Datasets:

hackercupai
/

hackercup

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+2014/finals/lunch_at_facebook.in filter=lfs diff=lfs merge=lfs -text
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+<p>
+Kit is competing on the popular game show, Fortunate Wheels. On this show, there is a secret word <b>S</b> consisting only of uppercase letters, known only to the host. Contestants can pay points to buy sequences of letters in hopes of matching part of S and earning more points! This show is clearly a scam, as the probability of earning more points than are spent is extremely low. Fortunately, Kit has come prepared -- he knows the secret word! Even so, getting as many points as possible will not be easy.
+</p>
+<p>
+There are <b>N</b> <i>basic deals</i> which contestants can take. The <i>i</i>th deal costs <b>A<sub>i</sub></b> points, and allows the contestant to purchase any sequence of <b>B<sub>i</sub></b> letters. Furthermore, deals can be combined to purchase longer sequences! Combining a deal with cost <b>C<sub>1</sub></b> and length <b>L<sub>1</sub></b> with another deal (potentially the same one) with cost <b>C<sub>2</sub></b> and length <b>L<sub>2</sub></b> creates a new deal with cost <b>C<sub>1</sub></b> + <b>C<sub>2</sub></b> + <b>W</b> and length <b>L<sub>1</sub></b> + <b>L<sub>2</sub></b> (as long as <b>L<sub>1</sub></b> + <b>L<sub>2</sub></b> &lt; |<n>S</b>|), which can in turn be used to create even bigger deals. For example, if W = 0, then a basic deal with cost and length equal to 1 could be combined with itself repeatedly to yield a new deal with both cost and length equal to any positive integer up to (but not including) |<b>S</b>|.
+</p>
+<p>
+Once Kit purchases a sequence of letters using one (potentially non-basic) deal, it will be matched against
+the secret word -- twice! The host will spin the First Fortunate Wheel to select the starting index in <b>S</b> for the
+first matching, which is chosen at uniform random such that the sequence will fit entirely within <b>S</b>. Then,
+the host will spin the Second Fortunate Wheel to select the starting index for the second matching, which is
+chosen at uniform random such that the sequence will fit entirely within <b>S</b> and such that the value given by
+the First Fortunate Wheel will not be repeated. For example, if the purchased sequence consists of a single letter, the
+First Fortunate Wheel might yield any of the indices in <b>S</b> with probability (1 / |<b>S</b>|) each, and then the Second
+Fortunate Wheel might yield any of the remaining indices with probability (1 / (|<b>S</b>|-1)) each. On the other hand,
+if the sequence has length |<b>S</b>| − 1, then the First Wheel can yield either 0 or 1, and the Second Wheel must yield the other. If, for both generated indices, the sequence miraculously happens to be equal to the substring of <b>S</b> of the same length starting at that index, then Kit will earn back <b>Y</b>(|<b>S</b>| - |<b>X</b> − <b>&#x2113;</b>|)<sup>2</sup> + <b>Z</b> points, where <b>&#x2113;</b> is the length of the sequence. If even one letter is off in either matching, however, Kit will earn no points at all!
+</p>
+<p>
+Kit is carefully considering his first turn of the game. He obviously wants to maximize the number of points he’ll gain, but worries that choosing the very best move might be suspicious. As such, he’d like to find the expected point values of the <b>M</b> best distinct moves before making his decision. Two moves are distinct iff they involve purchasing different sequences of letters - the deals used are ignored. Note that moves can have negative expected point values, due to the costs of deals.
+</p>
+<h3>Input</h3>
+<p>
+Input begins with an integer <T>, the number of test cases. Each test case begins with a line containing six integers, <b>N</b>, <b>M</b>, <b>W</b>, <b>X</b>, <b>Y</b>, <b>Z</b>. The next line contains the string <b>S</b>. The next <b>N</b> lines each contain two integers, <b>A<sub>i</sub></b> and <b>B<sub>i</sub></b>.
+</p>
+<h3>Output</h3>
+<p>
+For each test case <i>i</i>, output "Case #i: " followed by a space-separated list of real numbers, the <b>M</b> largest expected point values which can be earned, in order. Round these values off to 3 decimal places.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <b>T</b> &le; 20 <br/>
+2 &le; |<b>S</b>| &le; 10<sup>5</sup> <br/>
+1 &le; <b>N</b> &le; 20 <br/>
+1 &le; <b>A<sub>i</sub></b> &le; 10<sup>4</sup> <br/>
+1 &le; <b>B<sub>i</sub></b> &lt; |<b>S</b>| <br/>
+0 &le; <b>W</b> &le; 10<sup>4</sup> <br/>
+1 &le; <b>X</b> &lt; |<b>S</b>| <br/>
+0 &le; <b>Y</b> &le; 100 <br/>
+0 &le; <b>Z</b> &le; 100 <br/>
+1 &le; <b>M</b> &le; 20 <br/>
+</p>
+<h3>Explanation of Sample</h3>
+<p>
+In the first test case, Kit’s best move is to use the basic deal, costing 2 points, to purchase the sequence "Z". No matter what pair of indices the two Fortunate Wheels yield, this sequence will match and earn Kit 5(2 - |1 - 1|)<sup>2</sup> + 6 = 26 points. Any other sequence shorter than |<b>S</b>| cannot match at even a single index, so Kit’s second- and third-best moves consist of using the basic deal to purchase any other single-letter sequence, and simply losing the 2 points.
+</p>
+<p>
+In the second test case, Kit’s best move consists of combining the third basic deal with itself to yield a deal with cost 5 and length 4, and then purchasing the sequence "OXEN". His three next-best moves, which are the only other moves which get him a positive expected point value, involve using the third basic deal to purchase the sequences "OX", "XE", and "EN".
+</p>

2014/finals/fortunate_wheels.in ADDED Viewed

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2014/finals/fortunate_wheels.md ADDED Viewed

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+Kit is competing on the popular game show, Fortunate Wheels. On this show,
+there is a secret word **S** consisting only of uppercase letters, known only
+to the host. Contestants can pay points to buy sequences of letters in hopes
+of matching part of S and earning more points! This show is clearly a scam, as
+the probability of earning more points than are spent is extremely low.
+Fortunately, Kit has come prepared -- he knows the secret word! Even so,
+getting as many points as possible will not be easy.
+There are **N** _basic deals_ which contestants can take. The _i_th deal costs
+**Ai** points, and allows the contestant to purchase any sequence of **Bi**
+letters. Furthermore, deals can be combined to purchase longer sequences!
+Combining a deal with cost **C1** and length **L1** with another deal
+(potentially the same one) with cost **C2** and length **L2** creates a new
+deal with cost **C1** \+ **C2** \+ **W** and length **L1** \+ **L2** (as long
+as **L1** \+ **L2** < |S**|), which can in turn be used to create even bigger
+deals. For example, if W = 0, then a basic deal with cost and length equal to
+1 could be combined with itself repeatedly to yield a new deal with both cost
+and length equal to any positive integer up to (but not including) |**S**|.
+Once Kit purchases a sequence of letters using one (potentially non-basic)
+deal, it will be matched against the secret word -- twice! The host will spin
+the First Fortunate Wheel to select the starting index in **S** for the first
+matching, which is chosen at uniform random such that the sequence will fit
+entirely within **S**. Then, the host will spin the Second Fortunate Wheel to
+select the starting index for the second matching, which is chosen at uniform
+random such that the sequence will fit entirely within **S** and such that the
+value given by the First Fortunate Wheel will not be repeated. For example, if
+the purchased sequence consists of a single letter, the First Fortunate Wheel
+might yield any of the indices in **S** with probability (1 / |**S**|) each,
+and then the Second Fortunate Wheel might yield any of the remaining indices
+with probability (1 / (|**S**|-1)) each. On the other hand, if the sequence
+has length |**S**| − 1, then the First Wheel can yield either 0 or 1, and the
+Second Wheel must yield the other. If, for both generated indices, the
+sequence miraculously happens to be equal to the substring of **S** of the
+same length starting at that index, then Kit will earn back **Y**(|**S**| -
+|**X** − **ℓ**|)2 \+ **Z** points, where **ℓ** is the length of the sequence.
+If even one letter is off in either matching, however, Kit will earn no points
+at all!
+Kit is carefully considering his first turn of the game. He obviously wants to
+maximize the number of points he’ll gain, but worries that choosing the very
+best move might be suspicious. As such, he’d like to find the expected point
+values of the **M** best distinct moves before making his decision. Two moves
+are distinct iff they involve purchasing different sequences of letters - the
+deals used are ignored. Note that moves can have negative expected point
+values, due to the costs of deals.
+### Input
+Input begins with an integer , the number of test cases. Each test case begins
+with a line containing six integers, **N**, **M**, **W**, **X**, **Y**, **Z**.
+The next line contains the string **S**. The next **N** lines each contain two
+integers, **Ai** and **Bi**.
+### Output
+For each test case _i_, output "Case #i: " followed by a space-separated list
+of real numbers, the **M** largest expected point values which can be earned,
+in order. Round these values off to 3 decimal places.
+### Constraints
+1 ≤ **T** ≤ 20
+2 ≤ |**S**| ≤ 105
+1 ≤ **N** ≤ 20
+1 ≤ **Ai** ≤ 104
+1 ≤ **Bi** < |**S**|
+0 ≤ **W** ≤ 104
+1 ≤ **X** < |**S**|
+0 ≤ **Y** ≤ 100
+0 ≤ **Z** ≤ 100
+1 ≤ **M** ≤ 20
+### Explanation of Sample
+In the first test case, Kit’s best move is to use the basic deal, costing 2
+points, to purchase the sequence "Z". No matter what pair of indices the two
+Fortunate Wheels yield, this sequence will match and earn Kit 5(2 - |1 - 1|)2
+\+ 6 = 26 points. Any other sequence shorter than |**S**| cannot match at even
+a single index, so Kit’s second- and third-best moves consist of using the
+basic deal to purchase any other single-letter sequence, and simply losing the
+2 points.
+In the second test case, Kit’s best move consists of combining the third basic
+deal with itself to yield a deal with cost 5 and length 4, and then purchasing
+the sequence "OXEN". His three next-best moves, which are the only other moves
+which get him a positive expected point value, involve using the third basic
+deal to purchase the sequences "OX", "XE", and "EN".

