distinct real values of <strong>x</strong> for which the polynomial evaluates to 0.
+Then print <strong>K</strong> lines, each containing such a value of <strong>x</strong>, in increasing order.
+</p>
+
+<p>
+Absolute and relative errors of up to 10<sup>-6</sup> will be ignored in the x-intercepts you output. However, <strong>K</strong> must be exactly correct.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 200 <br />
+0 &le; <strong>N</strong> &le; 50 <br />
+-50 &le; <strong>P<sub>i</sub></strong> &le; 50 <br />
+<strong>P<sub>N</sub></strong> &ne; 0 <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+
+<p>
+In the first case, the polynomial is 1 * x<sup>1</sup> + 1 * x<sup>0</sup>. With the order of operations reversed, this is evaluated as (1 * x)<sup>(((1 + 1) * x)<sup>0</sup>)</sup>, which is equal to 0 only when x = 0.
+</p>
+
+<p>
+In the second case, the polynomial does not evaluate to 0 for any real value x.
+</p>

2018/quals/interception.in

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+-47
+-44
+38
+-20
+-3
+-7
+39
+41
+2
+-15
+39
+32
+29
+-5
+-25
+26
+15
+24
+2
+-6
+-17
+47
+21
+-29
+45
+33
+-35
+42
+-2
+17
+-32
+-26
+-44
+-20
+-32
+22
+-26
+-19
+-32
+38
+-29
+-38
+-29
+28
+-14
+-18
+-1
+-27
+-3
+2
+48
+-23
+30
+-33
+40
+-43
+-24
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+-7
+-12
+48
+-38
+-28
+50
+-7
+-17
+-18
+-16
+-10
+29
+11
+-14
+10
+15
+-38
+-3
+16
+25
+-7
+-8
+-44
+-36
+-39
+30
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+-2
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+-8
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+49
+1
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+8
+-15
+-7
+-41
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+0
+-16
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+11
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+-4
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+-19
+5
+1
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+15
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+3
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+-2
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+-3
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+28
+38
+38
+21
+0
+6
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+45
+5
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+-45
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+-4
+-3
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+-7
+-8
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+-20
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+-12
+-2
+30
+-9

2018/quals/interception.md

@@ -0,0 +1,48 @@
+Consider an N-degree polynomial, expressed as follows:
+
+**P**N * xN \+ **P**N-1 * xN-1 \+ ... + **P**1 * x1 \+ **P**0 * x0
+
+You'd like to find all of the polynomial's x-intercepts — in other words, all
+distinct real values of x for which the expression evaluates to 0.
+
+Unfortunately, the order of operations has been reversed: Addition (**+**) now
+has the highest precedence, followed by multiplication (*****), followed by
+exponentiation (**^**). In other words, an expression like ab \+ c * d should
+be evaluated as a((b+c)*d). For our purposes, exponentiation is right-
+associative (in other words, abc = a(bc)), and 00 = 1. The unary negation
+operator still has the highest precedence, so the expression -2-3 * -1 + -2
+evaluates to -2(-3 * (-1 + -2)) = -29 = -512.
+
+### Input
+
+Input begins with an integer **T**, the number of polynomials. For each
+polynomial, there is first a line containing the integer **N**, the degree of
+the polynomial. Then, **N**+1 lines follow. The _i_th of these lines contains
+the integer **Pi-1**.
+
+### Output
+
+For the _i_th polynomial, print a line containing "Case #_i_: **K**", where
+**K** is the number of distinct real values of **x** for which the polynomial
+evaluates to 0. Then print **K** lines, each containing such a value of **x**,
+in increasing order.
+
+Absolute and relative errors of up to 10-6 will be ignored in the x-intercepts
+you output. However, **K** must be exactly correct.
+
+### Constraints
+
+1 ≤ **T** ≤ 200  
+0 ≤ **N** ≤ 50  
+-50 ≤ **Pi** ≤ 50   
+**PN** ≠ 0   
+
+### Explanation of Sample
+
+In the first case, the polynomial is 1 * x1 \+ 1 * x0. With the order of
+operations reversed, this is evaluated as (1 * x)(((1 + 1) * x)0), which is
+equal to 0 only when x = 0.
+
+In the second case, the polynomial does not evaluate to 0 for any real value
+x.
+

