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// 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);
} |