Datasets:

hackercupai
/

hackercup

@@ -54,3 +54,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 *.jpeg filter=lfs diff=lfs merge=lfs -text
 *.webp filter=lfs diff=lfs merge=lfs -text
 2012/finals/possible_medians.in filter=lfs diff=lfs merge=lfs -text

 *.jpeg filter=lfs diff=lfs merge=lfs -text
 *.webp filter=lfs diff=lfs merge=lfs -text
 2012/finals/possible_medians.in filter=lfs diff=lfs merge=lfs -text
+2013/finals/archiver.in filter=lfs diff=lfs merge=lfs -text

2013/finals/archiver.html ADDED Viewed

	@@ -0,0 +1,28 @@

+<p>You are writing a new revolutionary archiver. The archive is essentially a
+pair of non-decreasing sequences of integers of equal length <strong>K</strong>: <strong>0&le;x<sub>1</sub>&le;...&le;x<sub>k</sub></strong> and
+<strong>0&le;y<sub>1</sub>&le;...&le;y<sub>k</sub></strong>.</p>
+<p>
+The decompression algorithm proceeds as follows:
+<ol>
+<li>Sequence <strong>(0,0), (x<sub>1</sub>,y<sub>1</sub>), ... (x<sub>k</sub>,y<sub>k</sub>), (x<sub>k</sub>, 0), (0, 0)</strong> defines a polygon <strong>P</strong></li>
+<li>Starting from the point <strong>(0,0)</strong>, increase either <strong>x</strong> or <strong>y</strong> coordinate by 1 without
+moving outside of <strong>P</strong>. If both moves are available, you should increase y.
+After each step write <strong>0</strong> to output if incremented <strong>x</strong> or <strong>1</strong> otherwise.</li>
+<li>Repeat step 2 until you end up in point <strong>(x<sub>k</sub>,y<sub>k</sub>)</strong>.</li>
+</ol>
+</p>
+<p>Example: decompression of sequence <strong>(3,4), (7,6), (7,8)</strong> will produce string <strong>010101100100111</strong>.</p>
+<p>Your task is to write a compression rate calculator, that is given
+binary string s find the smallest value of <strong>K</strong> for which there exists archive
+that decompresses to s.</p>
+<h2>Input</h2>
+<p>
+The first line contains a single integer <strong>T</strong>, <strong>T</strong> &le; 20. <strong>T</strong> test cases follow, where each test case consists of one binary string with length <strong>&le; 1,000,000</strong>.
+</p>
+<h2>Output</h2>
+<p>Output a single line containing the smallest possible <strong>K</strong>.</p>

2013/finals/archiver.in ADDED Viewed

	@@ -0,0 +1,3 @@

+version https://git-lfs.github.com/spec/v1
+oid sha256:02c72140d253087b17bf251243f140530d0efa0cbeae2c2f1434dca789811a7a
+size 53000149

2013/finals/archiver.md ADDED Viewed

	@@ -0,0 +1,27 @@

+You are writing a new revolutionary archiver. The archive is essentially a
+pair of non-decreasing sequences of integers of equal length **K**:
+**0≤x1≤...≤xk** and **0≤y1≤...≤yk**.
+The decompression algorithm proceeds as follows:
+  1. Sequence **(0,0), (x1,y1), ... (xk,yk), (xk, 0), (0, 0)** defines a polygon **P**
+  2. Starting from the point **(0,0)**, increase either **x** or **y** coordinate by 1 without moving outside of **P**. If both moves are available, you should increase y. After each step write **0** to output if incremented **x** or **1** otherwise.
+  3. Repeat step 2 until you end up in point **(xk,yk)**.
+Example: decompression of sequence **(3,4), (7,6), (7,8)** will produce string
+**010101100100111**.
+Your task is to write a compression rate calculator, that is given binary
+string s find the smallest value of **K** for which there exists archive that
+decompresses to s.
+## Input
+The first line contains a single integer **T**, **T** ≤ 20. **T** test cases
+follow, where each test case consists of one binary string with length **≤
+1,000,000**.
+## Output
+Output a single line containing the smallest possible **K**.