2018/quals/interception.out

@@ -0,0 +1,462 @@
+Case #1: 1
+0
+Case #2: 0
+Case #3: 0
+Case #4: 1
+0
+Case #5: 1
+0
+Case #6: 1
+0
+Case #7: 0
+Case #8: 1
+0
+Case #9: 1
+0
+Case #10: 1
+0
+Case #11: 1
+0
+Case #12: 1
+0
+Case #13: 1
+0
+Case #14: 0
+Case #15: 0
+Case #16: 1
+0
+Case #17: 0
+Case #18: 1
+0
+Case #19: 0
+Case #20: 0
+Case #21: 1
+0
+Case #22: 1
+0
+Case #23: 1
+0
+Case #24: 1
+0
+Case #25: 0
+Case #26: 1
+0
+Case #27: 0
+Case #28: 1
+0
+Case #29: 1
+0
+Case #30: 0
+Case #31: 0
+Case #32: 1
+0
+Case #33: 1
+0
+Case #34: 0
+Case #35: 0
+Case #36: 1
+0
+Case #37: 0
+Case #38: 0
+Case #39: 1
+0.0
+Case #40: 1
+0
+Case #41: 0
+Case #42: 0
+Case #43: 1
+0
+Case #44: 1
+0
+Case #45: 1
+0
+Case #46: 0
+Case #47: 1
+0
+Case #48: 1
+0
+Case #49: 0
+Case #50: 0
+Case #51: 0
+Case #52: 1
+0
+Case #53: 0
+Case #54: 1
+0
+Case #55: 1
+0
+Case #56: 0
+Case #57: 0
+Case #58: 0
+Case #59: 0
+Case #60: 1
+0
+Case #61: 1
+0
+Case #62: 0
+Case #63: 0
+Case #64: 0
+Case #65: 1
+0
+Case #66: 0
+Case #67: 1
+0
+Case #68: 1
+0
+Case #69: 1
+0
+Case #70: 1
+0
+Case #71: 1
+0
+Case #72: 0
+Case #73: 1
+0
+Case #74: 0
+Case #75: 1
+0
+Case #76: 1
+0
+Case #77: 1
+0
+Case #78: 1
+0
+Case #79: 0
+Case #80: 0
+Case #81: 0
+Case #82: 1
+0
+Case #83: 1
+0
+Case #84: 1
+0
+Case #85: 0
+Case #86: 1
+0
+Case #87: 1
+0
+Case #88: 1
+0
+Case #89: 1
+0
+Case #90: 0
+Case #91: 1
+0
+Case #92: 0
+Case #93: 1
+0
+Case #94: 1
+0
+Case #95: 1
+0
+Case #96: 1
+0
+Case #97: 1
+0
+Case #98: 1
+0
+Case #99: 1
+0
+Case #100: 1
+0
+Case #101: 1
+0
+Case #102: 1
+0
+Case #103: 1
+0
+Case #104: 1
+0
+Case #105: 0
+Case #106: 1
+0
+Case #107: 0
+Case #108: 1
+0
+Case #109: 1
+0
+Case #110: 0
+Case #111: 0
+Case #112: 0
+Case #113: 0
+Case #114: 0
+Case #115: 0
+Case #116: 0
+Case #117: 0
+Case #118: 0
+Case #119: 1
+0
+Case #120: 1
+0
+Case #121: 0
+Case #122: 0
+Case #123: 1
+0
+Case #124: 1
+0
+Case #125: 0
+Case #126: 1
+0
+Case #127: 0
+Case #128: 0
+Case #129: 0
+Case #130: 1
+0
+Case #131: 1
+0
+Case #132: 1
+0
+Case #133: 1
+0
+Case #134: 0
+Case #135: 0
+Case #136: 0
+Case #137: 1
+0
+Case #138: 0
+Case #139: 0
+Case #140: 1
+0
+Case #141: 1
+0
+Case #142: 0
+Case #143: 1
+0
+Case #144: 0
+Case #145: 0
+Case #146: 0
+Case #147: 0
+Case #148: 1
+0
+Case #149: 0
+Case #150: 1
+0
+Case #151: 1
+0
+Case #152: 1
+0
+Case #153: 0
+Case #154: 1
+0
+Case #155: 1
+0
+Case #156: 1
+0
+Case #157: 1
+0
+Case #158: 1
+0
+Case #159: 0
+Case #160: 0
+Case #161: 0
+Case #162: 1
+0
+Case #163: 0
+Case #164: 0
+Case #165: 1
+0
+Case #166: 0
+Case #167: 1
+0
+Case #168: 0
+Case #169: 1
+0
+Case #170: 0
+Case #171: 1
+0
+Case #172: 0
+Case #173: 1
+0
+Case #174: 1
+0
+Case #175: 1
+0
+Case #176: 1
+0
+Case #177: 1
+0
+Case #178: 0
+Case #179: 1
+0
+Case #180: 0
+Case #181: 1
+0
+Case #182: 0
+Case #183: 0
+Case #184: 0
+Case #185: 0
+Case #186: 0
+Case #187: 1
+0
+Case #188: 1
+0
+Case #189: 1
+0
+Case #190: 1
+0
+Case #191: 0
+Case #192: 0
+Case #193: 0
+Case #194: 1
+0
+Case #195: 0
+Case #196: 1
+0
+Case #197: 0
+Case #198: 1
+0
+Case #199: 0
+Case #200: 0
+Case #201: 1
+0
+Case #202: 0
+Case #203: 1
+0
+Case #204: 1
+0
+Case #205: 0
+Case #206: 1
+0
+Case #207: 0
+Case #208: 0
+Case #209: 1
+0
+Case #210: 0
+Case #211: 0
+Case #212: 1
+0
+Case #213: 0
+Case #214: 1
+0
+Case #215: 1
+0
+Case #216: 1
+0
+Case #217: 0
+Case #218: 1
+0
+Case #219: 0
+Case #220: 0
+Case #221: 1
+0
+Case #222: 0
+Case #223: 0
+Case #224: 0
+Case #225: 0
+Case #226: 0
+Case #227: 1
+0
+Case #228: 1
+0
+Case #229: 0
+Case #230: 0
+Case #231: 0
+Case #232: 1
+0
+Case #233: 1
+0
+Case #234: 1
+0
+Case #235: 0
+Case #236: 1
+0
+Case #237: 1
+0
+Case #238: 1
+0
+Case #239: 1
+0
+Case #240: 1
+0
+Case #241: 1
+0
+Case #242: 0
+Case #243: 0
+Case #244: 0
+Case #245: 1
+0
+Case #246: 0
+Case #247: 1
+0
+Case #248: 0
+Case #249: 0
+Case #250: 0
+Case #251: 1
+0
+Case #252: 0
+Case #253: 0
+Case #254: 1
+0
+Case #255: 1
+0
+Case #256: 1
+0
+Case #257: 1
+0
+Case #258: 1
+0
+Case #259: 0
+Case #260: 0
+Case #261: 0
+Case #262: 1
+0
+Case #263: 1
+0
+Case #264: 1
+0
+Case #265: 1
+0
+Case #266: 1
+0
+Case #267: 0
+Case #268: 0
+Case #269: 0
+Case #270: 1
+0
+Case #271: 0
+Case #272: 1
+0
+Case #273: 1
+0
+Case #274: 0
+Case #275: 1
+0
+Case #276: 1
+0
+Case #277: 0
+Case #278: 1
+0
+Case #279: 0
+Case #280: 0
+Case #281: 0
+Case #282: 1
+0
+Case #283: 0
+Case #284: 1
+0
+Case #285: 1
+0
+Case #286: 0
+Case #287: 1
+0
+Case #288: 0
+Case #289: 0
+Case #290: 1
+0
+Case #291: 0
+Case #292: 1
+0
+Case #293: 1
+0
+Case #294: 0
+Case #295: 1
+0
+Case #296: 1
+0
+Case #297: 0
+Case #298: 0
+Case #299: 0
+Case #300: 0
+Case #301: 1
+0
+Case #302: 0

2018/quals/tourist.cpp

@@ -0,0 +1,119 @@
+// Tourist
+// Solution by Jacob Plachta
+
+#define DEBUG 0
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <iostream>
+#include <iomanip>
+#include <cstdio>
+#include <cmath>
+#include <complex>
+#include <cstdlib>
+#include <ctime>
+#include <cstring>
+#include <cassert>
+#include <string>
+#include <vector>
+#include <list>
+#include <map>
+#include <set>
+#include <deque>
+#include <queue>
+#include <stack>
+#include <bitset>
+#include <sstream>
+using namespace std;
+
+#define LL long long
+#define LD long double
+#define PR pair<int,int>
+
+#define Fox(i,n) for (i=0; i<n; i++)
+#define Fox1(i,n) for (i=1; i<=n; i++)
+#define FoxI(i,a,b) for (i=a; i<=b; i++)
+#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
+#define FoxR1(i,n) for (i=n; i>0; i--)
+#define FoxRI(i,a,b) for (i=b; i>=a; i--)
+#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
+#define Min(a,b) a=min(a,b)
+#define Max(a,b) a=max(a,b)
+#define Sz(s) int((s).size())
+#define All(s) (s).begin(),(s).end()
+#define Fill(s,v) memset(s,v,sizeof(s))
+#define pb push_back
+#define mp make_pair
+#define x first
+#define y second
+
+template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
+template<typename T> T Sqr(T x) { return(x*x); }
+string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
+
+const int INF = (int)1e9;
+const LD EPS = 1e-12;
+const LD PI = acos(-1.0);
+
+#if DEBUG
+#define GETCHAR getchar
+#else
+#define GETCHAR getchar_unlocked
+#endif
+
+bool Read(int &x)
+{
+	char c,r=0,n=0;
+	x=0;
+		for(;;)
+		{
+			c=GETCHAR();
+				if ((c<0) && (!r))
+					return(0);
+				if ((c=='-') && (!r))
+					n=1;
+				else
+				if ((c>='0') && (c<='9'))
+					x=x*10+c-'0',r=1;
+				else
+				if (r)
+					break;
+		}
+		if (n)
+			x=-x;
+	return(1);
+}
+
+int main()
+{
+		if (DEBUG)
+			freopen("in.txt","r",stdin);
+	// vars
+	int T,t;
+	int N,K;
+	LL V;
+	int i,j;
+	char A[50][21];
+	int vis[50];
+	// testcase loop
+	Read(T);
+		Fox1(t,T)
+		{
+			// input
+			scanf("%d%d%lld",&N,&K,&V);
+				Fox(i,N)
+					scanf("%s",&A[i]);
+			// find visited attractions
+			i=K*(V-1)%N;
+				Fox(j,K)
+					vis[j]=(i+j)%N;
+			sort(vis,vis+K);
+			// output
+			printf("Case #%d:",t);
+				Fox(i,K)
+					printf(" %s",A[vis[i]]);
+			printf("\n");
+		}
+	return(0);
+}