2014/finals/fortunate_wheels.out ADDED Viewed

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+Case #1: 24.000 -2.000 -2.000
+Case #2: 7.056 3.491 3.491 3.491
+Case #3: 0.833 0.833 -2.000 -2.000 -2.000
+Case #4: 70.200 70.200 21.100 21.100 -2.000
+Case #5: 156.571 156.571 80.286 80.286 24.667
+Case #6: -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000 -2402.000
+Case #7: 461397439636.000 461387457483.000 461387455721.000 461377471914.000 461377470483.000 461367488546.000 461367488215.000 461357506717.000 461357504985.000 461347521502.000
+Case #8: -781.000 -781.000 -781.000 -781.000 -781.000 -781.000
+Case #9: 54984546.643 51124920.797 50872605.657 49496029.178 48506741.615 48138333.423 46799518.394 46077213.642 44531490.835 44061189.145 43826974.534 40164426.006 666366.275 666366.275 596117.543 542728.507 529771.519
+Case #10: 196.485 104.918 104.918 104.918 104.918 28.612 28.612 28.612 28.612 28.612 28.612 28.612 28.612 28.612 28.612 28.612
+Case #11: 7221339.359 7221339.359
+Case #12: -120.653 -120.653 -120.653 -133.000
+Case #13: 8771448.706 7634326.913 7371668.851 7150191.822 7077116.597 7040719.694 7040719.694 7040719.694 7004416.598 6896070.147 6788567.955 6752921.504 6752921.504 6401616.346 6401616.346 6195335.962
+Case #14: 728295186.528 723184860.602 721273126.975 713651493.892 707331056.955 706070343.092 691341187.859 689783393.077 672148720.404 10061159.314 9873839.659 9836586.594 9762291.331
+Case #15: -60.000 -60.000 -60.000 -60.000 -60.000 -60.000 -60.000 -60.000
+Case #16: 24170066037.239 23935575942.756 23888258685.318 23857666583.349 23238963805.693 1041901472.147 1023391896.929 991399310.524 987435958.423
+Case #17: -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -550.710 -644.000 -644.000 -644.000 -644.000 -644.000 -644.000
+Case #18: -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000 -1727.000
+Case #19: -4311.000 -4311.000 -4311.000 -4311.000 -4311.000 -4311.000 -4311.000 -4311.000 -4311.000 -4311.000 -4311.000
+Case #20: -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000 -106.000
+Case #21: 191967180.542 189928238.558 181422394.813 179592467.731
+Case #22: 9536.114 7422.212 7422.212 5432.658 3567.451 3567.451 3567.451 1826.591 1826.591 1826.591 1826.591 210.078 210.078 210.078 210.078 210.078 210.078 210.078 210.078
+Case #23: 8118631428.000 8117934228.000 8117925698.000 8117232319.000 8117232179.000 8116543550.000 8116542239.000 8115852189.000 8115837910.000 8115145973.000 8115137688.000 8114447453.000 8114441465.000 8113751505.000 8113741903.000 8113047073.000 8113041122.000
+Case #24: 368147588.335 364910674.291 362090099.216 357280287.034 355285690.060 355285690.060 354290485.271 353694032.381 350125867.285 349532931.809 348940498.821 345200092.111 343239552.635 339919448.962 337391433.387 334872853.414 1860234.039 1774631.144
+Case #25: 10366193237.398 9934586344.948 9804890976.809 9670622446.663 698446499.090 666266346.506 663421566.039
+Case #26: 199815.176 191453.128 183265.289
+Case #27: -5334.000
+Case #28: 3845114.424 3762437.196 3680656.684 3664408.188 3519785.809 3488042.058 3456441.781 3456441.781 3456441.781 3393671.652 3362501.799 3362501.799 3362501.799 3362501.799 3346970.675
+Case #29: 177910571851.309 177623847377.732 44725998783.001 44586280009.805 44228006820.763 44228006820.763
+Case #30: -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000 -2175.000
+Case #31: 46981516695.000 46979439396.000 46979437928.000 46977363921.000 46977359117.000 46975282642.000 46975282594.000 46973206213.000 46973204074.000 46971129830.000 46971123261.000 46969047970.000 46969047595.000
+Case #32: 142755136.756 142332852.943 140230816.226 139394379.969 135764388.908 135558407.293 134736044.556 134325801.422 134223338.371 133302930.105 133302930.105 133200857.986 131573020.737 130965161.914 130762855.051 129652962.464 129552297.696 127946978.081
+Case #33: -1501.000 -1501.000 -1501.000 -1501.000
+Case #34: 20991291497.274 20678722510.866 20554077881.306 2383574924.957 2366837494.801 2309637737.912 2309179293.497
+Case #35: -946.531 -946.531 -946.531 -946.531 -1033.000 -1033.000 -1033.000 -1033.000
+Case #36: 13540613161.926 13484452208.391 13378260621.988
+Case #37: 14872603813.696 14838843352.297 14681801753.468 14587977797.152 14574598926.024
+Case #38: 455561.962 424882.931 366689.467 357400.782 357400.782
+Case #39: 33527245.691 33279623.848 33180832.095 32689076.040 32493401.552 32347031.160 32249634.459 32200991.176 31813166.543 31523839.969 31235835.023 29815634.726 29675431.936 29675431.936 29210475.577 28428475.150 28200494.180 28155008.121 165030.529
+Case #40: 519353402725.000 519339807695.000 519339803177.000 519326207551.000 519326206559.000
+Case #41: 2953440.258 2898338.950 2870982.772 2683119.724 2683119.724 2683119.724 2683119.724 2656800.746 2630611.419 2630611.419 2630611.419 2604551.741 2604551.741 2578621.714 2552821.337 2527150.610 2501609.533
+Case #42: -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000 -1333.000
+Case #43: -1483.000 -1483.000 -1483.000 -1483.000 -1483.000 -1483.000 -1483.000 -1483.000
+Case #44: 931.812 536.374 536.374 360.624 360.624 360.624 360.624 360.624 360.624 360.624 360.624 360.624 199.520 199.520 199.520
+Case #45: -707.000 -707.000 -707.000 -707.000 -707.000 -707.000 -707.000 -707.000 -707.000 -707.000 -707.000 -707.000 -707.000
+Case #46: -253.000 -253.000 -253.000 -253.000 -253.000 -253.000 -253.000 -253.000 -253.000 -253.000
+Case #47: 557428139.383 550686817.324 547666602.512 544654692.599 541651087.585 540651731.446 540318817.792 538323488.993 529060758.690 526100523.702 524459537.245 518573209.629 516293053.565 514992362.893 514017921.451 513693312.696 3140032.656
+Case #48: 369043241.638 368275457.859 356854640.833 355596765.291 354341110.574 352086528.564 350337939.427 344623222.513 334065240.596 5891440.250 5384652.837 5322903.670 5230946.276 5139788.512 5079460.908 5079460.908 5049430.378 5049430.378 5019488.695 5019488.695
+Case #49: 7703.023 7703.023 6615.464 5591.880 5591.880 5591.880 5591.880 5591.880 5591.880 4632.270 4632.270 4632.270 4632.270 4632.270 4632.270 4632.270 4632.270
+Case #50: 1689293.383 1652731.168 1643652.964 1634599.700 1625571.377 1625571.377 1625571.377 1625571.377 1616567.994 1607589.550 1607589.550 1598636.047 1598636.047 1580803.862 1580803.862 1580803.862 1580803.862 1571925.179 1545438.772 1545438.772
+Case #51: 3022297032.367 3009194197.480 3006577046.257
+Case #52: 468647.121 435858.872 429441.744 429441.744 423071.456 423071.456 416748.008 416748.008 416748.008 416748.008 410471.400 404241.633 404241.633 404241.633 398058.706 398058.706
+Case #53: 1755308.091 1660440.260 1641782.920 1623230.989 1623230.989
+Case #54: 288297818.077 286426404.620 282495653.972 278592061.237 278182736.562 277978187.069
+Case #55: 646031.295 632719.208 619544.358 619544.358 606506.746 580843.237 580843.237 580843.237 568217.340 568217.340 555728.680 555728.680 543377.259
+Case #56: -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027 -3689.027
+Case #57: 134728441049.000 134723926605.000 134723922367.000 134719412237.000 134719404383.000 134714868367.000 134714862351.000 134710349913.000 134710348135.000 134705833995.000 134705814049.000 134701296369.000
+Case #58: 482260409783.000 482249209505.000 482249208094.000 482238016094.000 482238013272.000 482226816076.000 482226811934.000
+Case #59: 516519936585.000 516507240048.000 516507238882.000 516494546419.000 516494543667.000
+Case #60: 53264720233.930 52729063258.348 13648286750.036 13648286750.036 12989189367.307 12723355893.407 3636516125.507 3636516125.507 3568797020.124 3568797020.124 3257835135.875 3194752171.242 2880067358.442 2815157969.410 1053636864.383 972292918.106 950971775.462 920235278.883 897910409.906
+Case #61: 10144.054 3993.218 3993.218 3993.218 3993.218 3993.218 3993.218 3993.218 3993.218 3993.218
+Case #62: 11869156.020 7439833.851 7402596.186 7365451.850 7291443.158 7254578.804 7217807.777 6891068.272 6819486.096 6642163.885 6536890.488 6501986.011 6294519.024 6124196.374 6090411.827
+Case #63: 8642858.475 8160497.100 8018487.697 7784573.572 7417508.331 6753136.854
+Case #64: 966888850.228 966888850.228 963937962.913 936129461.872 935921917.028 930326903.801 900159432.419 894875437.336 18133845.252 17788784.251 17731596.270 17560584.645 17503764.876
+Case #65: 32765309276.000 32764165591.000 32764165148.000 32763021040.000 32763020119.000 32761876952.000 32761874667.000
+Case #66: 2414221.171 2264819.481 1795140.241 341831.246 296352.844 268156.273 235583.878 224254.847 215938.491 193648.900 185916.750 179173.553
+Case #67: 11361949380.770 10992470676.059 2939099847.196 2752671711.172 2743841493.276 2743290075.670
+Case #68: 20442.437 20442.437 20442.437 20442.437 20442.437 20442.437 20442.437 20442.437 20442.437 20442.437
+Case #69: 1748771269.376 1737209790.995 1566876591.211 1566876591.211 1475269419.513 1475269419.513 1412140098.230 1324896065.139 46449623.310 42938228.821 36099354.830 34960659.760 34960659.760 31707785.991 30959220.529 30799976.509 30641142.912
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+Case #150: 461529056.616 444945371.658 442655491.247 442655491.247 441893510.547 438472720.155 437335410.423 429040265.508 426791737.339 424175920.853 421568145.080 418227105.442 417116379.294 414530428.315 414161663.132 413056352.158 410483036.588 409749280.433 404995864.808 401721284.130
+Case #151: 41036.831 34561.601 34561.601 34561.601 28575.067 28575.067 28575.067 28575.067 28575.067 28575.067 28575.067 23077.230 23077.230 23077.230 23077.230 23077.230 23077.230 23077.230 23077.230 23077.230
+Case #152: 168838480353.737 166635569279.251 42477132059.595 41944793692.702 41941435152.524 41375773456.754 10636195779.227 10634504537.707 10607462961.438 10602396498.311 10363968289.018 10363968289.018 10337273109.994 10323938429.697 2730463602.142 2702257394.642 2683534614.680 2682685125.708 2634486544.234 2617678308.277
+Case #153: 13818149453.005 13627817475.324 13327736905.898 13259616126.435 13229868168.749 13208640080.960 12980462809.156 12867119700.220 256098255.432 239247184.768 237536697.375 234699521.227 228517732.859 226846108.558 226290264.075 226290264.075 226012597.512 225735101.401 225180620.535 224626821.478
+Case #154: 3757568.514 3757568.514 3649690.784 3578644.037 3508294.681 3473381.525 3438642.717 3335472.379 3335472.379 3301430.962 3301430.962 3267563.893 3267563.893 3267563.893 3267563.893 3267563.893 3233871.172 3233871.172 3233871.172 3233871.172
+Case #155: 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766 72.766

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+<p>
+Do you remember helping Prince Z.A.Y. rescue the princess of the kingdom of Hackadia from an evil dragon in Round 2? Well, as it so often happens, Z.A.Y. has fallen in love with his dearest princess. However, the princess has given Z.A.Y. a puzzle to solve to ensure that the one she marries is both brave and clever.
+</p>
+<p>
+The princess gives Z.A.Y a 0-indexed array of <b>N</b> integers, and she asks him a series of questions. In each question, she provides an inclusive interval to the prince, and asks him how many subarrays in that interval are slowly increasing.
+</p>
+<p>
+A subarray is defined as a contiguous set of integers in the given array.
+A subarray is slowly increasing iff each integer in the subarray after the first is exactly 1 more than the previous integer. For example, <b>[1, 2, 3]</b>, <b>[5]</b>, and <b>[10, 11, 12]</b> are slowly increasing, but <b>[7, 9]</b>, <b>[13, 12, 11]</b>, and <b>[1, 1, 2, 2]</b> are not.
+</p>
+<p>
+Easy problem, right? Yup, so the princess is going to make it more challenging since she knows the prince is seeking help from the best Hackers from the world. Sometimes, instead of asking a question, the princess will change an integer in the array.
+</p>
+<p>
+Still an easy problem, right? Probably, but the princess isn't going to make it any harder (the prince *did* rescue her from a dragon, and could probably use a break).
+</p>
+<h3>Input</h3><p>
+The first line consists of a single integer <b>T</b>, the number of test cases.
+Each test case starts with a line containing an integer <b>N</b>, the length of the array.
+Then 1 line follows with <b>N</b> integers <b>X<sub>i</sub></b> representing the elements of the array.
+Then 1 line follows with an integer <b>M</b>, the number of actions the princess takes (questions and updates).
+Then <b>M</b> lines follow, each with 3 integers.
+The first integer, <b>op</b>, represents the action the princess takes.
+If <b>op</b> is <b>0</b>, then 2 integers <b>P</b> and <b>K</b> follow, meaning that the princess will change the <b>P</b>th element of the array to <b>K</b>.
+If <b>op</b> is <b>1</b>, then 2 integers <b>L</b> and <b>R</b> follow, meaning that the princess will ask how many slowly increasing subarrays there are between <b>L</b> and <b>R</b> (inclusive).
+</p>
+<h3>Output</h3>
+<p>
+For each test case <i>i</i>, output "Case #i: " followed by a single integer, the sum of the answers to the princess's questions. Since this number might be large, output it modulo 1,000,000,007.
+</p>
+<h3>Explanation of Sample</h3>
+<p>
+In the first sample case, the answer to the first question is 6 (the slowly increasing subarrays are [4], [5], [6], [4, 5], [5, 6], [4, 5, 6]), and the answer to the second question is 12. So the sum is 18.
+</p>
+<p>
+In the second sample case, the answers are 3, 4, and 6 respectively, so the sum is 13.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <b>T</b> &le; 20 <br/>
+1 &le; <b>N</b> &le; 10<sup>6</sup> <br/>
+1 &le; <b>M</b> &le; 10<sup>6</sup> <br/>
+1 &le; <b>X<sub>i</sub></b>, <b>K</b> &le; 10<sup>9</sup><br/>
+0 &le; <b>P</b> &lt; <b>N</b> <br/>
+0 &le; <b>op</b> &le; 1 <br/>
+0 &le; <b>L</b> &le; <b>R</b> &lt; <b>N</b>
+</p>

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+version https://git-lfs.github.com/spec/v1
+oid sha256:b9ce8d134190e91106d7883ab347884d99bedffb88dd7bc430c60b74f0f29285
+size 66686480

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+Do you remember helping Prince Z.A.Y. rescue the princess of the kingdom of
+Hackadia from an evil dragon in Round 2? Well, as it so often happens, Z.A.Y.
+has fallen in love with his dearest princess. However, the princess has given
+Z.A.Y. a puzzle to solve to ensure that the one she marries is both brave and
+clever.
+The princess gives Z.A.Y a 0-indexed array of **N** integers, and she asks him
+a series of questions. In each question, she provides an inclusive interval to
+the prince, and asks him how many subarrays in that interval are slowly
+increasing.
+A subarray is defined as a contiguous set of integers in the given array. A
+subarray is slowly increasing iff each integer in the subarray after the first
+is exactly 1 more than the previous integer. For example, **[1, 2, 3]**,
+**[5]**, and **[10, 11, 12]** are slowly increasing, but **[7, 9]**, **[13,
+12, 11]**, and **[1, 1, 2, 2]** are not.
+Easy problem, right? Yup, so the princess is going to make it more challenging
+since she knows the prince is seeking help from the best Hackers from the
+world. Sometimes, instead of asking a question, the princess will change an
+integer in the array.
+Still an easy problem, right? Probably, but the princess isn't going to make
+it any harder (the prince *did* rescue her from a dragon, and could probably
+use a break).
+### Input
+The first line consists of a single integer **T**, the number of test cases.
+Each test case starts with a line containing an integer **N**, the length of
+the array. Then 1 line follows with **N** integers **Xi** representing the
+elements of the array. Then 1 line follows with an integer **M**, the number
+of actions the princess takes (questions and updates). Then **M** lines
+follow, each with 3 integers. The first integer, **op**, represents the action
+the princess takes. If **op** is **0**, then 2 integers **P** and **K**
+follow, meaning that the princess will change the **P**th element of the array
+to **K**. If **op** is **1**, then 2 integers **L** and **R** follow, meaning
+that the princess will ask how many slowly increasing subarrays there are
+between **L** and **R** (inclusive).
+### Output
+For each test case _i_, output "Case #i: " followed by a single integer, the
+sum of the answers to the princess's questions. Since this number might be
+large, output it modulo 1,000,000,007.
+### Explanation of Sample
+In the first sample case, the answer to the first question is 6 (the slowly
+increasing subarrays are [4], [5], [6], [4, 5], [5, 6], [4, 5, 6]), and the
+answer to the second question is 12. So the sum is 18.
+In the second sample case, the answers are 3, 4, and 6 respectively, so the
+sum is 13.
+### Constraints
+1 ≤ **T** ≤ 20
+1 ≤ **N** ≤ 106
+1 ≤ **M** ≤ 106
+1 ≤ **Xi**, **K** ≤ 109
+0 ≤ **P** < **N**
+0 ≤ **op** ≤ 1
+0 ≤ **L** ≤ **R** < **N**