2013/finals/archiver.out ADDED Viewed

	@@ -0,0 +1,63 @@

+Case #1: 1
+Case #2: 3
+Case #3: 1
+Case #4: 2
+Case #5: 2
+Case #6: 1
+Case #7: 6
+Case #8: 2
+Case #9: 2
+Case #10: 1
+Case #11: 6318
+Case #12: 6191
+Case #13: 111
+Case #14: 146
+Case #15: 5903
+Case #16: 10
+Case #17: 11
+Case #18: 868
+Case #19: 178535
+Case #20: 178229
+Case #21: 100
+Case #22: 38910
+Case #23: 178183
+Case #24: 805
+Case #25: 39091
+Case #26: 20
+Case #27: 33
+Case #28: 38890
+Case #29: 177854
+Case #30: 925
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+Case #32: 39262
+Case #33: 38829
+Case #34: 958
+Case #35: 15
+Case #36: 124
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+Case #38: 124
+Case #39: 178060
+Case #40: 115
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+Case #58: 831
+Case #59: 6253
+Case #60: 38800
+Case #61: 2
+Case #62: 2
+Case #63: 5

2013/finals/colored_trees.html ADDED Viewed

	@@ -0,0 +1,14 @@

+<p>You are given two integers <strong>N</strong> and <strong>K</strong>, 1 &le; <strong>N</strong> &le; 1000, 1 &le; <strong>K</strong> &le; 10<sup>9</sup>.
+Your task is to calculate how many distinct trees with <strong>N</strong> vertices there are with each vertex colored with one of <strong>K</strong> colors. Multiple vertices can have the same color, and not all colors need to be used. Two trees t1 and t2 are considered identical if there exists a
+bijective function f from vertices of t1 to vertices of t2 such that each vertex
+x in t1 is colored the same as f(x) in t2 and each pair of
+vertices x, y in t1 is connected by an edge if and only if f(x) and f(y) are
+connected by an edge in t2. A bijective function is a function that is both one-to-one and onto, meaning that f(x) = f(y) if and only if x = y, and for every vertex y in t2, there exists x in t1, such that f(x) = y.</p>
+<h2>Input</h2>
+<p>The first line contains a single integer <strong>T</strong>, <strong>T</strong> &le; 20. <strong>T</strong> test cases follow, where each test case consists of two integers: <strong>N</strong> and <strong>K</strong>.</p>
+<h2>Output</h2>
+<p>Output one single line with the number of colored trees.
+Since this number might be very big, output it modulo <strong>1,000,000,007</strong>.</p>
+<h2>Examples</h2>
+<img src="https://fbcdn-dragon-a.akamaihd.net/cfs-ak-ash3/676523/506/293813004081038_-/tmp-/IV3SsS" />

2013/finals/colored_trees.in ADDED Viewed

	@@ -0,0 +1,61 @@

+60
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+2 10
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2013/finals/colored_trees.md ADDED Viewed

	@@ -0,0 +1,27 @@

+You are given two integers **N** and **K**, 1 ≤ **N** ≤ 1000, 1 ≤ **K** ≤ 109.
+Your task is to calculate how many distinct trees with **N** vertices there
+are with each vertex colored with one of **K** colors. Multiple vertices can
+have the same color, and not all colors need to be used. Two trees t1 and t2
+are considered identical if there exists a bijective function f from vertices
+of t1 to vertices of t2 such that each vertex x in t1 is colored the same as
+f(x) in t2 and each pair of vertices x, y in t1 is connected by an edge if and
+only if f(x) and f(y) are connected by an edge in t2. A bijective function is
+a function that is both one-to-one and onto, meaning that f(x) = f(y) if and
+only if x = y, and for every vertex y in t2, there exists x in t1, such that
+f(x) = y.
+## Input
+The first line contains a single integer **T**, **T** ≤ 20. **T** test cases
+follow, where each test case consists of two integers: **N** and **K**.
+## Output
+Output one single line with the number of colored trees. Since this number
+might be very big, output it modulo **1,000,000,007**.
+## Examples
+![](https://fbcdn-dragon-a.akamaihd.net/cfs-ak-
+ash3/676523/506/293813004081038_-/tmp-/IV3SsS)

2013/finals/colored_trees.out ADDED Viewed

	@@ -0,0 +1,60 @@

+Case #1: 1
+Case #2: 55
+Case #3: 2
+Case #4: 6
+Case #5: 96237
+Case #6: 106
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+Case #53: 992415400
+Case #54: 299991045
+Case #55: 894288598
+Case #56: 963648258
+Case #57: 839265476
+Case #58: 853908598
+Case #59: 622783661
+Case #60: 555645540