2018/quals/tourist.html

@@ -0,0 +1,57 @@
+<p>
+The Facebook campus has <strong>N</strong> different attractions, numbered from 1 to <strong>N</strong> in decreasing order of popularity. 
+The name of the <em>i</em>th attraction is <strong>A<sub>i</sub></strong>, a unique, non-empty string consisting of at most 20 characters. Each character is either a lowercase letter ("a".."z"), uppercase letter ("A".."Z"), or digit ("0".."9").
+</p>
+
+<p>
+Alex enjoys visiting the campus repeatedly for tours (including the free food!). Each time he visits, he has time to see exactly <strong>K</strong> of the attractions. 
+To decide which <strong>K</strong> he'll see, he sorts the <strong>N</strong> attractions in non-decreasing order of how many times he's already seen them before, 
+breaking ties in decreasing order of popularity, and then chooses the first <strong>K</strong> attractions in the sorted list. 
+In other words, he prioritizes seeing attractions which he's seen the fewest number of times previously, 
+but also opts to see the most popular attractions out of the ones he's seen an equal number of times.
+</p>
+
+<p>
+Alex has visited the Facebook campus <strong>V</strong>-1 separate times already, and is about to go for his <strong>V</strong>th visit. 
+Given that he's always followed the rules stated above, and that he'll continue to, he'd like to determine which <strong>K</strong> attractions he'll see on his <strong>V</strong>th visit. 
+He'd like to list them in decreasing order of popularity (in other words, in the same relative order as they appear in the given list of all <strong>N</strong> attractions).
+</p>
+
+
+<h3>Input</h3>
+
+<p>
+Input begins with an integer <strong>T</strong>, the number of campuses.
+For each campus, there is first a line containing the space-separated integers <strong>N</strong>, <strong>K</strong>, and <strong>V</strong>.
+Then, <strong>N</strong> lines follow. The <em>i</em>th of these lines contains the string <strong>A<sub>i</sub></strong>.
+</p>
+
+
+<h3>Output</h3>
+
+<p>
+For the <em>i</em>th campus, print a line containing "Case #<em>i</em>: "
+followed by <strong>K</strong> space-separated strings, the names of the attractions that Alex sees on his <strong>V</strong>th visit,
+in decreasing order of popularity.
+</p>
+
+
+<h3>Constraints</h3>
+
+<p>
+1 &le; <strong>T</strong> &le; 80 <br />
+1 &le; <strong>K</strong> &le; <strong>N</strong> &le; 50 <br />
+1 &le; <strong>V</strong> &le; 10<sup>12</sup> <br />
+</p>
+
+
+<h3>Explanation of Sample</h3>
+
+<p>
+In the first case, Alex saw the LikeSign on his first visit and the Arcade on his second visit. On his third visit he sees the SweetStop as its the most popular of the attractions he hasn't yet seen.
+</p>
+
+<p>
+In the third and fourth cases, Alex sees {LikeSign, Arcade, SweetStop} on his first visit, then {LikeSign, Arcade, SwagStore}, then {LikeSign, SweetStop, SwagStore}.
+</p>
+

2018/quals/tourist.in

@@ -0,0 +1,3871 @@
+156
+49 47 350138265919
+HotfixBar
+RainbowStairs
+Sol
+SweetStop
+CafeEpic
+LivingTheDream
+ZucksOffice
+TuringInDominoes
+OculusDemoLab
+LightningBolts
+NailPolishRoomBlock
+DentalOffice
+Nanokitchen
+PhilzCoffee
+SwagStore
+BahnAppetit
+FreshOrangeJuice
+FoxGazebo
+VerveCoffee
+HackerSquare
+Ballpit
+ShuttlePlatform
+FakeCrosswalk
+BurgerShack
+TransportationHub
+FukiSushiInOldenDays
+ColdBrewMachine
+PopUpShop
+SonOfPingAndPong
+Harvest
+BlueBottle
+ZucksOldOffice
+MPK20Roof
+ChosHawkerCenter
+TechVendingMachine
+SugarShack
+WoodenSculpture
+FoxPainting
+Arcade
+Helpdesk
+BridgeClub
+ConstitutionDeli
+Microkitchen
+SaintFrank
+HalalTruck
+LateHarvest
+LikeSign
+MamaPennys
+WallOfPhones
+36 3 225802032479
+LateHarvest
+WallOfPhones
+TransportationHub
+BurgerShack
+Sol
+MamaPennys
+Ballpit
+TechVendingMachine
+ZucksOffice
+HalalTruck
+Arcade
+OculusDemoLab
+BahnAppetit
+HackerSquare
+FoxGazebo
+ShuttlePlatform
+ConstitutionDeli
+Harvest
+LikeSign
+SugarShack
+SwagStore
+PopUpShop
+FukiSushiInOldenDays
+RainbowStairs
+ChosHawkerCenter
+FoxPainting
+WoodenSculpture
+TuringInDominoes
+BlueBottle
+FullCircle
+CafeEpic
+SonOfPingAndPong
+SweetStop
+FakeCrosswalk
+BridgeClub
+LivingTheDream
+32 5 244436814629
+BurgerShack
+HalalTruck
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+BurgerShack
+TuringInDominoes
+NailPolishRoomBlock
+MamaPennys
+FoxGazebo
+PopUpShop
+LivingTheDream
+FakeCrosswalk
+HalalTruck
+CafeEpic
+TechVendingMachine
+ZucksOldOffice
+FoxPainting
+BlueBottle
+ShuttlePlatform
+SweetStop
+Ballpit
+ZucksOffice
+FreshOrangeJuice
+13 12 288611636879
+Nanokitchen
+Arcade
+Helpdesk
+PopUpShop
+OculusDemoLab
+HalalTruck
+FakeCrosswalk
+LikeSign
+HotfixBar
+BahnAppetit
+BridgeClub
+FoxPainting
+TechVendingMachine
+42 8 825873191774
+LightningBolts
+LateHarvest
+CafeEpic
+FoxPainting
+NailPolishRoomBlock
+BlueBottle
+WallOfPhones
+ShuttlePlatform
+Harvest
+FullCircle
+RainbowStairs
+LikeSign
+ZucksOffice
+TuringInDominoes
+WoodenSculpture
+SwagStore
+HotfixBar
+HalalTruck
+MPK20Roof
+MamaPennys
+SugarShack
+ConstitutionDeli
+FakeCrosswalk
+PhilzCoffee
+Nanokitchen
+TechVendingMachine
+FreshOrangeJuice
+ZucksOldOffice
+DentalOffice
+FoxGazebo
+Microkitchen
+ChosHawkerCenter
+ColdBrewMachine
+Sol
+Ballpit
+BahnAppetit
+LivingTheDream
+SonOfPingAndPong
+SweetStop
+PopUpShop
+OculusDemoLab
+VerveCoffee
+13 11 36591483009
+LivingTheDream
+ZucksOldOffice
+LightningBolts
+FukiSushiInOldenDays
+FreshOrangeJuice
+ZucksOffice
+FullCircle
+LikeSign
+ChosHawkerCenter
+TechVendingMachine
+TransportationHub
+WallOfPhones
+MamaPennys
+2 2 844764780508
+TechVendingMachine
+Arcade
+8 6 10658812981
+Harvest
+TechVendingMachine
+FreshOrangeJuice
+LightningBolts
+Sol
+DentalOffice
+BlueBottle
+ZucksOldOffice
+21 9 634654833041
+NailPolishRoomBlock
+LightningBolts
+BlueBottle
+OculusDemoLab
+FullCircle
+Microkitchen
+TechVendingMachine
+ShuttlePlatform
+WallOfPhones
+LivingTheDream
+Ballpit
+MPK20Roof
+FreshOrangeJuice
+ConstitutionDeli
+ZucksOffice
+RainbowStairs
+ChosHawkerCenter
+MamaPennys
+Helpdesk
+Arcade
+SonOfPingAndPong
+28 5 927739165937
+PhilzCoffee
+CafeEpic
+LightningBolts
+Harvest
+LateHarvest
+OculusDemoLab
+Arcade
+MamaPennys
+LikeSign
+Helpdesk
+SweetStop
+SwagStore
+RainbowStairs
+WoodenSculpture
+FakeCrosswalk
+ConstitutionDeli
+SugarShack
+ZucksOldOffice
+SaintFrank
+FoxPainting
+FreshOrangeJuice
+HotfixBar
+TechVendingMachine
+Microkitchen
+ZucksOffice
+BlueBottle
+HackerSquare
+ChosHawkerCenter
+41 3 603270301156
+TechVendingMachine
+HalalTruck
+ShuttlePlatform
+WallOfPhones
+MPK20Roof
+LikeSign
+DentalOffice
+FukiSushiInOldenDays
+TransportationHub
+CafeEpic
+RainbowStairs
+FakeCrosswalk
+ZucksOffice
+BurgerShack
+Nanokitchen
+Harvest
+Arcade
+SwagStore
+Sol
+HackerSquare
+LightningBolts
+HotfixBar
+LateHarvest
+ConstitutionDeli
+SweetStop
+BridgeClub
+TuringInDominoes
+BahnAppetit
+NailPolishRoomBlock
+Helpdesk
+SaintFrank
+PhilzCoffee
+VerveCoffee
+FoxPainting
+Microkitchen
+FreshOrangeJuice
+ZucksOldOffice
+Ballpit
+SugarShack
+FoxGazebo
+BlueBottle
+25 1 543645657850
+OculusDemoLab
+FakeCrosswalk
+LivingTheDream
+SwagStore
+Harvest
+ZucksOldOffice
+LikeSign
+MamaPennys
+ConstitutionDeli
+LightningBolts
+HotfixBar
+FreshOrangeJuice
+SaintFrank
+ChosHawkerCenter
+BurgerShack
+TransportationHub
+ZucksOffice
+WallOfPhones
+BridgeClub
+Ballpit
+RainbowStairs
+HalalTruck
+SweetStop
+Helpdesk
+TechVendingMachine
+13 11 666195881624
+Sol
+WoodenSculpture
+ShuttlePlatform
+TechVendingMachine
+CafeEpic
+ConstitutionDeli
+MPK20Roof
+BlueBottle
+TuringInDominoes
+FukiSushiInOldenDays
+Nanokitchen
+LightningBolts
+FreshOrangeJuice