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+Case #1: 18
+Case #2: 13
+Case #3: 14
+Case #4: 16
+Case #5: 13
+Case #6: 10
+Case #7: 12
+Case #8: 611
+Case #9: 1244
+Case #10: 993
+Case #11: 930
+Case #12: 1249
+Case #13: 83785
+Case #14: 86801
+Case #15: 82883
+Case #16: 76552
+Case #17: 82847
+Case #18: 235227063
+Case #19: 346924584
+Case #20: 999496508

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+<p>
+What's the best thing about working at Facebook? It's hard to say, but the free food doesn't hurt. Every day there are long lines for food, and sometimes guests visit the campus, as hungry as everybody else. It pays to be a good host, so sometimes we'll let guests cut ahead in the line. But obviously nobody wants to miss out on delicious Facebook food.
+</p>
+<p>
+Every day, <b>N</b> Facebook employees are lined up for lunch, and every day <b>M</b> visitors come to the campus looking for food. Each person has an appetite <b>A<sub>i</sub></b>, which is a positive integer. Curiously, no two people have the same appetite.
+</p>
+<p>
+If people with large appetites eat first, there's a concern that the food might run out before the people at the back get to eat, so it's ideal to have people with smaller appetites further ahead in the line. With this in mind, we'd like to squeeze all of the guests into the lunch line as efficiently as possible.
+</p>
+<p>
+We define the <i>unsuitableness</i> of a line as the number of pairs of people in the line, <b>P<sub>i</sub></b> and <b>P<sub>j</sub></b>, such that <b>P<sub>i</sub></b> is ahead of <b>P<sub>j</sub></b> in the line, and <b>P<sub>i</sub></b> has a larger appetite than <b>P<sub>j</sub></b>. Your task is to find a way to get all the visitors into the lunch line such that the unsuitableness of the resulting line is minimized. The employees that are standing in line won't change order, but you can put guests in any place you want.
+</p>
+<h3>Input</h3>
+<p>
+The first line contains an integer <b>T</b>, the number of test cases. <br/>
+Each test case has three lines: <br/>
+A line with <b>N</b> and <b>M</b>. <br/>
+A line with <b>N</b> integers, the appetites of the employees in order, beginning with the first employee. <br/>
+A line with <b>M</b> integers, the appetites of the visitors. <br/>
+</p>
+<h3>Output</h3>
+<p>
+For each test case <i>i</i>, output "Case #i: " followed by the minimum possible unsuitableness of the resulting line.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <b>T</b> &le; 20 <br/>
+1 &le; <b>N</b> &le; 10<sup>5</sup> <br/>
+1 &le; <b>M</b> &le; 10<sup>5</sup> <br/>
+1 &le; <b>A<sub>i</sub></b> &le; 10<sup>9</sup> <br/>
+</p>
+<h3>Explanation of Sample</h3>
+<p>
+For the first test case the optimal lunch line has the following appetites in order: 1, 2, 3, 4 <br/>
+For the second test case the optimal lunch line is: 1, 2, 4, 7, 5, 3 <br/>
+</p>

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+version https://git-lfs.github.com/spec/v1
+oid sha256:40170322d59a7ef21c7066d8d7e240a2ff9fc0022b0333ab873f50215b8193e2
+size 29222524

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+What's the best thing about working at Facebook? It's hard to say, but the
+free food doesn't hurt. Every day there are long lines for food, and sometimes
+guests visit the campus, as hungry as everybody else. It pays to be a good
+host, so sometimes we'll let guests cut ahead in the line. But obviously
+nobody wants to miss out on delicious Facebook food.
+Every day, **N** Facebook employees are lined up for lunch, and every day
+**M** visitors come to the campus looking for food. Each person has an
+appetite **Ai**, which is a positive integer. Curiously, no two people have
+the same appetite.
+If people with large appetites eat first, there's a concern that the food
+might run out before the people at the back get to eat, so it's ideal to have
+people with smaller appetites further ahead in the line. With this in mind,
+we'd like to squeeze all of the guests into the lunch line as efficiently as
+possible.
+We define the _unsuitableness_ of a line as the number of pairs of people in
+the line, **Pi** and **Pj**, such that **Pi** is ahead of **Pj** in the line,
+and **Pi** has a larger appetite than **Pj**. Your task is to find a way to
+get all the visitors into the lunch line such that the unsuitableness of the
+resulting line is minimized. The employees that are standing in line won't
+change order, but you can put guests in any place you want.
+### Input
+The first line contains an integer **T**, the number of test cases.
+Each test case has three lines:
+A line with **N** and **M**.
+A line with **N** integers, the appetites of the employees in order, beginning
+with the first employee.
+A line with **M** integers, the appetites of the visitors.
+### Output
+For each test case _i_, output "Case #i: " followed by the minimum possible
+unsuitableness of the resulting line.
+### Constraints
+1 ≤ **T** ≤ 20
+1 ≤ **N** ≤ 105
+1 ≤ **M** ≤ 105
+1 ≤ **Ai** ≤ 109
+### Explanation of Sample
+For the first test case the optimal lunch line has the following appetites in
+order: 1, 2, 3, 4
+For the second test case the optimal lunch line is: 1, 2, 4, 7, 5, 3

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+Case #1: 0
+Case #2: 4
+Case #3: 35
+Case #4: 33
+Case #5: 25
+Case #6: 32
+Case #7: 36
+Case #8: 2490850215
+Case #9: 2509829169
+Case #10: 2498479441
+Case #11: 2483548921
+Case #12: 2495058489
+Case #13: 5003931491
+Case #14: 4997483609
+Case #15: 5005753015
+Case #16: 5010400648
+Case #17: 5001567701
+Case #18: 5009444374
+Case #19: 4997430848
+Case #20: 5000697190
+Case #21: 5003216558
+Case #22: 5005851841
+Case #23: 5004269719
+Case #24: 4999117576
+Case #25: 5004842589
+Case #26: 4993330195
+Case #27: 4985587191

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+<p>
+Facebook HQ -- a mysterious place full of magical code and trade secrets.
+If outsiders were ever to breach the walls of the compound, which are
+protected by a legion of security foxes, the entire company could well
+be brought to its knees!
+</p>
+<p>
+Hmmm. Actually, campus tours are given regularly.
+</p>
+<p>
+The compound consists of <b>N</b> buildings, with <b>M</b> walkways running amongst them.
+The <i>i</i>th walkway connects buildings <b>A<sub>i</sub></b> and <b>B<sub>i</sub></b>, (<b>A<sub>i</sub></b> != <b>B<sub>i</sub></b>)
+and no two buildings are
+directly connected by more than one walkway. There are no other ways to
+move from building to building.
+</p>
+<p>
+Over a period of <b>D</b> days, some events will occur at Facebook HQ. One
+of two types of events will happen on the <i>i</i>th day, indicated by a character
+<b>E<sub>i</sub></b>. If <b>E<sub>i</sub></b> = 'T', then a tour will take place. Otherwise, <b>E<sub>i</sub></b> = 'S', and a
+security sweep of one building will take place.
+</p>
+<p>
+If a tour is given on the <i>i</i>th day, visitors will plan to enter the compound at
+building <b>X<sub>i</sub></b>, and leave from building <b>Y<sub>i</sub></b> (<b>X<sub>i</sub></b> != <b>Y<sub>i</sub></b>). If it turns out that
+these two buildings are not actually connected by any sequence of walkways,
+then the tour will be cancelled, and the unfortunate visitors will be
+given Facebook T-shirts on the way out. Otherwise, a large number of people
+will be led from building <b>X<sub>i</sub></b> to building <b>Y<sub>i</sub></b> along various routes. No route
+will involve travelling along the same walkway multiple times (even in
+different directions), but a route might revisit the same building repeatedly,
+including buildings <b>X<sub>i</sub></b> and <b>Y<sub>i</sub></b>. Along the way some visitors will inevitably
+get themselves "lost", and fail to rejoin the tour group. In total, <b>O<sub>i</sub></b> new
+outsiders will be left behind in each building which could possibly be part of
+any valid tour route from building <b>X<sub>i</sub></b> and building <b>Y<sub>i</sub></b>. Good thing they'll no
+doubt have brought cameras to amuse themselves with while they wait to be
+found.
+</p>
+<p>
+On the other hand, if a security sweep is conducted on the <i>i</i>th day, then the
+security foxes will carefully search building <b>Z<sub>i</sub></b> for any trespassers
+remaining from previous tours, and kindly escort them out.
+</p>
+<p>
+Since Facebook likes data, you've been hired to record how many outsiders
+were found in each sweep.
+</p>
+<h3>Input</h3>
+<p>
+Input begins with an integer <b>T</b>, the number of test cases. Each test case
+begins with a line containing three integers, <b>N</b>, <b>M</b>, and <b>D</b>.
+The next <b>M</b> lines contain two integers <b>A<sub>i</sub></b> and <b>B<sub>i</sub></b>.
+The next <b>D</b> lines contain a character <b>E<sub>i</sub></b>, followed by either three integers
+<b>X<sub>i</sub></b>, <b>Y<sub>i</sub></b>, <b>O<sub>i</sub></b> if <b>E<sub>i</sub></b> = 'T', or a single integer <b>Z<sub>i</sub></b> if <b>E<sub>i</sub></b> = 'S'.
+</p>
+<h3>Output</h3>
+<p>
+For each test case <i>i</i>, output "Case #i: " followed by the total number of visitors the foxes escort off the campus. Since this number may be quite large, output it modulo 1,000,000,007.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le;  <b>T</b> &le; 20 <br/>
+1 &le;  <b>N</b> &le;  10<sup>5</sup> <br/>
+1 &le;  <b>M</b> &le;  10<sup>6</sup> <br/>
+1 &le;  <b>D</b> &le;  10<sup>6</sup> <br/>
+1 &le; <b>O<sub>i</sub></b> &le; 1,000 <br/>
+1 &le;  <b>A<sub>i</sub></b>, <b>B<sub>i</sub></b>, <b>X<sub>i</sub></b>, <b>Y<sub>i</sub></b>, <b>Z<sub>i</sub></b> &le;  <b>N</b> <br/>
+</p>
+<h3>Explanation of Sample</h3>
+<p>
+In the first sample case:
+</p>
+<p>
+On the first day, a tour is given from building 1 to building 2. The only
+valid route consists of simply crossing the walkway between these two
+buildings. As such, by the end of the day, 5 outsiders are left hiding in each
+of buildings 1 and 2.
+</p>
+<p>
+On the second day, the tour cannot take place.
+</p>
+<p>
+On the third and fourth days, security sweeps of buildings 2 and 6 are carried
+out, with 5 and 0 outsiders found respectively.
+</p>
+<p>
+On the fifth day, a tour is given from building 2 to building 3. There are
+exactly three valid routes (2, 3), (2, 3, 4, 5, 3), (2, 3, 5, 4, 3). As such,
+one new outsider remains behind in each of buildings 2, 3, 4, and 5.
+</p>
+<p>
+On the sixth day, the valid tour routes are (5, 3) and (5, 4, 3), so 14 new
+outsiders take up residence in each of buildings 3, 4, and 5.
+</p>
+<p>
+Finally, security sweeps of buildings 1, 2, and 4 are conducted evicting 5, 1,
+and 15 people respectively, for a grand total of 26.
+</p>

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+Facebook HQ -- a mysterious place full of magical code and trade secrets. If
+outsiders were ever to breach the walls of the compound, which are protected
+by a legion of security foxes, the entire company could well be brought to its
+knees!
+Hmmm. Actually, campus tours are given regularly.
+The compound consists of **N** buildings, with **M** walkways running amongst
+them. The _i_th walkway connects buildings **Ai** and **Bi**, (**Ai** !=
+**Bi**) and no two buildings are directly connected by more than one walkway.
+There are no other ways to move from building to building.
+Over a period of **D** days, some events will occur at Facebook HQ. One of two
+types of events will happen on the _i_th day, indicated by a character **Ei**.
+If **Ei** = 'T', then a tour will take place. Otherwise, **Ei** = 'S', and a
+security sweep of one building will take place.
+If a tour is given on the _i_th day, visitors will plan to enter the compound
+at building **Xi**, and leave from building **Yi** (**Xi** != **Yi**). If it
+turns out that these two buildings are not actually connected by any sequence
+of walkways, then the tour will be cancelled, and the unfortunate visitors
+will be given Facebook T-shirts on the way out. Otherwise, a large number of
+people will be led from building **Xi** to building **Yi** along various
+routes. No route will involve travelling along the same walkway multiple times
+(even in different directions), but a route might revisit the same building
+repeatedly, including buildings **Xi** and **Yi**. Along the way some visitors
+will inevitably get themselves "lost", and fail to rejoin the tour group. In
+total, **Oi** new outsiders will be left behind in each building which could
+possibly be part of any valid tour route from building **Xi** and building
+**Yi**. Good thing they'll no doubt have brought cameras to amuse themselves
+with while they wait to be found.
+On the other hand, if a security sweep is conducted on the _i_th day, then the
+security foxes will carefully search building **Zi** for any trespassers
+remaining from previous tours, and kindly escort them out.
+Since Facebook likes data, you've been hired to record how many outsiders were
+found in each sweep.
+### Input
+Input begins with an integer **T**, the number of test cases. Each test case
+begins with a line containing three integers, **N**, **M**, and **D**. The
+next **M** lines contain two integers **Ai** and **Bi**. The next **D** lines
+contain a character **Ei**, followed by either three integers **Xi**, **Yi**,
+**Oi** if **Ei** = 'T', or a single integer **Zi** if **Ei** = 'S'.
+### Output
+For each test case _i_, output "Case #i: " followed by the total number of
+visitors the foxes escort off the campus. Since this number may be quite
+large, output it modulo 1,000,000,007.
+### Constraints
+1 ≤ **T** ≤ 20
+1 ≤ **N** ≤ 105
+1 ≤ **M** ≤ 106
+1 ≤ **D** ≤ 106
+1 ≤ **Oi** ≤ 1,000
+1 ≤ **Ai**, **Bi**, **Xi**, **Yi**, **Zi** ≤ **N**
+### Explanation of Sample
+In the first sample case:
+On the first day, a tour is given from building 1 to building 2. The only
+valid route consists of simply crossing the walkway between these two
+buildings. As such, by the end of the day, 5 outsiders are left hiding in each
+of buildings 1 and 2.
+On the second day, the tour cannot take place.
+On the third and fourth days, security sweeps of buildings 2 and 6 are carried
+out, with 5 and 0 outsiders found respectively.
+On the fifth day, a tour is given from building 2 to building 3. There are
+exactly three valid routes (2, 3), (2, 3, 4, 5, 3), (2, 3, 5, 4, 3). As such,
+one new outsider remains behind in each of buildings 2, 3, 4, and 5.
+On the sixth day, the valid tour routes are (5, 3) and (5, 4, 3), so 14 new
+outsiders take up residence in each of buildings 3, 4, and 5.
+Finally, security sweeps of buildings 1, 2, and 4 are conducted evicting 5, 1,
+and 15 people respectively, for a grand total of 26.