2013/finals/minesweeping.html ADDED Viewed

	@@ -0,0 +1,17 @@

+Do you know Minesweeper, the famous video game?  The player is initially presented with a grid of undifferentiated squares. Some randomly selected squares, unknown to the player, are designated to contain mines. One square can contain at most one mine.<br>
+<br>
+The game is played by revealing squares of the grid, typically by clicking them. After that, a digit is revealed in the square, indicating the number of adjacent squares (under 8-way connectivity, that is, if two squares share either an edge or a corner, they are considered adjacent) that contain mines. If this number is zero then the surrounding squares are automatically also revealed. This process applies recursively and automatically every time a new square with count zero is revealed.<br>
+<br>
+Now, given a Minesweeper situation, you need to check if it is possible that such a situation can occur after <strong>exactly</strong> 1 click on the grid. Note that the game is designed in such a way, that the first clicked square never contains a mine.<br>
+<br>
+<h2>Input:</h2>
+The first line contains a single integer <strong>T</strong>, <strong>T</strong> &le; 20. <br>
+Then <strong>T</strong> test cases follow.<br>
+The first line of each test case contains two integers <strong>n</strong>, <strong>m</strong> which indicate the size of the grid (<strong>1 &le; n &le; 16, 1 &le; m &le; 32</strong>).<br>
+<strong>n</strong> lines follow, each line contains <strong>m</strong> characters describing the situation of the grid.<br>
+The meaning of the characters are as follows:<br>
+x: the square is not revealed after the first click<br>
+0 - 8: the number of mines that are adjacent to this square<br>
+<br>
+<h2>Output:</h2>
+Output a single line containing 'Yes' if the situation is valid after 1 click, and 'No' otherwise (quotes for clarity).<br>

2013/finals/minesweeping.in ADDED Viewed

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2013/finals/minesweeping.md ADDED Viewed

	@@ -0,0 +1,36 @@

+Do you know Minesweeper, the famous video game? The player is initially
+presented with a grid of undifferentiated squares. Some randomly selected
+squares, unknown to the player, are designated to contain mines. One square
+can contain at most one mine.
+The game is played by revealing squares of the grid, typically by clicking
+them. After that, a digit is revealed in the square, indicating the number of
+adjacent squares (under 8-way connectivity, that is, if two squares share
+either an edge or a corner, they are considered adjacent) that contain mines.
+If this number is zero then the surrounding squares are automatically also
+revealed. This process applies recursively and automatically every time a new
+square with count zero is revealed.
+Now, given a Minesweeper situation, you need to check if it is possible that
+such a situation can occur after **exactly** 1 click on the grid. Note that
+the game is designed in such a way, that the first clicked square never
+contains a mine.
+## Input:
+The first line contains a single integer **T**, **T** ≤ 20.
+Then **T** test cases follow.
+The first line of each test case contains two integers **n**, **m** which
+indicate the size of the grid (**1 ≤ n ≤ 16, 1 ≤ m ≤ 32**).
+**n** lines follow, each line contains **m** characters describing the situation of the grid.
+The meaning of the characters are as follows:
+x: the square is not revealed after the first click
+0 - 8: the number of mines that are adjacent to this square
+## Output:
+Output a single line containing 'Yes' if the situation is valid after 1 click,
+and 'No' otherwise (quotes for clarity).

2013/finals/minesweeping.out ADDED Viewed

	@@ -0,0 +1,20 @@

+Case #1: Yes
+Case #2: No
+Case #3: Yes
+Case #4: Yes
+Case #5: No
+Case #6: Yes
+Case #7: No
+Case #8: Yes
+Case #9: No
+Case #10: Yes
+Case #11: No
+Case #12: Yes
+Case #13: Yes
+Case #14: No
+Case #15: Yes
+Case #16: Yes
+Case #17: No
+Case #18: Yes
+Case #19: Yes
+Case #20: No

2013/finals/teleports.html ADDED Viewed

	@@ -0,0 +1,7 @@

+<p>Your house has <strong>2 &le; N &le; 500,000</strong> distinct rooms. None of the rooms have doors, but every room has a one way teleport which takes you to a different room. The same teleport will always go to the same room. You want to make sure that every room can be reached from every room, via a series of teleports. To do this, you are allowed to change the destination of some (or all) of the teleports.</p>
+<p>What is the sum of the minimum number of teleports you have to change to achieve this, over all possible different starting configurations? Two starting configurations are different if for some room, the outgoing teleport goes to different rooms in the two configurations.</p>
+<h2>Input</h2>
+<p>The first line contains a single integer <strong>T</strong>, <strong>T</strong> &le; 20. <strong>T</strong> test cases follow, where each test case consists of one integer: <strong>N</strong></p>
+<h2>Output</h2>
+<p>Output one single line with the sum of the minimum number of teleports you have to change over all possible different starting configurations. Since this number might be very big, output it modulo <strong>1,000,000,007</strong></p>