2018/quals/tourist.md

@@ -0,0 +1,52 @@
+The Facebook campus has **N** different attractions, numbered from 1 to **N**
+in decreasing order of popularity. The name of the _i_th attraction is **Ai**,
+a unique, non-empty string consisting of at most 20 characters. Each character
+is either a lowercase letter ("a".."z"), uppercase letter ("A".."Z"), or digit
+("0".."9").
+
+Alex enjoys visiting the campus repeatedly for tours (including the free
+food!). Each time he visits, he has time to see exactly **K** of the
+attractions. To decide which **K** he'll see, he sorts the **N** attractions
+in non-decreasing order of how many times he's already seen them before,
+breaking ties in decreasing order of popularity, and then chooses the first
+**K** attractions in the sorted list. In other words, he prioritizes seeing
+attractions which he's seen the fewest number of times previously, but also
+opts to see the most popular attractions out of the ones he's seen an equal
+number of times.
+
+Alex has visited the Facebook campus **V**-1 separate times already, and is
+about to go for his **V**th visit. Given that he's always followed the rules
+stated above, and that he'll continue to, he'd like to determine which **K**
+attractions he'll see on his **V**th visit. He'd like to list them in
+decreasing order of popularity (in other words, in the same relative order as
+they appear in the given list of all **N** attractions).
+
+### Input
+
+Input begins with an integer **T**, the number of campuses. For each campus,
+there is first a line containing the space-separated integers **N**, **K**,
+and **V**. Then, **N** lines follow. The _i_th of these lines contains the
+string **Ai**.
+
+### Output
+
+For the _i_th campus, print a line containing "Case #_i_: " followed by **K**
+space-separated strings, the names of the attractions that Alex sees on his
+**V**th visit, in decreasing order of popularity.
+
+### Constraints
+
+1 ≤ **T** ≤ 80  
+1 ≤ **K** ≤ **N** ≤ 50  
+1 ≤ **V** ≤ 1012  
+
+### Explanation of Sample
+
+In the first case, Alex saw the LikeSign on his first visit and the Arcade on
+his second visit. On his third visit he sees the SweetStop as its the most
+popular of the attractions he hasn't yet seen.
+
+In the third and fourth cases, Alex sees {LikeSign, Arcade, SweetStop} on his
+first visit, then {LikeSign, Arcade, SwagStore}, then {LikeSign, SweetStop,
+SwagStore}.
+