2014/finals/tours.out ADDED Viewed

	@@ -0,0 +1,25 @@

+Case #1: 26
+Case #2: 20
+Case #3: 25
+Case #4: 30
+Case #5: 10
+Case #6: 321312244
+Case #7: 961408044
+Case #8: 638903740
+Case #9: 739155438
+Case #10: 206324915
+Case #11: 224475276
+Case #12: 601704477
+Case #13: 273863365
+Case #14: 966711072
+Case #15: 591408789
+Case #16: 258257037
+Case #17: 979432230
+Case #18: 445325208
+Case #19: 411713723
+Case #20: 609503086
+Case #21: 999022143
+Case #22: 847504615
+Case #23: 312082737
+Case #24: 195455291
+Case #25: 217890383

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+<p>A group of <strong>N</strong> high school students wants to play a basketball game. To divide
+themselves into two teams they first rank all the players in the following
+way:<p>
+<ul>
+<li>Players with a higher shot percentage are rated higher than players with a lower
+  shot percentage.</li>
+<li>If two players have the same shot percentage, the taller player is rated
+  higher.</li>
+</ul>
+<p>
+Luckily there are no two players with both the same shot percentage and height
+so they are able to order themselves in an unambiguous way. Based on that
+ordering each player is assigned
+a draft number from the range [1..<strong>N</strong>], where the highest-rated player gets the
+number 1, the second highest-rated gets the number 2, and so on.
+Now the first team contains all the players with the odd draft numbers and the
+second team all the players with the even draft numbers.</p>
+<p>
+Each team can only have <strong>P</strong> players playing at a time, so to ensure that
+everyone gets similar time on the court both teams will rotate their players
+according to the following algorithm:</p>
+<ul>
+<li>Each team starts the game with the <strong>P</strong> players who have the lowest draft numbers.</li>
+<li>If there are more than <strong>P</strong> players on a team after each minute of the game the player with the highest total
+  time played leaves the playing field. Ties are broken by the player with the higher draft number leaving first.</li>
+<li>To replace her the player on the bench with the lowest total time played
+  joins the game. Ties are broken by the player with the lower draft number
+entering first.</li>
+</ul>
+<p>
+The game has been going on for <strong>M</strong> minutes now. Your task is to print out the
+names of all the players currently on the field, (that is after <strong>M</strong> rotations).
+</p>
+<h3>Input</h3>
+<p>
+The first line of the input consists of a single number <strong>T</strong>, the number of test
+cases.
+</p>
+<p>
+Each test case starts with a line containing three space separated integers <strong>N</strong> <strong>M</strong> <strong>P</strong>
+</p>
+<p>
+The subsequent <strong>N</strong> lines are in the format "&lt;name&gt; &lt;shot_percentage&gt; &lt;height&gt;".
+See the example for clarification.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <strong>T</strong> &le; 50<br/>
+2 * <strong>P</strong> &le; <strong>N</strong> &le; 30<br/>
+1 &le; <strong>M</strong> &le; 120<br/>
+1 &le; <strong>P</strong> &le; 5<br/>
+Each name starts with an uppercase English letter, followed by 0 to 20 lowercase English letters. <br/>
+There can be players sharing the same name. <br/>
+Each shot percentage is an integer from the range [0..100]. <br/>
+Each height is an integer from the range [100..240].
+</p>
+<h3>Output</h3>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by 2 * <strong>P</strong> space separated names of the players playing after <strong>M</strong> rotations. The names should be printed in lexicographical order.</p>
+<h3>Example</h3>
+<p>In the first example if you sort all the players by their shot percentage you get the list: [Wai, Purav, Weiyan, Slawek, Lin, Meihong]. This makes the two teams:</p>
+[Wai, Weiyan, Lin]</br>
+[Purav, Slawek, Meihong]</br>
+<p>
+The game starts with Lin and Meihong sitting on the bench in their respective teams. After the first minute passes it's time for Weiyan and Slawek to sit out since they have the highest draft numbers of the people who played. After the second minute passes Lin and Meihong will keep playing since they only played one minute so far and it's Wai and Purav who have to sit out.</p>
+<p>Finally after the third minute Lin and Maihong go back to the bench
+and all the players currently playing again are:<br/><samp>Purav Slawek Wai Weiyan</samp></p>

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+30
+6 3 2
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+Weiyan 81 155
+Lin 80 100
+Purav 86 198
+Slawek 80 192
+Meihong 44 109
+7 93 2
+Paul 82 189
+Kittipat 62 126
+Thomas 17 228
+Fabien 57 233
+Yifei 65 138
+Liang 92 100
+Victor 53 124
+6 62 3
+Meihong 33 192
+Duc 62 162
+Wai 70 148
+Fabien 19 120
+Bhuwan 48 176
+Vlad 30 225
+8 59 3
+Anil 38 180
+Song 7 187
+David 65 159
+Lin 45 121
+Ranjeeth 39 183
+Torbjorn 26 181
+Clifton 57 158
+Phil 3 183
+4 72 1
+Anh 2 187
+Erling 69 226
+Purav 0 199
+Zejia 29 163
+4 98 2
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+Bhuwan 94 192
+Igor 85 183
+Aleksandar 66 128
+19 86 5
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+David 90 125
+Vladislav 11 103
+Erling 90 119
+Doan 20 207
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+Chi 60 173
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+Yingsheng 92 143
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+Yingsheng 20 105
+Anh 11 187
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+29 69 1
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+Erling 10 219
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+Erling 36 190
+Philip 0 160
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+Fabien 45 162
+Wesley 31 166
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+Wesley 88 174
+Song 91 234
+Purav 5 230
+Andrei 88 178
+Jordan 56 104
+24 119 3
+Meihong 33 155
+Lovro 46 175
+Manohar 60 137
+Nima 24 233
+Erling 67 110
+Viswanath 43 162
+Andras 69 210
+Yintao 59 116
+Weitao 12 115
+Weiyan 41 198
+Erling 40 108
+Weiyan 54 160
+Yintao 88 211
+Xiao 10 106
+Chad 95 158
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+Aleksandar 75 140
+Wai 48 176
+Anshuman 44 208
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+Luiz 37 117
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+Saransh 68 107
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+Tom 25 141
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+Rajat 42 150
+Lovro 83 116
+Rudradev 19 167
+Mehdi 90 213
+Paul 10 235
+Xiao 27 100
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+Sanjeet 74 216
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+Purav 21 142
+Dhruv 8 198
+Nima 9 233
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+Aravind 31 101
+Oleksandr 97 240
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+Igor 28 178
+Keegan 62 149
+Vasily 89 103
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+Lin 57 140
+Gaurav 3 195
+Viswanath 69 178
+Yintao 85 228
+Saransh 97 129
+Rajat 86 193
+Jan 13 198
+Anh 71 183
+Anil 18 137
+Sanjeet 12 180
+Mehdi 28 129
+14 18 5
+Jordan 38 176
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+Gaurav 62 118
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+Duc 54 102
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+Doan 99 154
+Thomas 11 142
+Song 77 189
+John 98 109
+John 9 202
+Liang 63 161
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+Anshuman 95 154
+Nima 92 132
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+Dmytro 37 222
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+Roman 83 107
+Tom 43 238
+John 31 220
+Tom 60 169
+Paul 46 187
+Steaphan 81 123
+Andriy 26 103
+Chad 99 101
+Jan 31 129
+Torbjorn 84 207
+Slawek 28 159
+Nathan 40 140
+Daniel 61 129
+Yintao 52 162
+Ekansh 14 223
+Sharad 53 232
+Josh 51 174
+Anil 86 206
+Atol 0 218
+Torbjorn 40 141
+25 50 5
+Aleksandar 34 200
+Zihing 41 124
+Andrii 14 226
+Voja 91 228
+Lin 83 182
+Erling 53 150
+Liang 74 233
+Luiz 49 125
+Atol 9 182
+Yingsheng 82 170
+Nima 71 228
+Rudradev 99 142
+Song 24 221
+Chad 39 195
+Bhuwan 54 146
+Bhuwan 12 233
+Zainab 88 180
+Voja 79 135
+Purav 79 203
+Fabien 90 230
+Nathan 12 148
+Ranjeeth 75 133
+Vladislav 88 148
+Viswanath 61 158
+Luiz 13 163
+23 82 3
+Lingjuan 50 198
+Zhen 74 108
+Ranjeeth 48 192
+Wesley 64 176
+Saransh 22 204
+Mehdi 68 117
+Wei 25 102
+Jan 97 150
+Torbjorn 12 198
+Jan 41 170
+Xiao 12 237
+Xiao 27 171
+Gaurav 87 237
+Andriy 90 178
+David 72 235
+Oleksandr 30 190
+Ekansh 7 155
+Zihing 80 196
+Wenjie 7 166
+Zhen 64 214
+Yingsheng 0 139
+Andriy 79 166
+Ajay 78 152
+19 109 3
+Atol 21 171
+Jan 56 128
+Yintao 17 176
+Ekansh 44 194
+Jan 40 216
+Ahmed 26 219
+Victor 82 131
+Amol 33 174
+Doan 16 175
+Zejia 9 214
+Viswanath 68 139
+Kittipat 93 124
+Ajay 35 103
+Anil 1 185
+Paul 6 217
+Zihing 34 196
+Aravind 60 183
+Rudradev 48 163
+Wenjie 19 229
+25 98 1
+Aravind 7 216
+Ekansh 57 142
+Zainab 95 117
+Josh 83 236
+Lin 86 185
+Andrei 82 184
+Victor 75 130
+Doan 81 178
+Liang 38 221
+Ahmed 44 212
+Chirag 62 101
+Sarang 9 186
+Meihong 76 167
+Philip 27 105
+John 53 226
+Andrii 75 152
+Vladislav 75 221
+Doan 96 152
+Andrei 40 180
+Dhruv 73 231
+Vladislav 66 195
+Jordan 65 231
+Slawek 59 124
+Anil 5 202
+Viswanath 82 136
+18 95 2
+Liang 53 146
+Wesley 12 197
+Wenjie 86 238
+Manohar 94 129
+Anshuman 27 180
+Chi 73 162
+David 16 238
+Purav 57 227
+Wai 42 196
+Chad 48 239
+Zainab 46 175
+Wai 98 114
+Chi 45 209
+Paul 17 135
+Paul 10 171
+Atol 23 162
+Yifei 99 197
+Wei 0 164
+10 57 3
+Fabien 0 111
+Duc 49 198
+Ekansh 98 121
+Zef 30 122
+Dmytro 50 124
+Chirag 39 209
+Doan 20 229
+Clifton 50 129
+Andrei 91 177
+Erling 0 118

2014/quals/basketball_game.md ADDED Viewed

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+A group of **N** high school students wants to play a basketball game. To
+divide themselves into two teams they first rank all the players in the
+following way:
+  * Players with a higher shot percentage are rated higher than players with a lower shot percentage.
+  * If two players have the same shot percentage, the taller player is rated higher.
+Luckily there are no two players with both the same shot percentage and height
+so they are able to order themselves in an unambiguous way. Based on that
+ordering each player is assigned a draft number from the range [1..**N**],
+where the highest-rated player gets the number 1, the second highest-rated
+gets the number 2, and so on. Now the first team contains all the players with
+the odd draft numbers and the second team all the players with the even draft
+numbers.
+Each team can only have **P** players playing at a time, so to ensure that
+everyone gets similar time on the court both teams will rotate their players
+according to the following algorithm:
+  * Each team starts the game with the **P** players who have the lowest draft numbers.
+  * If there are more than **P** players on a team after each minute of the game the player with the highest total time played leaves the playing field. Ties are broken by the player with the higher draft number leaving first.
+  * To replace her the player on the bench with the lowest total time played joins the game. Ties are broken by the player with the lower draft number entering first.
+The game has been going on for **M** minutes now. Your task is to print out
+the names of all the players currently on the field, (that is after **M**
+rotations).
+### Input
+The first line of the input consists of a single number **T**, the number of
+test cases.
+Each test case starts with a line containing three space separated integers
+**N** **M** **P**
+The subsequent **N** lines are in the format "<name> <shot_percentage>
+<height>". See the example for clarification.
+### Constraints
+1 ≤ **T** ≤ 50
+2 * **P** ≤ **N** ≤ 30
+1 ≤ **M** ≤ 120
+1 ≤ **P** ≤ 5
+Each name starts with an uppercase English letter, followed by 0 to 20
+lowercase English letters.
+There can be players sharing the same name.
+Each shot percentage is an integer from the range [0..100].
+Each height is an integer from the range [100..240].
+### Output
+For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
+followed by 2 * **P** space separated names of the players playing after **M**
+rotations. The names should be printed in lexicographical order.
+### Example
+In the first example if you sort all the players by their shot percentage you
+get the list: [Wai, Purav, Weiyan, Slawek, Lin, Meihong]. This makes the two
+teams:
+[Wai, Weiyan, Lin] [Purav, Slawek, Meihong]
+The game starts with Lin and Meihong sitting on the bench in their respective
+teams. After the first minute passes it's time for Weiyan and Slawek to sit
+out since they have the highest draft numbers of the people who played. After
+the second minute passes Lin and Meihong will keep playing since they only
+played one minute so far and it's Wai and Purav who have to sit out.
+Finally after the third minute Lin and Maihong go back to the bench and all
+the players currently playing again are:
+Purav Slawek Wai Weiyan

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+Case #1: Purav Slawek Wai Weiyan
+Case #2: Fabien Kittipat Liang Paul
+Case #3: Bhuwan Duc Fabien Meihong Vlad Wai
+Case #4: Anil Lin Phil Ranjeeth Song Torbjorn
+Case #5: Erling Zejia
+Case #6: Aleksandar Aravind Bhuwan Igor
+Case #7: Andras Anh Doan Lingjuan Meihong Saransh Torbjorn Vladislav Vladislav Yingsheng
+Case #8: Aravind Ekansh
+Case #9: Ahmed Anshuman Jan Ranjeeth
+Case #10: Philip Tom Wesley Zhen
+Case #11: Lingjuan Zejia
+Case #12: Amol Andrei Andrii Aravind David John Nima Paul Rudradev Vladislav
+Case #13: Fabien Weiyan
+Case #14: Doan John
+Case #15: Andrei Wesley
+Case #16: Aleksandar Andras Anshuman Erling Manohar Xiao
+Case #17: Atol Clifton Clifton Doan John John Purav Song
+Case #18: Aravind Mehdi Weiyan Xiao
+Case #19: Anh Luiz Ranjeeth Roman Steaphan Weitao Weitao Zihing
+Case #20: Anil Doan Duc Fabien Manohar Paul Rajat Yintao
+Case #21: Anil Igor Purav Sanjeet
+Case #22: Doan Duc Gaurav John John Jordan Liang Rudradev Thomas Viswanath
+Case #23: Anshuman Manohar Meihong Nima
+Case #24: Andriy David Dmytro Jan John Slawek
+Case #25: Atol Bhuwan Bhuwan Lin Nima Vladislav Voja Voja Yingsheng Zainab
+Case #26: Andriy Jan Lingjuan Wenjie Xiao Yingsheng
+Case #27: Anil Aravind Jan Jan Victor Viswanath
+Case #28: Chirag Viswanath
+Case #29: Anshuman Atol Paul Wai
+Case #30: Andrei Doan Ekansh Erling Fabien Zef

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+<p>
+You want to write an image detection system that is able to recognize different geometric shapes.
+In the first version of the system you settled with just being able to detect filled squares on a grid.</p>
+<p>
+You are given a grid of <strong>N</strong>&times;<strong>N</strong> square cells. Each cell is either white or black. Your task is to detect whether all the black cells form a square shape.
+</p>
+<h3>Input</h3>
+<p>
+The first line of the input consists of a single number <strong>T</strong>, the number of test
+cases.
+</p>
+<p>
+Each test case starts with a line containing a single integer <strong>N</strong>. Each of the subsequent <strong>N</strong> lines contain <strong>N</strong> characters. Each character is either "." symbolizing a white cell, or "#" symbolizing a black cell. Every test case contains at least one black cell.
+</p>
+<h3>Output</h3>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by <samp>YES</samp> or <samp>NO</samp> depending on whether or not all the black cells form a completely filled square with edges parallel to the grid of cells.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <strong>T</strong> &le; 20<br />
+1 &le; <strong>N</strong> &le; 20
+</p>
+<h3>Example</h3>
+<p> Test cases 1 and 5 represent valid squares. Case 2 has an extra cell that is outside of the square. Case 3 shows a square not filled inside. And case 4 is a rectangle but not a square.</p>

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+25
+4
+..##
+..##
+....
+....
+4
+..##
+..##
+#...
+....
+4
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+#..#
+####
+5
+#####
+#####
+#####
+#####
+.....
+5
+#####
+#####
+#####
+#####
+#####
+1
+#
+10
+..........
+..........
+.......###
+.......###
+.......###
+..........
+..........
+..........
+..........
+..........
+10
+..........
+..........
+..........
+...##.....
+...##.....
+...##.....
+..........
+..........
+..........
+..........
+10
+..........
+..........
+..........
+.....#....
+..........
+..#.......
+..........
+..........
+..........
+..........
+10
+..........
+.######...
+.#####.#..
+.######...
+.######...
+.######...
+.######...
+..........
+..........
+..........
+10
+..........
+..........
+.##.......
+.##.......
+..........
+..........
+......##..
+......##..
+..........
+..........
+10
+..........
+..........
+####......
+####......
+####......
+####......
+..........
+..........
+..........
+.........#
+10
+..........
+..........
+..........
+..........
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+###.
+.###
+.###
+....

2014/quals/square_detector.md ADDED Viewed

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+You want to write an image detection system that is able to recognize
+different geometric shapes. In the first version of the system you settled
+with just being able to detect filled squares on a grid.
+You are given a grid of **N**×**N** square cells. Each cell is either white or
+black. Your task is to detect whether all the black cells form a square shape.
+### Input
+The first line of the input consists of a single number **T**, the number of
+test cases.
+Each test case starts with a line containing a single integer **N**. Each of
+the subsequent **N** lines contain **N** characters. Each character is either
+"." symbolizing a white cell, or "#" symbolizing a black cell. Every test case
+contains at least one black cell.
+### Output
+For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
+followed by YES or NO depending on whether or not all the black cells form a
+completely filled square with edges parallel to the grid of cells.
+### Constraints
+1 ≤ **T** ≤ 20
+1 ≤ **N** ≤ 20
+### Example
+Test cases 1 and 5 represent valid squares. Case 2 has an extra cell that is
+outside of the square. Case 3 shows a square not filled inside. And case 4 is
+a rectangle but not a square.

2014/quals/square_detector.out ADDED Viewed

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+Case #1: YES
+Case #2: NO
+Case #3: NO
+Case #4: NO
+Case #5: YES
+Case #6: YES
+Case #7: YES
+Case #8: NO
+Case #9: NO
+Case #10: NO
+Case #11: NO
+Case #12: NO
+Case #13: YES
+Case #14: YES
+Case #15: YES
+Case #16: NO
+Case #17: NO
+Case #18: NO
+Case #19: NO
+Case #20: NO
+Case #21: NO
+Case #22: NO
+Case #23: YES
+Case #24: YES
+Case #25: NO

2014/quals/tennison.html ADDED Viewed

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+<p>You may be familiar with the works of Alfred, Lord Tennyson, the famous
+English poet. In this problem we will concern ourselves with Tennison,
+the less famous English tennis player. As you know, tennis is not so much
+a game of skill as a game of luck and weather patterns. The goal of tennis is
+to win <strong>K</strong> sets before the other player. However, the chance of winning a set is
+largely dependent on whether or not there is weather.
+</p>
+<p>Tennison plays best when it's sunny, but sometimes, of course, it rains.
+Tennison wins a set with probability <strong>p<sub>s</sub></strong> when it's sunny, and with probability
+<strong>p<sub>r</sub></strong> when it's raining. The chance that there will be sun for the first set is
+<strong>p<sub>i</sub></strong>. Luckily for Tennison, whenever he wins a set, the probability that there
+will be sun increases by <strong>p<sub>u</sub></strong> with probability <strong>p<sub>w</sub></strong>. Unfortunately, when Tennison
+loses a set, the probability of sun decreases by <strong>p<sub>d</sub></strong> with probability <strong>p<sub>l</sub></strong>.
+What is the chance that Tennison will be successful in his match?</p>
+<p>Rain and sun are the only weather conditions, so P(rain) = 1 - P(sun) at all
+times. Also, probabilities always stay in the range [0, 1]. If P(sun) would
+ever be less than 0, it is instead 0. If it would ever be greater than 1, it
+is instead 1.</p>
+<h2>Input</h2>
+<p>
+Input begins with an integer <strong>T</strong>, the number of tennis matches
+that Tennison plays. For each match, there is a line containing an integer
+<strong>K</strong>, followed by the
+probabilities <strong>p<sub>s</sub>, p<sub>r</sub>, p<sub>i</sub>, p<sub>u</sub>, p<sub>w</sub>, p<sub>d</sub>, p<sub>l</sub></strong> in that order. All of these
+values are given with exactly three places after the decimal point.
+<h2>Output</h2>
+<p>
+For each match, output "Case #i: " followed by the probability that Tennison wins the match, rounded to 6 decimal places
+(quotes for clarity only). It is guaranteed that the output is unaffected by deviations as large as 10<sup>-8</sup>.
+</p>
+<h2>Constraints</h2>
+<ul>
+<li>1 &le; <strong>T</strong> &le; 100</li>
+<li>1 &le; <strong>K</strong> &le; 100</li>
+<li>0 &le; <strong>p<sub>s</sub>, p<sub>r</sub>, p<sub>i</sub>, p<sub>u</sub>, p<sub>w</sub>, p<sub>d</sub>, p<sub>l</sub></strong> &le; 1</li>
+<li><strong>p<sub>s</sub></strong> &gt; <strong>p<sub>r</sub></strong></li>
+</ul>

2014/quals/tennison.in ADDED Viewed

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+92
+1 0.800 0.100 0.500 0.500 0.500 0.500 0.500
+2 0.600 0.200 0.500 0.100 1.000 0.100 1.000
+1 1.000 0.000 1.000 1.000 1.000 1.000 1.000
+25 0.984 0.222 0.993 0.336 0.207 0.084 0.478
+58 0.472 0.182 0.418 0.097 0.569 0.816 0.711
+27 0.620 0.014 0.817 0.451 0.090 0.229 0.504
+8 0.838 0.389 0.829 0.592 0.594 0.669 0.480
+2 0.180 0.156 0.548 0.790 0.004 0.311 0.019
+62 0.740 0.653 0.323 0.642 0.837 0.773 0.610
+28 0.918 0.381 0.851 0.346 0.278 0.369 0.757
+89 0.812 0.547 0.657 0.131 0.302 0.379 0.955
+67 0.213 0.172 0.842 0.786 0.933 0.253 0.273
+75 0.583 0.469 0.241 0.940 0.053 0.770 0.129
+27 0.576 0.415 0.480 0.105 0.952 0.391 0.633
+59 0.060 0.031 0.085 0.919 0.931 0.539 0.372
+53 0.355 0.185 0.299 0.939 0.295 0.063 0.155
+17 0.706 0.216 0.713 0.435 0.885 0.951 0.396
+10 0.708 0.493 0.709 0.273 0.687 0.353 0.593
+58 0.667 0.638 0.471 0.028 0.597 0.439 0.945
+61 0.633 0.071 0.634 0.946 0.641 0.946 0.710
+99 0.835 0.833 0.989 0.059 0.672 0.824 0.508
+37 0.399 0.287 0.317 0.870 0.520 0.686 0.954
+87 0.447 0.384 0.187 0.898 0.240 0.964 0.301
+40 0.114 0.096 0.671 0.372 0.708 0.742 0.378
+85 0.705 0.704 0.874 0.098 0.324 0.252 0.534
+38 0.887 0.847 0.004 0.716 0.148 0.543 0.058
+71 0.649 0.181 0.358 0.197 0.773 0.810 0.348
+50 0.718 0.450 0.928 0.207 0.675 0.390 0.937
+95 0.394 0.045 0.961 0.263 0.896 0.214 0.382
+25 0.674 0.528 0.625 0.971 0.805 0.782 0.177
+80 0.580 0.480 0.189 0.356 0.890 0.732 0.662
+11 0.698 0.348 0.651 0.528 0.828 0.526 0.129
+7 0.845 0.096 0.965 0.401 0.698 0.213 0.703
+47 0.960 0.088 0.081 0.628 0.777 0.948 0.515
+42 0.890 0.226 0.829 0.910 0.700 0.045 0.566
+66 0.820 0.682 0.189 0.313 0.558 0.181 0.919
+42 0.219 0.065 0.968 0.173 0.045 0.878 0.889
+37 0.916 0.809 0.178 0.801 0.235 0.996 0.077
+99 0.753 0.662 0.810 0.984 0.645 0.511 0.015
+78 0.603 0.393 0.706 0.415 0.422 0.564 0.083
+65 0.477 0.013 0.439 0.346 0.125 0.582 0.894
+13 0.556 0.023 0.797 0.208 0.603 0.820 0.890
+83 0.449 0.407 0.053 0.078 0.212 0.345 0.121
+47 0.919 0.906 0.703 0.151 0.851 0.311 0.505
+41 0.433 0.015 0.159 0.938 0.137 0.191 0.507
+45 0.889 0.664 0.232 0.454 0.785 0.637 0.611
+13 0.600 0.495 0.830 0.178 0.768 0.678 0.387
+59 0.916 0.520 0.917 0.588 0.808 0.719 0.404
+97 0.847 0.236 0.244 0.150 0.361 0.734 0.242
+21 0.588 0.423 0.572 0.307 0.703 0.268 0.000
+6 0.807 0.331 0.737 0.825 0.406 0.018 0.704
+52 0.799 0.361 0.083 0.223 0.593 0.354 0.895
+26 0.928 0.246 0.915 0.726 0.009 0.732 0.041
+27 0.828 0.611 0.901 0.082 0.043 0.435 0.723
+12 0.915 0.628 0.785 0.748 0.986 0.089 0.091
+35 0.721 0.098 0.455 0.201 0.752 0.090 0.297
+3 0.589 0.284 0.742 0.325 0.342 0.370 0.512
+14 0.572 0.439 0.467 0.725 0.471 0.556 0.085
+12 0.743 0.714 0.911 0.552 0.964 0.776 0.356
+67 0.329 0.065 0.937 0.810 0.385 0.159 0.381
+3 0.532 0.063 0.517 0.565 0.208 0.142 0.525
+21 0.545 0.188 0.239 0.929 0.709 0.554 0.356
+34 0.464 0.371 0.105 0.424 0.121 0.433 0.857
+92 0.383 0.095 0.110 0.799 0.490 0.795 0.312
+26 0.928 0.032 0.852 0.335 0.771 0.136 0.471
+50 0.578 0.060 0.723 0.176 0.456 0.935 0.488
+55 0.571 0.148 0.741 0.231 0.824 0.618 0.671
+73 0.733 0.648 0.371 0.866 0.469 0.782 0.003
+64 0.219 0.179 0.825 0.561 0.154 0.754 0.543
+28 0.533 0.166 0.964 0.588 0.681 0.652 0.211
+32 0.958 0.820 0.554 0.677 0.849 0.905 0.797
+41 0.411 0.033 0.972 0.669 0.828 0.748 0.402
+40 0.763 0.659 0.378 0.149 0.117 0.487 0.657
+93 0.840 0.170 0.216 0.738 0.031 0.854 0.345
+99 0.882 0.661 0.805 0.288 0.495 0.955 0.788
+5 0.360 0.102 0.939 0.331 0.806 0.837 0.328
+7 0.646 0.195 0.437 0.617 0.120 0.642 0.828
+99 0.731 0.067 0.977 0.213 0.573 0.793 0.888
+55 0.419 0.097 0.088 0.922 0.455 0.094 0.638
+15 0.514 0.308 0.711 0.295 0.287 0.827 0.991
+20 0.284 0.273 0.854 0.914 0.086 0.198 0.653
+65 0.964 0.395 0.549 0.741 0.686 0.702 0.686
+86 0.893 0.699 0.423 0.734 0.127 0.997 0.018
+29 0.767 0.586 0.279 0.921 0.407 0.019 0.732
+18 0.299 0.181 0.255 0.016 0.760 0.497 0.791
+58 0.239 0.204 0.010 0.535 0.911 0.130 0.369
+62 0.719 0.156 0.014 0.837 0.613 0.376 0.707
+92 0.851 0.655 0.970 0.768 0.448 0.576 0.394
+86 0.633 0.095 0.166 0.183 0.960 0.823 0.176
+86 0.579 0.110 0.861 0.275 0.848 0.350 0.123
+53 0.623 0.075 0.451 0.830 0.258 0.036 0.105
+30 0.889 0.482 0.277 0.194 0.392 0.339 0.886