2018/quals/tourist.out

@@ -0,0 +1,156 @@
+Case #1: HotfixBar RainbowStairs Sol SweetStop CafeEpic LivingTheDream ZucksOffice TuringInDominoes OculusDemoLab LightningBolts NailPolishRoomBlock DentalOffice Nanokitchen PhilzCoffee SwagStore BahnAppetit FreshOrangeJuice FoxGazebo VerveCoffee ShuttlePlatform FakeCrosswalk BurgerShack TransportationHub FukiSushiInOldenDays ColdBrewMachine PopUpShop SonOfPingAndPong Harvest BlueBottle ZucksOldOffice MPK20Roof ChosHawkerCenter TechVendingMachine SugarShack WoodenSculpture FoxPainting Arcade Helpdesk BridgeClub ConstitutionDeli Microkitchen SaintFrank HalalTruck LateHarvest LikeSign MamaPennys WallOfPhones
+Case #2: CafeEpic SonOfPingAndPong SweetStop
+Case #3: LightningBolts Ballpit PopUpShop TuringInDominoes VerveCoffee
+Case #4: RainbowStairs WallOfPhones FoxGazebo Helpdesk Arcade Harvest NailPolishRoomBlock FullCircle PopUpShop OculusDemoLab SaintFrank MamaPennys Sol FoxPainting HalalTruck LateHarvest FakeCrosswalk SugarShack BlueBottle SweetStop TuringInDominoes CafeEpic LivingTheDream DentalOffice ZucksOffice SonOfPingAndPong Nanokitchen ColdBrewMachine MPK20Roof WoodenSculpture PhilzCoffee BahnAppetit SwagStore FreshOrangeJuice ConstitutionDeli ShuttlePlatform LightningBolts ZucksOldOffice LikeSign TechVendingMachine Ballpit
+Case #5: FullCircle FukiSushiInOldenDays WallOfPhones NailPolishRoomBlock Ballpit
+Case #6: WoodenSculpture MPK20Roof Harvest Nanokitchen
+Case #7: PopUpShop
+Case #8: VerveCoffee LightningBolts BlueBottle SwagStore
+Case #9: ShuttlePlatform
+Case #10: FoxPainting BahnAppetit SweetStop LightningBolts ChosHawkerCenter ZucksOldOffice
+Case #11: MamaPennys SwagStore LightningBolts FullCircle PhilzCoffee Harvest HackerSquare TransportationHub ShuttlePlatform FoxGazebo NailPolishRoomBlock WallOfPhones BlueBottle PopUpShop LikeSign HotfixBar
+Case #12: FullCircle Sol MPK20Roof Arcade FoxPainting HotfixBar
+Case #13: ShuttlePlatform NailPolishRoomBlock LightningBolts MamaPennys Microkitchen HalalTruck CafeEpic BahnAppetit PhilzCoffee SaintFrank BurgerShack FoxPainting HotfixBar FoxGazebo HackerSquare SwagStore LikeSign FullCircle Arcade VerveCoffee
+Case #14: ConstitutionDeli TuringInDominoes Harvest HackerSquare NailPolishRoomBlock Ballpit BlueBottle OculusDemoLab Nanokitchen TechVendingMachine BahnAppetit VerveCoffee HalalTruck LivingTheDream SugarShack FoxPainting LateHarvest SonOfPingAndPong DentalOffice HotfixBar BridgeClub LikeSign MamaPennys SwagStore RainbowStairs BurgerShack
+Case #15: LivingTheDream
+Case #16: SaintFrank OculusDemoLab LikeSign DentalOffice FakeCrosswalk
+Case #17: MamaPennys FukiSushiInOldenDays FoxPainting
+Case #18: LikeSign SweetStop SwagStore
+Case #19: SaintFrank HotfixBar Ballpit MPK20Roof PopUpShop ChosHawkerCenter HalalTruck FoxPainting Sol LivingTheDream SweetStop WallOfPhones HackerSquare LateHarvest TuringInDominoes LightningBolts ColdBrewMachine BurgerShack Nanokitchen
+Case #20: Nanokitchen PhilzCoffee SaintFrank VerveCoffee LivingTheDream FakeCrosswalk FoxGazebo LikeSign FreshOrangeJuice BurgerShack NailPolishRoomBlock SonOfPingAndPong FoxPainting PopUpShop RainbowStairs TransportationHub ColdBrewMachine ZucksOffice ZucksOldOffice BahnAppetit
+Case #21: MamaPennys FakeCrosswalk DentalOffice NailPolishRoomBlock HotfixBar Harvest ShuttlePlatform ConstitutionDeli BlueBottle BridgeClub LateHarvest VerveCoffee SweetStop HalalTruck SwagStore FreshOrangeJuice ZucksOldOffice FukiSushiInOldenDays CafeEpic SaintFrank Arcade MPK20Roof FoxPainting SugarShack ZucksOffice FullCircle LivingTheDream Helpdesk WallOfPhones RainbowStairs
+Case #22: MPK20Roof BridgeClub FukiSushiInOldenDays ConstitutionDeli Sol TransportationHub BlueBottle LivingTheDream SugarShack MamaPennys BahnAppetit Nanokitchen HotfixBar LateHarvest Microkitchen HalalTruck BurgerShack Ballpit OculusDemoLab LightningBolts Harvest
+Case #23: DentalOffice MamaPennys Microkitchen LightningBolts ConstitutionDeli Harvest FakeCrosswalk WoodenSculpture VerveCoffee PhilzCoffee CafeEpic SugarShack FoxPainting Arcade LateHarvest ColdBrewMachine SonOfPingAndPong
+Case #24: Helpdesk ChosHawkerCenter SugarShack BlueBottle LivingTheDream
+Case #25: MPK20Roof MamaPennys SugarShack FoxPainting RainbowStairs ColdBrewMachine FukiSushiInOldenDays PhilzCoffee Ballpit ZucksOldOffice TechVendingMachine
+Case #26: LightningBolts HotfixBar ShuttlePlatform FukiSushiInOldenDays TransportationHub FoxGazebo NailPolishRoomBlock CafeEpic BahnAppetit ColdBrewMachine SugarShack
+Case #27: TransportationHub SaintFrank
+Case #28: Harvest TechVendingMachine
+Case #29: DentalOffice Microkitchen TechVendingMachine Harvest PopUpShop SonOfPingAndPong ConstitutionDeli Helpdesk TuringInDominoes FoxPainting ZucksOldOffice SweetStop MamaPennys LikeSign TransportationHub BlueBottle LivingTheDream CafeEpic WoodenSculpture FukiSushiInOldenDays FoxGazebo SwagStore Sol SaintFrank RainbowStairs BurgerShack ShuttlePlatform BahnAppetit Nanokitchen LightningBolts PhilzCoffee Ballpit HotfixBar ColdBrewMachine FakeCrosswalk VerveCoffee FreshOrangeJuice OculusDemoLab FullCircle MPK20Roof LateHarvest SugarShack WallOfPhones ChosHawkerCenter NailPolishRoomBlock
+Case #30: RainbowStairs LateHarvest CafeEpic LightningBolts SugarShack BridgeClub ShuttlePlatform ChosHawkerCenter TransportationHub SonOfPingAndPong
+Case #31: OculusDemoLab Nanokitchen MPK20Roof CafeEpic LivingTheDream TuringInDominoes BurgerShack DentalOffice NailPolishRoomBlock Sol Harvest SonOfPingAndPong SwagStore FakeCrosswalk FoxGazebo TechVendingMachine FullCircle ZucksOldOffice ConstitutionDeli SugarShack PopUpShop FukiSushiInOldenDays ZucksOffice FoxPainting BlueBottle SweetStop MamaPennys RainbowStairs WallOfPhones LightningBolts SaintFrank ShuttlePlatform ChosHawkerCenter Arcade TransportationHub HackerSquare WoodenSculpture PhilzCoffee Microkitchen BahnAppetit
+Case #32: CafeEpic
+Case #33: DentalOffice BlueBottle
+Case #34: ShuttlePlatform BlueBottle
+Case #35: ShuttlePlatform TuringInDominoes FukiSushiInOldenDays WoodenSculpture TechVendingMachine ZucksOffice LikeSign ZucksOldOffice HalalTruck Sol OculusDemoLab RainbowStairs LightningBolts SugarShack FakeCrosswalk LateHarvest WallOfPhones ConstitutionDeli HotfixBar TransportationHub MamaPennys Arcade Ballpit FoxPainting
+Case #36: BridgeClub ZucksOldOffice FreshOrangeJuice BurgerShack Microkitchen ColdBrewMachine NailPolishRoomBlock
+Case #37: Nanokitchen ConstitutionDeli SaintFrank DentalOffice Ballpit FullCircle BlueBottle FakeCrosswalk OculusDemoLab FoxPainting Harvest ZucksOldOffice BurgerShack FreshOrangeJuice TransportationHub Microkitchen ShuttlePlatform FukiSushiInOldenDays LikeSign LateHarvest BridgeClub
+Case #38: FukiSushiInOldenDays ColdBrewMachine FreshOrangeJuice CafeEpic SwagStore Helpdesk FullCircle MamaPennys BahnAppetit LateHarvest Harvest
+Case #39: Helpdesk NailPolishRoomBlock HalalTruck ChosHawkerCenter BurgerShack LateHarvest SweetStop FukiSushiInOldenDays Nanokitchen SonOfPingAndPong MamaPennys Sol FullCircle PopUpShop VerveCoffee MPK20Roof ShuttlePlatform HackerSquare RainbowStairs SugarShack ColdBrewMachine LivingTheDream WallOfPhones ZucksOldOffice Ballpit
+Case #40: WoodenSculpture Harvest FukiSushiInOldenDays PopUpShop ShuttlePlatform BahnAppetit NailPolishRoomBlock SwagStore SugarShack
+Case #41: MPK20Roof FreshOrangeJuice LightningBolts BahnAppetit WoodenSculpture TransportationHub Helpdesk CafeEpic WallOfPhones Arcade FullCircle Microkitchen SugarShack Nanokitchen BurgerShack SweetStop ZucksOffice Sol SaintFrank DentalOffice BlueBottle VerveCoffee
+Case #42: Microkitchen VerveCoffee HackerSquare PopUpShop
+Case #43: FullCircle
+Case #44: HalalTruck LikeSign Arcade Harvest LivingTheDream LightningBolts ChosHawkerCenter WoodenSculpture Helpdesk SwagStore NailPolishRoomBlock ColdBrewMachine CafeEpic BlueBottle ConstitutionDeli ZucksOldOffice FakeCrosswalk SugarShack WallOfPhones FukiSushiInOldenDays ZucksOffice SweetStop SonOfPingAndPong PopUpShop Microkitchen Nanokitchen DentalOffice BridgeClub ShuttlePlatform FoxPainting TransportationHub HotfixBar
+Case #45: DentalOffice BahnAppetit WoodenSculpture LateHarvest BurgerShack ConstitutionDeli FoxGazebo VerveCoffee SweetStop
+Case #46: LivingTheDream
+Case #47: Arcade ConstitutionDeli HotfixBar
+Case #48: CafeEpic SonOfPingAndPong FoxPainting BlueBottle Arcade SwagStore Sol BurgerShack FoxGazebo HotfixBar HalalTruck BridgeClub OculusDemoLab MPK20Roof Nanokitchen SugarShack ZucksOldOffice HackerSquare SaintFrank FakeCrosswalk Helpdesk ZucksOffice FukiSushiInOldenDays NailPolishRoomBlock LivingTheDream DentalOffice Harvest BahnAppetit WoodenSculpture PopUpShop LightningBolts MamaPennys FullCircle ConstitutionDeli Microkitchen PhilzCoffee WallOfPhones RainbowStairs VerveCoffee FreshOrangeJuice TransportationHub SweetStop TuringInDominoes
+Case #49: ZucksOffice TransportationHub OculusDemoLab ChosHawkerCenter DentalOffice Microkitchen ShuttlePlatform CafeEpic SugarShack TuringInDominoes LivingTheDream ConstitutionDeli
+Case #50: HackerSquare VerveCoffee HalalTruck ConstitutionDeli SugarShack PopUpShop Sol PhilzCoffee ShuttlePlatform BurgerShack LikeSign BlueBottle RainbowStairs LateHarvest Microkitchen ZucksOldOffice ZucksOffice SaintFrank TransportationHub FakeCrosswalk WallOfPhones SweetStop Harvest DentalOffice Ballpit LightningBolts FukiSushiInOldenDays SonOfPingAndPong WoodenSculpture TechVendingMachine HotfixBar ColdBrewMachine FoxGazebo
+Case #51: ColdBrewMachine ZucksOldOffice
+Case #52: WallOfPhones Ballpit ZucksOldOffice
+Case #53: ChosHawkerCenter Arcade FoxGazebo FukiSushiInOldenDays WallOfPhones HackerSquare VerveCoffee BurgerShack HotfixBar FreshOrangeJuice WoodenSculpture
+Case #54: WoodenSculpture
+Case #55: SweetStop Harvest ZucksOffice OculusDemoLab HalalTruck Arcade BridgeClub MamaPennys SwagStore PhilzCoffee Sol CafeEpic LivingTheDream Microkitchen SugarShack NailPolishRoomBlock RainbowStairs BahnAppetit BlueBottle TransportationHub FullCircle ColdBrewMachine PopUpShop SaintFrank ChosHawkerCenter ZucksOldOffice Nanokitchen LateHarvest ConstitutionDeli FoxGazebo
+Case #56: VerveCoffee PopUpShop OculusDemoLab ZucksOldOffice ZucksOffice
+Case #57: BahnAppetit HackerSquare ZucksOffice Arcade FoxPainting NailPolishRoomBlock SonOfPingAndPong BlueBottle FreshOrangeJuice Helpdesk DentalOffice MamaPennys MPK20Roof Ballpit SweetStop TechVendingMachine ChosHawkerCenter LivingTheDream FullCircle SaintFrank CafeEpic PopUpShop ShuttlePlatform WoodenSculpture SugarShack TransportationHub PhilzCoffee LikeSign
+Case #58: LikeSign Arcade SwagStore
+Case #59: WallOfPhones
+Case #60: ZucksOffice Sol HalalTruck Nanokitchen ConstitutionDeli TechVendingMachine ShuttlePlatform ColdBrewMachine BurgerShack Microkitchen Ballpit DentalOffice OculusDemoLab
+Case #61: TransportationHub SonOfPingAndPong
+Case #62: SaintFrank BlueBottle TransportationHub DentalOffice ColdBrewMachine MamaPennys
+Case #63: NailPolishRoomBlock SonOfPingAndPong Helpdesk
+Case #64: LivingTheDream Harvest PhilzCoffee MamaPennys
+Case #65: FakeCrosswalk FreshOrangeJuice LightningBolts TuringInDominoes Sol SonOfPingAndPong ColdBrewMachine SaintFrank BahnAppetit
+Case #66: ZucksOffice ChosHawkerCenter LivingTheDream FullCircle SaintFrank RainbowStairs MamaPennys ConstitutionDeli SugarShack TuringInDominoes MPK20Roof BridgeClub LightningBolts WallOfPhones FreshOrangeJuice SweetStop Nanokitchen Ballpit Sol LikeSign TransportationHub SonOfPingAndPong OculusDemoLab
+Case #67: LateHarvest HalalTruck LightningBolts MamaPennys Harvest Helpdesk DentalOffice ColdBrewMachine TransportationHub SonOfPingAndPong RainbowStairs LikeSign FakeCrosswalk Ballpit FukiSushiInOldenDays FullCircle SugarShack CafeEpic FreshOrangeJuice ShuttlePlatform Nanokitchen TuringInDominoes NailPolishRoomBlock MPK20Roof BurgerShack SaintFrank HackerSquare
+Case #68: TuringInDominoes VerveCoffee FukiSushiInOldenDays ShuttlePlatform TechVendingMachine ColdBrewMachine LightningBolts BridgeClub HotfixBar OculusDemoLab CafeEpic FakeCrosswalk SonOfPingAndPong FullCircle ZucksOffice Arcade SugarShack FoxGazebo MPK20Roof ConstitutionDeli WallOfPhones ChosHawkerCenter WoodenSculpture
+Case #69: ColdBrewMachine WoodenSculpture LightningBolts SweetStop BahnAppetit FukiSushiInOldenDays BurgerShack ConstitutionDeli ChosHawkerCenter ShuttlePlatform LikeSign MPK20Roof Ballpit Sol TechVendingMachine NailPolishRoomBlock
+Case #70: MPK20Roof DentalOffice LateHarvest Arcade SonOfPingAndPong FakeCrosswalk BurgerShack HackerSquare FoxGazebo Helpdesk ZucksOldOffice ZucksOffice LivingTheDream SwagStore WallOfPhones LikeSign ChosHawkerCenter BahnAppetit NailPolishRoomBlock Ballpit ShuttlePlatform HotfixBar SweetStop MamaPennys
+Case #71: MPK20Roof ShuttlePlatform Sol TuringInDominoes FoxPainting WoodenSculpture Harvest Microkitchen SwagStore ZucksOffice BurgerShack Arcade
+Case #72: TuringInDominoes SonOfPingAndPong
+Case #73: WoodenSculpture WallOfPhones OculusDemoLab HalalTruck FreshOrangeJuice LivingTheDream MamaPennys Arcade
+Case #74: BlueBottle NailPolishRoomBlock HackerSquare WallOfPhones LateHarvest BridgeClub Harvest Microkitchen WoodenSculpture ConstitutionDeli LightningBolts DentalOffice FullCircle SugarShack LivingTheDream PopUpShop RainbowStairs ChosHawkerCenter HotfixBar PhilzCoffee ColdBrewMachine ShuttlePlatform MPK20Roof Arcade CafeEpic SweetStop VerveCoffee SwagStore ZucksOffice FukiSushiInOldenDays TransportationHub HalalTruck Sol TechVendingMachine