2014/quals/tennison.md ADDED Viewed

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+You may be familiar with the works of Alfred, Lord Tennyson, the famous
+English poet. In this problem we will concern ourselves with Tennison, the
+less famous English tennis player. As you know, tennis is not so much a game
+of skill as a game of luck and weather patterns. The goal of tennis is to win
+**K** sets before the other player. However, the chance of winning a set is
+largely dependent on whether or not there is weather.
+Tennison plays best when it's sunny, but sometimes, of course, it rains.
+Tennison wins a set with probability **ps** when it's sunny, and with
+probability **pr** when it's raining. The chance that there will be sun for
+the first set is **pi**. Luckily for Tennison, whenever he wins a set, the
+probability that there will be sun increases by **pu** with probability
+**pw**. Unfortunately, when Tennison loses a set, the probability of sun
+decreases by **pd** with probability **pl**. What is the chance that Tennison
+will be successful in his match?
+Rain and sun are the only weather conditions, so P(rain) = 1 - P(sun) at all
+times. Also, probabilities always stay in the range [0, 1]. If P(sun) would
+ever be less than 0, it is instead 0. If it would ever be greater than 1, it
+is instead 1.
+## Input
+Input begins with an integer **T**, the number of tennis matches that Tennison
+plays. For each match, there is a line containing an integer **K**, followed
+by the probabilities **ps, pr, pi, pu, pw, pd, pl** in that order. All of
+these values are given with exactly three places after the decimal point.
+## Output
+For each match, output "Case #i: " followed by the probability that Tennison
+wins the match, rounded to 6 decimal places (quotes for clarity only). It is
+guaranteed that the output is unaffected by deviations as large as 10-8.
+## Constraints
+  * 1 ≤ **T** ≤ 100
+  * 1 ≤ **K** ≤ 100
+  * 0 ≤ **ps, pr, pi, pu, pw, pd, pl** ≤ 1
+  * **ps** > **pr**

2014/quals/tennison.out ADDED Viewed

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+Case #1: 0.450000
+Case #2: 0.352000
+Case #3: 1.000000
+Case #4: 0.999956
+Case #5: 0.000000
+Case #6: 0.008258
+Case #7: 0.885871
+Case #8: 0.076117
+Case #9: 0.999998
+Case #10: 0.812133
+Case #11: 0.956193
+Case #12: 0.000000
+Case #13: 0.551872
+Case #14: 0.241770
+Case #15: 0.000000
+Case #16: 0.000427
+Case #17: 0.452012
+Case #18: 0.834152
+Case #19: 0.998829
+Case #20: 0.000044
+Case #21: 1.000000
+Case #22: 0.001462
+Case #23: 0.009297
+Case #24: 0.000000
+Case #25: 1.000000
+Case #26: 1.000000
+Case #27: 0.005814
+Case #28: 0.652831
+Case #29: 0.000005
+Case #30: 0.982684
+Case #31: 0.714924
+Case #32: 0.910761
+Case #33: 0.925189
+Case #34: 0.724935
+Case #35: 1.000000
+Case #36: 1.000000
+Case #37: 0.000000
+Case #38: 1.000000
+Case #39: 1.000000
+Case #40: 0.936158
+Case #41: 0.000000
+Case #42: 0.001031
+Case #43: 0.012372
+Case #44: 1.000000
+Case #45: 0.000002
+Case #46: 1.000000
+Case #47: 0.668061
+Case #48: 1.000000
+Case #49: 0.103853
+Case #50: 0.853627
+Case #51: 0.956042
+Case #52: 0.339817
+Case #53: 0.924908
+Case #54: 0.976706
+Case #55: 1.000000
+Case #56: 0.937467
+Case #57: 0.468936
+Case #58: 0.692741
+Case #59: 0.992276
+Case #60: 0.000000
+Case #61: 0.186419
+Case #62: 0.182569
+Case #63: 0.020824
+Case #64: 0.000000
+Case #65: 0.997141
+Case #66: 0.000001
+Case #67: 0.000028
+Case #68: 1.000000
+Case #69: 0.000000
+Case #70: 0.204542
+Case #71: 1.000000
+Case #72: 0.000005
+Case #73: 0.998624
+Case #74: 0.002118
+Case #75: 1.000000
+Case #76: 0.089279
+Case #77: 0.057463
+Case #78: 0.000000
+Case #79: 0.001279
+Case #80: 0.036810
+Case #81: 0.001556
+Case #82: 0.999999
+Case #83: 1.000000
+Case #84: 0.999939
+Case #85: 0.000011
+Case #86: 0.000000
+Case #87: 0.254354
+Case #88: 1.000000
+Case #89: 0.014762
+Case #90: 0.678187
+Case #91: 0.890621
+Case #92: 0.716511

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+<p>
+Al is the proprietor of Al's Awesome and Amazing Amusement Arcade,
+called AAAAAA by some, AAaAAA by others, AAAAA by others still, and
+alternately A<sup>5</sup> or A<sup>6</sup> by math majors.
+</p>
+<p>
+The problem with operating such a spectacular business is managing the line of
+people waiting to get in. City by-laws prevent people from loitering on Al's
+property, so anybody who wants to experience the wonders Al has in store has
+to queue in the parking lot. Not wanting to turn people away, Al is interested
+in cramming as many hapless souls into the parking lot as he can. However,
+customers are a whiny bunch, and refuse to stand in any queue that makes too
+many detours before getting to the entrance.
+</p>
+<p>
+You can imagine that the parking lot is a grid, with the Arcade's entrance in
+the upper-left corner. All queues must begin here. There may be cars in the
+parking lot, denoted '#'. Customers refuse to queue on top of cars. All other
+cells will contain '.'. Due to customer complaints, all queues must generally
+extend only rightwards and downwards. However, Al's clientele is not entirely
+unreasonable, so a queue may have a single contiguous section that runs
+upwards, or a single contiguous section that runs leftwards, but not both.
+Queues only extend in these four directions (i.e., not diagonally).
+</p>
+<p>
+There is only room for one customer in each empty space. Each pair of consecutive customers in the queue must stand in adjacent spaces, i.e. there can't be any gaps in the queue.
+</p>
+<h3>Input</h3>
+<p>
+The first line of the input consists of a single integer <strong>T</strong>, the number of test
+cases. <br />
+Each test case begins with a line containing two integers, <strong>N</strong> and <strong>M</strong>, the number of rows and columns in the lot's grid.<br />
+The next <strong>N</strong> lines each contain a string with exactly <strong>M</strong> characters, where the <strong>i</strong>th line correspond to the <strong>i</strong>th row in the grid. <br />
+</p>
+<h3>Output</h3>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by the size of the largest queue starting in the top left corner that Al can fit into his parking lot.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <strong>T</strong> &le; 20 <br />
+1 &le; <strong>N</strong>, <strong>M</strong> &le; 500 <br />
+Each character in the grid will be either '.' or '#'. <br />
+The character in the upper left corner will always be '.' <br />
+</p>

2014/round1/aaaaaa.in ADDED Viewed

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2014/round1/aaaaaa.md ADDED Viewed

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+Al is the proprietor of Al's Awesome and Amazing Amusement Arcade, called
+AAAAAA by some, AAaAAA by others, AAAAA by others still, and alternately A5 or
+A6 by math majors.
+The problem with operating such a spectacular business is managing the line of
+people waiting to get in. City by-laws prevent people from loitering on Al's
+property, so anybody who wants to experience the wonders Al has in store has
+to queue in the parking lot. Not wanting to turn people away, Al is interested
+in cramming as many hapless souls into the parking lot as he can. However,
+customers are a whiny bunch, and refuse to stand in any queue that makes too
+many detours before getting to the entrance.
+You can imagine that the parking lot is a grid, with the Arcade's entrance in
+the upper-left corner. All queues must begin here. There may be cars in the
+parking lot, denoted '#'. Customers refuse to queue on top of cars. All other
+cells will contain '.'. Due to customer complaints, all queues must generally
+extend only rightwards and downwards. However, Al's clientele is not entirely
+unreasonable, so a queue may have a single contiguous section that runs
+upwards, or a single contiguous section that runs leftwards, but not both.
+Queues only extend in these four directions (i.e., not diagonally).
+There is only room for one customer in each empty space. Each pair of
+consecutive customers in the queue must stand in adjacent spaces, i.e. there
+can't be any gaps in the queue.
+### Input
+The first line of the input consists of a single integer **T**, the number of
+test cases.
+Each test case begins with a line containing two integers, **N** and **M**,
+the number of rows and columns in the lot's grid.
+The next **N** lines each contain a string with exactly **M** characters,
+where the **i**th line correspond to the **i**th row in the grid.
+### Output
+For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
+followed by the size of the largest queue starting in the top left corner that
+Al can fit into his parking lot.
+### Constraints
+1 ≤ **T** ≤ 20
+1 ≤ **N**, **M** ≤ 500
+Each character in the grid will be either '.' or '#'.
+The character in the upper left corner will always be '.'