+Case #75: LightningBolts VerveCoffee
+Case #76: CafeEpic Sol TransportationHub TuringInDominoes
+Case #77: ZucksOldOffice FullCircle TransportationHub Helpdesk LivingTheDream
+Case #78: HackerSquare SugarShack Harvest ConstitutionDeli BurgerShack WoodenSculpture FukiSushiInOldenDays TuringInDominoes ShuttlePlatform Sol SweetStop BridgeClub SonOfPingAndPong TransportationHub Helpdesk ZucksOldOffice Microkitchen FoxGazebo FullCircle
+Case #79: Helpdesk SonOfPingAndPong MPK20Roof WoodenSculpture CafeEpic LivingTheDream HalalTruck FukiSushiInOldenDays OculusDemoLab
+Case #80: SaintFrank SonOfPingAndPong WallOfPhones SweetStop VerveCoffee WoodenSculpture Nanokitchen
+Case #81: SonOfPingAndPong
+Case #82: ColdBrewMachine ConstitutionDeli Harvest MamaPennys
+Case #83: LateHarvest ZucksOldOffice CafeEpic MPK20Roof SwagStore Microkitchen NailPolishRoomBlock FullCircle TuringInDominoes FukiSushiInOldenDays Harvest WoodenSculpture Arcade FoxGazebo WallOfPhones LikeSign ZucksOffice BridgeClub HackerSquare Nanokitchen BurgerShack FakeCrosswalk ConstitutionDeli
+Case #84: MamaPennys TechVendingMachine LikeSign BurgerShack NailPolishRoomBlock FoxPainting FukiSushiInOldenDays TuringInDominoes
+Case #85: OculusDemoLab VerveCoffee ZucksOffice BahnAppetit HalalTruck MPK20Roof FakeCrosswalk
+Case #86: LikeSign Arcade SweetStop
+Case #87: ZucksOffice HackerSquare Helpdesk SugarShack
+Case #88: OculusDemoLab Ballpit ZucksOffice VerveCoffee SugarShack SaintFrank FoxGazebo RainbowStairs Nanokitchen TransportationHub LightningBolts BlueBottle BurgerShack WallOfPhones ConstitutionDeli MPK20Roof ChosHawkerCenter HalalTruck WoodenSculpture MamaPennys PopUpShop CafeEpic LivingTheDream LateHarvest FukiSushiInOldenDays FoxPainting
+Case #89: ChosHawkerCenter FukiSushiInOldenDays HalalTruck TransportationHub LivingTheDream RainbowStairs ColdBrewMachine TechVendingMachine SugarShack
+Case #90: Ballpit Helpdesk NailPolishRoomBlock MPK20Roof FullCircle TuringInDominoes BlueBottle OculusDemoLab HackerSquare LivingTheDream FakeCrosswalk FreshOrangeJuice PhilzCoffee FukiSushiInOldenDays Nanokitchen BridgeClub WallOfPhones LateHarvest ConstitutionDeli LikeSign VerveCoffee Microkitchen DentalOffice Sol ChosHawkerCenter TransportationHub ZucksOffice RainbowStairs HotfixBar SonOfPingAndPong BurgerShack PopUpShop Harvest LightningBolts TechVendingMachine HalalTruck
+Case #91: BridgeClub LivingTheDream SaintFrank ZucksOldOffice
+Case #92: ZucksOffice SweetStop
+Case #93: BahnAppetit SaintFrank PopUpShop ColdBrewMachine BridgeClub
+Case #94: PopUpShop FoxPainting LateHarvest TuringInDominoes BurgerShack LivingTheDream ChosHawkerCenter SugarShack BahnAppetit ColdBrewMachine Ballpit
+Case #95: WallOfPhones RainbowStairs HackerSquare NailPolishRoomBlock DentalOffice ConstitutionDeli Harvest LivingTheDream BridgeClub Nanokitchen HalalTruck LightningBolts BurgerShack SonOfPingAndPong OculusDemoLab VerveCoffee ShuttlePlatform ZucksOffice TechVendingMachine TuringInDominoes LateHarvest Microkitchen
+Case #96: TransportationHub BahnAppetit MamaPennys BlueBottle FreshOrangeJuice Microkitchen BurgerShack CafeEpic ShuttlePlatform
+Case #97: WallOfPhones ConstitutionDeli BridgeClub TuringInDominoes BahnAppetit ZucksOffice OculusDemoLab Microkitchen Arcade ShuttlePlatform NailPolishRoomBlock SweetStop SwagStore HackerSquare TechVendingMachine SonOfPingAndPong
+Case #98: Nanokitchen Arcade Ballpit SwagStore FreshOrangeJuice ShuttlePlatform LikeSign HotfixBar LivingTheDream RainbowStairs FoxPainting Harvest BahnAppetit VerveCoffee TransportationHub ConstitutionDeli CafeEpic SweetStop Helpdesk Sol FakeCrosswalk BurgerShack Microkitchen ColdBrewMachine MamaPennys
+Case #99: ZucksOldOffice Harvest PopUpShop SonOfPingAndPong LikeSign SwagStore PhilzCoffee
+Case #100: SweetStop
+Case #101: PopUpShop PhilzCoffee MPK20Roof LightningBolts ChosHawkerCenter Microkitchen CafeEpic BlueBottle ZucksOffice BridgeClub Ballpit VerveCoffee ColdBrewMachine WoodenSculpture
+Case #102: HackerSquare OculusDemoLab ZucksOldOffice FakeCrosswalk BridgeClub Harvest LateHarvest WoodenSculpture ZucksOffice Microkitchen LightningBolts Sol BlueBottle FullCircle SaintFrank SonOfPingAndPong PopUpShop LivingTheDream TransportationHub LikeSign Arcade BurgerShack ConstitutionDeli Nanokitchen ChosHawkerCenter SweetStop CafeEpic DentalOffice MamaPennys RainbowStairs FoxGazebo NailPolishRoomBlock
+Case #103: SaintFrank Helpdesk ConstitutionDeli SweetStop Microkitchen LateHarvest MamaPennys PhilzCoffee Sol BlueBottle SonOfPingAndPong FullCircle
+Case #104: FoxGazebo MPK20Roof WoodenSculpture Biryani
+Case #105: SwagStore CafeEpic FreshOrangeJuice FullCircle WallOfPhones TuringInDominoes HalalTruck
+Case #106: ConstitutionDeli LikeSign FoxGazebo BlueBottle BurgerShack Microkitchen TransportationHub TuringInDominoes SugarShack ZucksOldOffice HotfixBar LateHarvest LightningBolts NailPolishRoomBlock LivingTheDream FullCircle ZucksOffice CafeEpic SaintFrank SonOfPingAndPong OculusDemoLab Nanokitchen
+Case #107: ConstitutionDeli VerveCoffee WoodenSculpture MPK20Roof LikeSign ZucksOffice Sol ZucksOldOffice MamaPennys
+Case #108: PhilzCoffee CafeEpic FukiSushiInOldenDays Microkitchen RainbowStairs LivingTheDream WoodenSculpture FoxGazebo FoxPainting OculusDemoLab Sol SaintFrank FullCircle SweetStop ChosHawkerCenter ColdBrewMachine BahnAppetit Ballpit VerveCoffee TechVendingMachine PopUpShop TransportationHub ConstitutionDeli WallOfPhones FakeCrosswalk ZucksOldOffice MamaPennys NailPolishRoomBlock Helpdesk LikeSign HotfixBar LateHarvest Harvest Nanokitchen BridgeClub ZucksOffice BurgerShack DentalOffice Arcade ShuttlePlatform FreshOrangeJuice BlueBottle
+Case #109: TuringInDominoes Microkitchen BridgeClub FreshOrangeJuice
+Case #110: Microkitchen BurgerShack FukiSushiInOldenDays Nanokitchen HackerSquare Helpdesk
+Case #111: SugarShack SweetStop ConstitutionDeli BlueBottle TransportationHub Helpdesk SonOfPingAndPong FakeCrosswalk FoxGazebo MamaPennys TechVendingMachine VerveCoffee LightningBolts Nanokitchen FukiSushiInOldenDays OculusDemoLab PopUpShop Harvest Ballpit MPK20Roof RainbowStairs TuringInDominoes ChosHawkerCenter DentalOffice FoxPainting
+Case #112: ShuttlePlatform BridgeClub Microkitchen BlueBottle LightningBolts OculusDemoLab NailPolishRoomBlock SweetStop LikeSign ZucksOffice FullCircle HotfixBar SaintFrank LivingTheDream Helpdesk MPK20Roof Arcade ColdBrewMachine Sol WallOfPhones FoxPainting RainbowStairs DentalOffice FakeCrosswalk PhilzCoffee TuringInDominoes PopUpShop
+Case #113: PhilzCoffee HalalTruck Microkitchen MPK20Roof ColdBrewMachine
+Case #114: HalalTruck FreshOrangeJuice
+Case #115: ColdBrewMachine
+Case #116: FreshOrangeJuice ColdBrewMachine OculusDemoLab ZucksOffice FoxPainting Ballpit WoodenSculpture VerveCoffee BlueBottle HackerSquare LikeSign
+Case #117: Harvest FukiSushiInOldenDays ZucksOldOffice NailPolishRoomBlock MPK20Roof
+Case #118: HackerSquare FukiSushiInOldenDays BlueBottle ConstitutionDeli FoxGazebo
+Case #119: ZucksOldOffice ChosHawkerCenter Harvest SonOfPingAndPong Nanokitchen TuringInDominoes HotfixBar MPK20Roof FoxGazebo Arcade HackerSquare Ballpit FukiSushiInOldenDays SugarShack CafeEpic Helpdesk ColdBrewMachine
+Case #120: SwagStore BahnAppetit Harvest BridgeClub ZucksOffice WallOfPhones TechVendingMachine LateHarvest Microkitchen Nanokitchen ZucksOldOffice NailPolishRoomBlock DentalOffice FoxPainting Arcade VerveCoffee BlueBottle ShuttlePlatform Sol SugarShack LightningBolts TuringInDominoes MPK20Roof WoodenSculpture FakeCrosswalk HotfixBar BurgerShack FreshOrangeJuice FoxGazebo LikeSign ChosHawkerCenter MamaPennys LivingTheDream PopUpShop FullCircle TransportationHub SweetStop RainbowStairs PhilzCoffee SaintFrank HackerSquare
+Case #121: FukiSushiInOldenDays FoxPainting LivingTheDream Helpdesk Arcade SweetStop RainbowStairs ConstitutionDeli Harvest VerveCoffee TechVendingMachine BlueBottle NailPolishRoomBlock Microkitchen CafeEpic Ballpit DentalOffice FreshOrangeJuice Sol FullCircle Nanokitchen SaintFrank PopUpShop LikeSign HackerSquare FoxGazebo LightningBolts SonOfPingAndPong PhilzCoffee WallOfPhones FakeCrosswalk
+Case #122: Nanokitchen MPK20Roof BlueBottle Microkitchen BridgeClub ConstitutionDeli TechVendingMachine FukiSushiInOldenDays WallOfPhones SweetStop BurgerShack LikeSign Helpdesk OculusDemoLab HackerSquare MamaPennys PopUpShop ZucksOldOffice PhilzCoffee FullCircle NailPolishRoomBlock ChosHawkerCenter SwagStore
+Case #123: HotfixBar
+Case #124: WallOfPhones HalalTruck SugarShack BurgerShack
+Case #125: HotfixBar MamaPennys SweetStop SwagStore Microkitchen FullCircle ZucksOldOffice ConstitutionDeli FoxGazebo
+Case #126: ChosHawkerCenter BlueBottle FukiSushiInOldenDays ZucksOldOffice LateHarvest WallOfPhones VerveCoffee ConstitutionDeli PopUpShop TechVendingMachine ZucksOffice ShuttlePlatform RainbowStairs FoxPainting MPK20Roof SwagStore Microkitchen BridgeClub ColdBrewMachine WoodenSculpture OculusDemoLab Harvest HackerSquare Sol SugarShack BurgerShack FreshOrangeJuice
+Case #127: SwagStore CafeEpic FullCircle WoodenSculpture Microkitchen VerveCoffee ZucksOffice PhilzCoffee SweetStop ColdBrewMachine SonOfPingAndPong HotfixBar SaintFrank BahnAppetit DentalOffice Ballpit Helpdesk ZucksOldOffice PopUpShop FoxPainting Nanokitchen LikeSign BridgeClub SugarShack
+Case #128: PhilzCoffee HalalTruck Ballpit LivingTheDream SweetStop BridgeClub Nanokitchen SwagStore WallOfPhones SonOfPingAndPong Arcade ZucksOffice FakeCrosswalk
+Case #129: TransportationHub Ballpit RainbowStairs SwagStore BridgeClub ZucksOffice
+Case #130: Arcade
+Case #131: Ballpit Harvest TransportationHub
+Case #132: ShuttlePlatform NailPolishRoomBlock TechVendingMachine PopUpShop FukiSushiInOldenDays ChosHawkerCenter Arcade BridgeClub LightningBolts HotfixBar MPK20Roof
+Case #133: VerveCoffee FullCircle LikeSign
+Case #134: ZucksOldOffice Harvest FakeCrosswalk WallOfPhones LateHarvest HotfixBar Helpdesk
+Case #135: BahnAppetit LightningBolts FakeCrosswalk SwagStore HotfixBar VerveCoffee FukiSushiInOldenDays ColdBrewMachine PopUpShop LikeSign WallOfPhones BlueBottle TechVendingMachine FullCircle Arcade
+Case #136: ZucksOldOffice ZucksOffice BlueBottle TransportationHub
+Case #137: PhilzCoffee TransportationHub ShuttlePlatform FreshOrangeJuice FakeCrosswalk Sol OculusDemoLab Harvest BlueBottle LikeSign LateHarvest ZucksOffice WoodenSculpture FukiSushiInOldenDays TechVendingMachine VerveCoffee ChosHawkerCenter ColdBrewMachine Helpdesk FoxPainting PopUpShop BahnAppetit ConstitutionDeli TuringInDominoes SugarShack HalalTruck ZucksOldOffice LightningBolts RainbowStairs FoxGazebo Nanokitchen HackerSquare LivingTheDream Microkitchen MamaPennys BurgerShack DentalOffice BridgeClub
+Case #138: PhilzCoffee NailPolishRoomBlock FukiSushiInOldenDays ColdBrewMachine
+Case #139: Sol Helpdesk PhilzCoffee OculusDemoLab VerveCoffee LateHarvest Ballpit SweetStop DentalOffice NailPolishRoomBlock SwagStore BurgerShack SonOfPingAndPong MamaPennys ColdBrewMachine ConstitutionDeli FullCircle Nanokitchen ShuttlePlatform CafeEpic Microkitchen TuringInDominoes MPK20Roof SaintFrank Harvest LikeSign ZucksOffice ChosHawkerCenter WoodenSculpture SugarShack WallOfPhones HotfixBar FoxPainting
+Case #140: Nanokitchen DentalOffice SwagStore BlueBottle FoxGazebo SonOfPingAndPong VerveCoffee ChosHawkerCenter NailPolishRoomBlock Microkitchen
+Case #141: WallOfPhones Nanokitchen MamaPennys HalalTruck TransportationHub
+Case #142: TuringInDominoes LivingTheDream HackerSquare WoodenSculpture
+Case #143: BridgeClub WoodenSculpture DentalOffice FukiSushiInOldenDays BahnAppetit Nanokitchen LivingTheDream TuringInDominoes ShuttlePlatform ZucksOffice TechVendingMachine
+Case #144: Sol FoxGazebo HotfixBar PhilzCoffee NailPolishRoomBlock SaintFrank WoodenSculpture CafeEpic WallOfPhones HackerSquare BurgerShack DentalOffice ZucksOldOffice Nanokitchen ShuttlePlatform
+Case #145: WallOfPhones CafeEpic
+Case #146: PhilzCoffee SonOfPingAndPong LikeSign ChosHawkerCenter Sol ConstitutionDeli Arcade SugarShack LateHarvest DentalOffice TransportationHub LightningBolts Helpdesk VerveCoffee FukiSushiInOldenDays WallOfPhones BridgeClub WoodenSculpture BurgerShack TuringInDominoes HalalTruck CafeEpic TechVendingMachine ZucksOldOffice FoxPainting BlueBottle ShuttlePlatform SweetStop Ballpit ZucksOffice FreshOrangeJuice
+Case #147: Nanokitchen Arcade Helpdesk PopUpShop OculusDemoLab HalalTruck LikeSign HotfixBar BahnAppetit BridgeClub FoxPainting TechVendingMachine
+Case #148: WoodenSculpture SwagStore HotfixBar HalalTruck MPK20Roof MamaPennys SugarShack ConstitutionDeli
+Case #149: LivingTheDream ZucksOldOffice LightningBolts FukiSushiInOldenDays FreshOrangeJuice ZucksOffice FullCircle TechVendingMachine TransportationHub WallOfPhones MamaPennys
+Case #150: TechVendingMachine Arcade
+Case #151: Harvest TechVendingMachine FreshOrangeJuice LightningBolts Sol DentalOffice
+Case #152: NailPolishRoomBlock LightningBolts BlueBottle RainbowStairs ChosHawkerCenter MamaPennys Helpdesk Arcade SonOfPingAndPong
+Case #153: PhilzCoffee ZucksOffice BlueBottle HackerSquare ChosHawkerCenter
+Case #154: FoxPainting Microkitchen FreshOrangeJuice
+Case #155: TechVendingMachine
+Case #156: ShuttlePlatform TechVendingMachine CafeEpic ConstitutionDeli MPK20Roof BlueBottle TuringInDominoes FukiSushiInOldenDays Nanokitchen LightningBolts FreshOrangeJuice