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+Case #1: 17
+Case #2: 10
+Case #3: 17
+Case #4: 5
+Case #5: 10
+Case #6: 13
+Case #7: 1
+Case #8: 11
+Case #9: 9
+Case #10: 9
+Case #11: 1821
+Case #12: 1034
+Case #13: 748
+Case #14: 719
+Case #15: 869
+Case #16: 770
+Case #17: 637
+Case #18: 524
+Case #19: 716
+Case #20: 676
+Case #21: 591
+Case #22: 591
+Case #23: 554
+Case #24: 700
+Case #25: 533
+Case #26: 673
+Case #27: 685
+Case #28: 592
+Case #29: 456
+Case #30: 475
+Case #31: 990
+Case #32: 374
+Case #33: 654
+Case #34: 516
+Case #35: 466
+Case #36: 604
+Case #37: 404
+Case #38: 464
+Case #39: 514
+Case #40: 473
+Case #41: 427
+Case #42: 345
+Case #43: 603
+Case #44: 373
+Case #45: 418
+Case #46: 526
+Case #47: 327
+Case #48: 435
+Case #49: 475
+Case #50: 297

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+<p>Alice and Bob like to play what they call the "Coins Game". In this game Bob starts with <strong>K</strong> identical coins and <strong>N</strong> identical jars. A jar can fit any number of coins and Bob has to distribute all the coins in whatever way he wants.</p>
+<p>After the coins are distributed Alice takes the jars and shuffles them at random while Bob isn't looking. Alice will move jars around but will not move any coins between the jars. The jars are opaque so after the shuffle Bob doesn't see how many coins are in each.</p>
+<p>Now Bob has <strong>P</strong> moves. In each move he points at one of the jars. If the jar contains any coins Alice takes a single coin from it and hands it to Bob. If the jar is empty Alice tells Bob. Bob remembers his initial distribution and the moves he has made so far.</p>
+<p>The goal of the game is to check whether Bob is able to acquire at least <strong>C</strong> coins after his <strong>P</strong> moves. If he can do that he wins the game. After losing the first few games Bob is determined to figure out what's the minimal number of moves <strong>P</strong> that can guarantee his win. Your job is to help him, that is find the minimal value <strong>P</strong> for which there exists an initial coins distribution and moves strategy that makes Bob win no matter what order the jars are in.</p>
+<h3>Input</h3>
+<p>
+The first line of the input consists of a single integer <strong>T</strong>, the number of test
+cases. <br />
+Each test case is a single line with three integers: <strong>N</strong> <strong>K</strong> <strong>C</strong>
+</p>
+<h3>Output</h3>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by an integer <strong>P</strong>, the minimal number of moves for which there exists a winning strategy.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <strong>T</strong> &le; 20<br />
+1 &le; <strong>N</strong> &le; 1,000,000<br />
+1 &le; <strong>C</strong> &le; <strong>K</strong> &le; 1,000,000<br />
+</p>
+<h3>Examples</h3>
+<p>In the first test case we start with three jars and six coins. Bob needs to get four of them to win. A winning strategy is to put two coins in each jar. Then he can point twice at one jar and twice at another one to always get four coins.
+</p>
+<p>In the second example he can put the five coins in a different jar each. In the worst case he will point at an empty jar three times so he will need five total moves to get two coins. There is no way to guarantee a win with fewer than five moves.</p>

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	@@ -0,0 +1,32 @@

+31
+3 6 4
+8 5 2
+3 4 4
+1 3 1
+2 10 9
+576 681 559
+941881 995305 928192
+7 1 1
+619 689 338
+140703 585535 72412
+8 4 1
+569 922 304
+843139 399718 227764
+7 4 2
+872 462 237
+506626 517245 198959
+7 9 5
+787 42 42
+226147 298339 251609
+1 3 1
+999999 1000000 1000000
+1000000 1000000 1000000
+999999 1000000 999999
+1000000 500000 1
+497 999999 999999
+1000 12345 12340
+1000000 10 1
+1 1 1
+1 1000000 1000
+1000 1000000 1337
+10 55 55

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+Alice and Bob like to play what they call the "Coins Game". In this game Bob
+starts with **K** identical coins and **N** identical jars. A jar can fit any
+number of coins and Bob has to distribute all the coins in whatever way he
+wants.
+After the coins are distributed Alice takes the jars and shuffles them at
+random while Bob isn't looking. Alice will move jars around but will not move
+any coins between the jars. The jars are opaque so after the shuffle Bob
+doesn't see how many coins are in each.
+Now Bob has **P** moves. In each move he points at one of the jars. If the jar
+contains any coins Alice takes a single coin from it and hands it to Bob. If
+the jar is empty Alice tells Bob. Bob remembers his initial distribution and
+the moves he has made so far.
+The goal of the game is to check whether Bob is able to acquire at least **C**
+coins after his **P** moves. If he can do that he wins the game. After losing
+the first few games Bob is determined to figure out what's the minimal number
+of moves **P** that can guarantee his win. Your job is to help him, that is
+find the minimal value **P** for which there exists an initial coins
+distribution and moves strategy that makes Bob win no matter what order the
+jars are in.
+### Input
+The first line of the input consists of a single integer **T**, the number of
+test cases.
+Each test case is a single line with three integers: **N** **K** **C**
+### Output
+For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
+followed by an integer **P**, the minimal number of moves for which there
+exists a winning strategy.
+### Constraints
+1 ≤ **T** ≤ 20
+1 ≤ **N** ≤ 1,000,000
+1 ≤ **C** ≤ **K** ≤ 1,000,000
+### Examples
+In the first test case we start with three jars and six coins. Bob needs to
+get four of them to win. A winning strategy is to put two coins in each jar.
+Then he can point twice at one jar and twice at another one to always get four
+coins.
+In the second example he can put the five coins in a different jar each. In
+the worst case he will point at an empty jar three times so he will need five
+total moves to get two coins. There is no way to guarantee a win with fewer
+than five moves.

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+Case #1: 4
+Case #2: 5
+Case #3: 5
+Case #4: 1
+Case #5: 9
+Case #6: 559
+Case #7: 928192
+Case #8: 7
+Case #9: 338
+Case #10: 72412
+Case #11: 5
+Case #12: 304
+Case #13: 671185
+Case #14: 5
+Case #15: 647
+Case #16: 198959
+Case #17: 5
+Case #18: 787
+Case #19: 328587
+Case #20: 1
+Case #21: 1499999
+Case #22: 1000000
+Case #23: 999999
+Case #24: 500001
+Case #25: 1000000
+Case #26: 12391
+Case #27: 999991
+Case #28: 1
+Case #29: 1000
+Case #30: 1337
+Case #31: 56

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+<p>David is labelling boxes in a giant warehouse. He has a *lot* of boxes to
+label, but unfortunately his labeling machine is broken, so only some of the
+letters work. In order to be efficient, David labels the boxes by first using
+every possible 1-letter label in alphabetical order, then using every possible
+2-letter label in alphabetical order, then every 3-letter label, etc.</p>
+<p>For example, suppose only the letters 'D', 'T', and 'Z' work. David would
+label the first 15 boxes as follows: D, T, Z, DD, DT, DZ, TD, TT, TZ, ZD, ZT,
+ZZ, DDD, DDT, DDZ. The first box is considered box #1, not box #0.</p>
+<p>Given a set of working letters <strong>L</strong> on David's labelling
+machine and a number <strong>N</strong> of boxes to label, return the label on
+the last box.</p>
+<h2>Input</h2>
+<p>
+The first line of the input consists of a single integer <strong>T</strong>, the number of test
+cases. <br />
+Each test case consists of the string <strong>L</strong> and the integer <strong>N</strong>, separated by a space. </p>
+<h2>Output</h2>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by the label on the last box.</p>
+<h2>Constraints</h2>
+<p>
+1 &le; <strong>T</strong> &le; 20 <br />
+1 &le; length(<strong>L</strong>) &le; 25 <br />
+<strong>L</strong> will be in alphabetical order, consist of only uppercase letters A-Z, and contain each letter at most once <br />
+1 &le; <strong>N</strong> &le; 2<sup>63</sup>-1 <br />
+The test cases will be designed so that no label is longer than 50 letters<br />
+</p>

2014/round1/labelmaker.in ADDED Viewed

	@@ -0,0 +1,54 @@

+53
+EHT 34
+ABCEFKO 4296473
+ACEHKMPRTU 4125383079316
+CDEGHIKLOSUWY 8333092520403744490
+ADEFHNOPSUVY 3365973428406169086
+ACEGINPRTW 216739905614156
+ADELSV 17951
+EFZ 32
+BORT 301
+CGOS 232
+BCJLSU 57129589
+ABCEKLMNPQRTUVXZ 1768121230346226325
+ACDFKLPQRTVWXYZ 4377150318864029777
+ABCDEFGHIJKLNPQRSTUWXYZ 2786177327716752394
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+DNU 1638316335360577913
+ABCDEFGHIJKLMNOPQRSTUVXYZ 8883877996430784020
+ABCDEFGJKLMNOPQRSTVWXYZ 7500116989582893490
+ABCDEFGHIKLMNOPQRSTUWXYZ 7287455102662719573
+ABCFGHJKMPQRSUWXYZ 4167747996316020220
+AEFGHINPTUVXY 2728835088585628917
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+ABCDEFHILMNOQRSTUVWXYZ 8694095846111680941
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+AEHI 3162899471468513059
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+ASVXY 4497350103187099823
+BCEFGHIJKLMNOQRUWX 2521148479268919809
+ABCDEFHJLMOPQSTVXYZ 8133275048742667438
+ABCDEFGIJKLMNOPQRSTUVWXYZ 46161240430628997
+AENX 6006165053007207027
+EGOQZ 2252821188768047387
+BCDEFGIKLMOPQRTUVWXYZ 3656373470406921887
+ADFJKLNPRUVWZ 7094110536991615573
+BCDEGILNQVWX 7127002846485494400
+GOQRSV 6903040442723570976
+CDEFGHIKLMNOPQRUVZ 6306903453412365520
+Z 50
+ABC 9223372036854775807

2014/round1/labelmaker.md ADDED Viewed

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+David is labelling boxes in a giant warehouse. He has a *lot* of boxes to
+label, but unfortunately his labeling machine is broken, so only some of the
+letters work. In order to be efficient, David labels the boxes by first using
+every possible 1-letter label in alphabetical order, then using every possible
+2-letter label in alphabetical order, then every 3-letter label, etc.
+For example, suppose only the letters 'D', 'T', and 'Z' work. David would
+label the first 15 boxes as follows: D, T, Z, DD, DT, DZ, TD, TT, TZ, ZD, ZT,
+ZZ, DDD, DDT, DDZ. The first box is considered box #1, not box #0.
+Given a set of working letters **L** on David's labelling machine and a number
+**N** of boxes to label, return the label on the last box.
+## Input
+The first line of the input consists of a single integer **T**, the number of
+test cases.
+Each test case consists of the string **L** and the integer **N**, separated
+by a space.
+## Output
+For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
+followed by the label on the last box.
+## Constraints
+1 ≤ **T** ≤ 20
+1 ≤ length(**L**) ≤ 25
+**L** will be in alphabetical order, consist of only uppercase letters A-Z, and contain each letter at most once
+1 ≤ **N** ≤ 263-1
+The test cases will be designed so that no label is longer than 50 letters

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+Case #1: THE
+Case #2: FACEBOOK
+Case #3: HACKERCUPTEAM
+Case #4: WISHESYOUGOODLUCK
+Case #5: ANDHOPESYOUHAVEFUN
+Case #6: CANPETRWINAGAIN
+Case #7: DALVES
+Case #8: ZEF
+Case #9: TORB
+Case #10: OGCS
+Case #11: SJSUCSCLUB
+Case #12: ANNPPZVEAVPTZQPK
+Case #13: RYYADDFVZDLKYKTC
+Case #14: ELCCWRKSFUNYKP
+Case #15: YDDTSUSYEBUVYYDQ
+Case #16: NIJFJKNNTTTPTKIIIJPI
+Case #17: CCZSIYYWKLLLLJHJSW
+Case #18: BAYBYGYLGAGLFAGBHHF
+Case #19: MOMXMPMOPOXMOXXPPXXOXXPMPMOPPOMX
+Case #20: JQSAAVLHAJSRXHHCL
+Case #21: DFFHLLFDFLLDHHFHDLDFFFHHFHHHFLFF
+Case #22: CIQSCDTIPTLZGHQAQ
+Case #23: LDUNDNQXVNKNCQV
+Case #24: DVEUKQQMVBMKWAKA
+Case #25: ACPPBQEFZPEBZAH
+Case #26: AORFKOHPCBFOUIAJ
+Case #27: RKXRHRAAXXHAWOWWPAKHR
+Case #28: UDNDUDNUUDDUNNDUDNUDDNNUUUNUNUNNDUDUNN
+Case #29: EYADEGTXILTDJT
+Case #30: PWEOGBYEKFDCGE
+Case #31: HGNAXYLOBNYFHW
+Case #32: QBBSAQPSUYXJMUF
+Case #33: GAFYTYAXPXUYYPGIV
+Case #34: DOXLRCSUTIRANV
+Case #35: AITFZWTLHHVZYMQ
+Case #36: AAXOORSDIFRORTTATST
+Case #37: SRSBGRAKKORGCBGUCS
+Case #38: CLACJALJCBTTJQN
+Case #39: EEHHAIIHAHHIIHHEHHIIEAEEIAEIAIH
+Case #40: AFIEMVDZVDDWIRIR
+Case #41: SXYSAASYVAVSYXSVAAVXXAXVSXV
+Case #42: HOBHIMLGGQINCCG
+Case #43: MCHQFTBBELZFAFB
+Case #44: TIZWGPUBKFJW
+Case #45: XXNAAEAXENEXXEEXENENAENXAEEAEXN
+Case #46: EGGOQQGGOGOQOGOZQOZZQQZOZGG
+Case #47: BCRBMPTPIEZTGQR
+Case #48: UPNRNFRPDAVDWLNWN
+Case #49: DCIIWNQIVQDLDWIGDX
+Case #50: GOROQVGVQQQSVGROOVOVSOOQV
+Case #51: UQRRQIVIOLKFCFF
+Case #52: ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+Case #53: ACACCCBBCCCBBACBCAACCABCBCBABABCCABACBBA

2014/round1/preventing_alzheimers.html ADDED Viewed

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+<p>
+It is a truth universally acknowledged that a grandparent in possession of a good fortune must furnish his or her grandchildren with cash on their birthdays. Your usual approach is to give each of your <strong>N</strong> grandchildren a number of dollars equal to their age,  (That means 0 dollars for newborns; it's important that they learn what a rough place the world is from the very start).
+</p>
+<p>
+One of your younger, and more precocious, grandchildren, Elly, has read online that trying out new things is a good way to prevent Alzheimer's. So, out of concern for your mental well-being (and in the hopes that she might receive more money), she's posed a new distribution scheme. "If any two grandchildren compare the size of their presents, they should find that both presents are divisible by an integer <strong>K</strong>. They should also find that there is no larger integer that divides the size of both presents," she states.
+</p>
+<p>
+Well, that seems harmless enough, you think. Of course, each grandchild will still have to receive at least as much money as they would have under the old scheme, to avoid any family drama. As you're getting on in years, your mathematical prowess isn't what it used to be. It would be easier to write a program that computes the additional drain on your pocketbook.
+</p>
+<p>
+Note that 0 is divisible by all other numbers.
+</p>
+<h3>Input</h3>
+<p>
+The first line of the input consists of a single integer <strong>T</strong>, the number of test
+cases. <br />
+Each test case starts with a line with the integers <strong>N</strong> and <strong>K</strong>.<br />
+The next line consists of the ages of your grandchildren as <strong>N</strong> integers <strong>A<sub>1</sub></strong>, <strong>A<sub>2</sub></strong>, ..., <strong>A<sub>N</sub></strong>.<br/ >
+</p>
+<h3>Output</h3>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by the minimum extra amount of money you would have to spend compared to giving everyone money equal to their age.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <strong>T</strong> &le; 20<br />
+2 &le; <strong>N</strong> &le; 20<br />
+1 &le; <strong>K</strong> &le; 20<br />
+0 &le; <strong>A<sub>i</sub></strong> &le; 50 <br />
+</p>
+<h3>Examples</h3>
+<p>
+In the first example, you would have to pay 2 to one of them and 3 to the other. The total cost would be 5. Under the old constraints, both grandchildren would get 2, for a total sum of 4. The answer is 5-4 = 1. You can't pay 2 to both, because their gifts would be divisible by 2 as well as 1.
+</p>
+<p>
+In the second example, a possible solution is to give them 3, 7, 5 and 16 dollars, for a total of 31. Under the old constraints, you would give them a total of 28. The answer is 31-28 = 3.
+</p>
+<p>
+In the third example, all gifts have to be divisible by 3. A possible solution is 6, 21, 51. This is 6 more than the sum of their ages. Note that 6, 18, 51 are all divisible by 3, but 6 and 18 are both divisible by 6 as well, so that solution is not valid.
+</p>

2014/round1/preventing_alzheimers.in ADDED Viewed

	@@ -0,0 +1,113 @@

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+19 12
+3 29 25 5 48 36 3 15 1 10 5 31 9 36 40 9 2 19 32

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+It is a truth universally acknowledged that a grandparent in possession of a
+good fortune must furnish his or her grandchildren with cash on their
+birthdays. Your usual approach is to give each of your **N** grandchildren a
+number of dollars equal to their age, (That means 0 dollars for newborns; it's
+important that they learn what a rough place the world is from the very
+start).
+One of your younger, and more precocious, grandchildren, Elly, has read online
+that trying out new things is a good way to prevent Alzheimer's. So, out of
+concern for your mental well-being (and in the hopes that she might receive
+more money), she's posed a new distribution scheme. "If any two grandchildren
+compare the size of their presents, they should find that both presents are
+divisible by an integer **K**. They should also find that there is no larger
+integer that divides the size of both presents," she states.
+Well, that seems harmless enough, you think. Of course, each grandchild will
+still have to receive at least as much money as they would have under the old
+scheme, to avoid any family drama. As you're getting on in years, your
+mathematical prowess isn't what it used to be. It would be easier to write a
+program that computes the additional drain on your pocketbook.
+Note that 0 is divisible by all other numbers.
+### Input
+The first line of the input consists of a single integer **T**, the number of
+test cases.
+Each test case starts with a line with the integers **N** and **K**.
+The next line consists of the ages of your grandchildren as **N** integers
+**A1**, **A2**, ..., **AN**.
+### Output
+For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
+followed by the minimum extra amount of money you would have to spend compared
+to giving everyone money equal to their age.
+### Constraints
+1 ≤ **T** ≤ 20
+2 ≤ **N** ≤ 20
+1 ≤ **K** ≤ 20
+0 ≤ **Ai** ≤ 50
+### Examples
+In the first example, you would have to pay 2 to one of them and 3 to the
+other. The total cost would be 5. Under the old constraints, both
+grandchildren would get 2, for a total sum of 4. The answer is 5-4 = 1. You
+can't pay 2 to both, because their gifts would be divisible by 2 as well as 1.
+In the second example, a possible solution is to give them 3, 7, 5 and 16
+dollars, for a total of 31. Under the old constraints, you would give them a
+total of 28. The answer is 31-28 = 3.
+In the third example, all gifts have to be divisible by 3. A possible solution
+is 6, 21, 51. This is 6 more than the sum of their ages. Note that 6, 18, 51
+are all divisible by 3, but 6 and 18 are both divisible by 6 as well, so that
+solution is not valid.

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+Case #1: 1
+Case #2: 3
+Case #3: 6
+Case #4: 0
+Case #5: 3
+Case #6: 690
+Case #7: 3015
+Case #8: 1026
+Case #9: 1452
+Case #10: 4034
+Case #11: 1996
+Case #12: 5208
+Case #13: 2973
+Case #14: 2257
+Case #15: 1520
+Case #16: 3773
+Case #17: 19
+Case #18: 1820
+Case #19: 1973
+Case #20: 1838
+Case #21: 3835
+Case #22: 2361
+Case #23: 616
+Case #24: 1945
+Case #25: 969
+Case #26: 697
+Case #27: 5789
+Case #28: 854
+Case #29: 2297
+Case #30: 19
+Case #31: 2948
+Case #32: 1170
+Case #33: 3482
+Case #34: 3344
+Case #35: 4037
+Case #36: 2961
+Case #37: 3424
+Case #38: 1623
+Case #39: 1904
+Case #40: 2486
+Case #41: 1228
+Case #42: 1679
+Case #43: 0
+Case #44: 1758
+Case #45: 55
+Case #46: 499
+Case #47: 2251
+Case #48: 2665
+Case #49: 1275
+Case #50: 1238
+Case #51: 1923
+Case #52: 1676
+Case #53: 4378
+Case #54: 1838
+Case #55: 643
+Case #56: 1298

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+<p>
+In the game of Hold'em Numbers, 4 players play with a deck of <strong>N</strong> cards, where each card has a distinct number from the range [1..<strong>N</strong>] on it.
+Each player is dealt two cards and the player who has the highest sum of the two numbers wins.
+If multiple players have the highest sum, the one of them who holds the highest card wins.
+All 8 cards are dealt simultaneously so it's impossible for two players to have the same card.
+</p>
+<p>
+After seeing your two cards you can bet $1. If you win the hand you get $4 back but if another player wins you lose your dollar.
+You can also fold, in which case you don't win nor lose any money. Your opponents play very aggressively and they will always bet.
+After the winner is determined all cards are reshuffled to play another hand for the total of <strong>H</strong> games.
+It's possible you get dealt the same hand more than once.</p>
+</p>
+<p>
+You want to maximize your winnings and only bet if your expected winnings are strictly greater than zero.
+To help yourself you decided to write a program that for the given deck size and hands you were dealt returns whether you should bet or fold.
+</p>
+<h3>Input</h3>
+The first line of the input consists of a single integer <strong>T</strong>, the number of test
+cases. <br />
+Each test case starts with a line containing two integers <strong>N</strong> and <strong>H</strong><br />
+The subsequent <strong>H</strong> lines each contain two integers, <strong>C1</strong> and <strong>C2</strong>, the cards you were dealt.
+</p>
+<h3>Output</h3>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by a string of <strong>H</strong> characters.
+Each character being either "B" if you should bet, or "F" if should fold. The order of characters corresponds to the order of hands given in the input.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <strong>T</strong> &le; 20 <br />
+8 &le; <strong>N</strong> &le; 100 <br />
+1 &le; <strong>H</strong> &le; 10000 <br />
+1 &le; <strong>C1</strong>, <strong>C2</strong> &le; <strong>N</strong> <br />
+<strong>C1</strong> &ne; <strong>C2</strong>
+</p>
+<h3>Examples</h3>
+<p>In the first three examples we are playing a single hand with a deck of eight cards. The first case is a clear winner so you should bet.
+The second case gives no chance to win and you should fold.
+Finally the third case gives you 40% chance of winning. This is good enough to make the bet profitable.</p>

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+In the game of Hold'em Numbers, 4 players play with a deck of **N** cards,
+where each card has a distinct number from the range [1..**N**] on it. Each
+player is dealt two cards and the player who has the highest sum of the two
+numbers wins. If multiple players have the highest sum, the one of them who
+holds the highest card wins. All 8 cards are dealt simultaneously so it's
+impossible for two players to have the same card.
+After seeing your two cards you can bet $1. If you win the hand you get $4
+back but if another player wins you lose your dollar. You can also fold, in
+which case you don't win nor lose any money. Your opponents play very
+aggressively and they will always bet. After the winner is determined all
+cards are reshuffled to play another hand for the total of **H** games. It's
+possible you get dealt the same hand more than once.
+You want to maximize your winnings and only bet if your expected winnings are
+strictly greater than zero. To help yourself you decided to write a program
+that for the given deck size and hands you were dealt returns whether you
+should bet or fold.
+### Input
+The first line of the input consists of a single integer **T**, the number of
+test cases.
+Each test case starts with a line containing two integers **N** and **H**
+The subsequent **H** lines each contain two integers, **C1** and **C2**, the
+cards you were dealt.
+### Output
+For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
+followed by a string of **H** characters. Each character being either "B" if
+you should bet, or "F" if should fold. The order of characters corresponds to
+the order of hands given in the input.
+### Constraints
+1 ≤ **T** ≤ 20
+8 ≤ **N** ≤ 100
+1 ≤ **H** ≤ 10000
+1 ≤ **C1**, **C2** ≤ **N**
+**C1** ≠ **C2**
+### Examples
+In the first three examples we are playing a single hand with a deck of eight
+cards. The first case is a clear winner so you should bet. The second case
+gives no chance to win and you should fold. Finally the third case gives you
+40% chance of winning. This is good enough to make the bet profitable.

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+<p>
+The princess of the kingdom of Hackadia has been kidnapped by an evil dragon. As always the prince Z.A.Y. is going to try to rescue her. The evil dragon is keeping the princess prisoner in his deepest dungeon, and the prince has to solve a puzzle to get her out safely.
+</p>
+<p>
+There are two straight boards in front of the dungeon, both divided into a large number of sections. Each section contains a sparkling gemstone. Each stone has a color. We will denote these colors with numbers.
+</p>
+<p>
+Let's say these boards <strong>Board<sub>1</sub></strong> and <strong>Board<sub>2</sub></strong> contain <strong>N</strong> and <strong>M</strong> sections respectively. Let's call a pair of integers <strong>x</strong>, <strong>y</strong> a magic pair if they have the following properties:
+<ol>
+<li>0 &le; <strong>x</strong> &lt; <strong>N</strong></li>
+<li>0 &le; <strong>y</strong> &lt; <strong>M</strong></li>
+<li>The set of different colors in <strong>Board<sub>1</sub></strong>[0...<strong>x</strong>] equals the set of different colors in <strong>Board<sub>2</sub></strong>[0...<strong>y</strong>]</li>
+</ol>
+</p>
+<p>
+The prince has asked you to find out how many magic pairs exist for the given two boards, so he can free the princess and become the hero. He will take all the glory from this, so you will have to make do with points in this competition as payment for your help.
+</p>
+<p>
+Since the numbers <strong>N</strong> and <strong>M</strong> might be very large, the colors of the gemstones will be supplied through a pseudo random generator. This works as follows:<br />
+<strong>Board<sub>1</sub></strong>[0] = <strong>x1</strong><br />
+<strong>Board<sub>2</sub></strong>[0] = <strong>x2</strong><br/>
+<strong>Board<sub>1</sub></strong>[<strong>i</strong>] = (<strong>a1</strong> * <strong>Board<sub>1</sub></strong>[(<strong>i</strong>-1) % <strong>N</strong>] + <strong>b1</strong> * <strong>Board<sub>2</sub></strong>[(<strong>i</strong>-1) % <strong>M</strong>] + <strong>c1</strong>) % <strong>r1</strong>, for 0 &lt; <strong>i</strong> &lt; <strong>N</strong><br />
+<strong>Board<sub>2</sub></strong>[<strong>i</strong>] = (<strong>a2</strong> * <strong>Board<sub>1</sub></strong>[(<strong>i</strong>-1) % <strong>N</strong>] + <strong>b2</strong> * <strong>Board<sub>2</sub></strong>[(<strong>i</strong>-1) % <strong>M</strong>] + <strong>c2</strong>) % <strong>r2</strong>, for 0 &lt; <strong>i</strong> &lt; <strong>M</strong><br />
+</p>
+<h3>Input</h3>
+<p>
+The first line of the input consists of a single integer <strong>T</strong>, the number of test
+cases. <br />
+Each test case starts with a line containing the integers <strong>N</strong>, <strong>M</strong> <br />
+The second line of each test case contains five integers <strong>x1</strong>, <strong>a1</strong>, <strong>b1</strong>, <strong>c1</strong>, <strong>r1</strong><br/>
+The third line of each test case contains five integers <strong>x2</strong>, <strong>a2</strong>, <strong>b2</strong>, <strong>c2</strong>, <strong>r2</strong><br />
+</p>
+<h3>Output</h3>
+<p>
+For each test case <strong>i</strong> numbered from 1 to <strong>T</strong>, output "Case #<strong>i</strong>: ", followed by the number of magic pairs for the two boards.
+</p>
+<h3>Constraints</h3>
+<p>
+1 &le; <strong>T</strong> &le; 20 <br />
+1 &le; <strong>N</strong>, <strong>M</strong> &le; 10^6<br />
+0 &le; <strong>x1</strong>, <strong>x2</strong>, <strong>a1</strong>, <strong>a2</strong>, <strong>b1</strong>, <strong>b2</strong>, <strong>c1</strong>, <strong>c2</strong> &le; 10^9<br />
+1 &le; <strong>r1</strong>, <strong>r2</strong> &le; 10^9 <br />
+</p>
+<h3>Examples</h3>
+The first example produces the following boards:<br />
+<strong>Board<sub>1</sub></strong> = [0, 3, 2, 0, 4, 2, 1, 3]<br />
+<strong>Board<sub>2</sub></strong> = [0, 4, 2, 1, 4, 3]<br />
+There are 3 magic pairs:<br />
+pair(0, 0) ==&gt; (0)<br>
+pair(6, 5) ==&gt; (0, 1, 2, 3, 4)<br>
+pair(7, 5) ==&gt; (0, 1, 2, 3, 4)<br>