2013/finals/teleports.in ADDED Viewed

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

+31
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2013/finals/teleports.md ADDED Viewed

	@@ -0,0 +1,23 @@

+Your house has **2 ≤ N ≤ 500,000** distinct rooms. None of the rooms have
+doors, but every room has a one way teleport which takes you to a different
+room. The same teleport will always go to the same room. You want to make sure
+that every room can be reached from every room, via a series of teleports. To
+do this, you are allowed to change the destination of some (or all) of the
+teleports.
+What is the sum of the minimum number of teleports you have to change to
+achieve this, over all possible different starting configurations? Two
+starting configurations are different if for some room, the outgoing teleport
+goes to different rooms in the two configurations.
+## Input
+The first line contains a single integer **T**, **T** ≤ 20. **T** test cases
+follow, where each test case consists of one integer: **N**
+## Output
+Output one single line with the sum of the minimum number of teleports you
+have to change over all possible different starting configurations. Since this
+number might be very big, output it modulo **1,000,000,007**

2013/finals/teleports.out ADDED Viewed

	@@ -0,0 +1,31 @@

+Case #1: 0
+Case #2: 6
+Case #3: 1720
+Case #4: 435035973
+Case #5: 93930085
+Case #6: 445549105
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+Case #10: 638779500
+Case #11: 547781467
+Case #12: 625115175
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+Case #14: 408509902
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+Case #16: 87704054
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+Case #19: 111081362
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+Case #21: 613941079
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+Case #23: 606986861
+Case #24: 344050087
+Case #25: 959115003
+Case #26: 362655882
+Case #27: 266807035
+Case #28: 436450540
+Case #29: 991573175
+Case #30: 9962767
+Case #31: 314954537

2013/quals/balanced_smileys.html ADDED Viewed

	@@ -0,0 +1,29 @@

+<p>Your friend John uses a lot of emoticons when you talk to him on Messenger. In addition to being a person who likes to express himself through emoticons, he hates unbalanced parenthesis so much that it makes him go :(</p>
+<p>Sometimes he puts emoticons within parentheses, and you find it hard to tell if a parenthesis really is a parenthesis or part of an emoticon.</p>
+<p>A message has balanced parentheses if it consists of one of the following:</p>
+<ul>
+<li>- An empty string ""</li>
+<li>- One or more of the following characters: 'a' to 'z', ' ' (a space) or  ':' (a colon)</li>
+<li>- An open parenthesis '(', followed by a message with balanced parentheses, followed by a close parenthesis ')'. </li>
+<li>- A message with balanced parentheses followed by another message with balanced parentheses.
+<li>- A smiley face ":)" or a frowny face ":("</li>
+</ul>
+<p>Write a program that determines if there is a way to interpret his message while leaving the parentheses balanced. </p>
+<h2>Input</h2>
+<p>
+The first line of the input contains a number <b>T </b>(1 &le; <b>T</b> &le; 50), the number of test cases. <br/>
+The following <b>T</b> lines each contain a message of length <b>s</b> that you got from John.</p>
+<h2>Output</h2>
+<p>
+For each of the test cases numbered in order from 1 to <b>T</b>, output "Case #i: " followed by a string stating whether or not it is possible that the message had balanced parentheses. If it is, the string should be "YES", else it should be "NO" (all quotes for clarity only)</p>
+<h2>Constraints</h2>
+<ul>
+<li>1 &le; length of <b>s</b> &le; 100</li>
+</ul>
+<p>&nbsp;</p>

2013/quals/balanced_smileys.in ADDED Viewed

	@@ -0,0 +1,63 @@

+62
+hacker cup: started :):)
+:((
+)(
+i am sick today (:()
+(:)
+(:a))
+:):)(::)a)()a((:a(a(((((a):)))(::()))(a)):))((a))):a:():)):()a(())aa(a(:))(aa()()::)):)(())
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+((:):::(()()):)(()()():())aaa)(:(a:)a:((())a(((a(:())aa():a:)((()):)(()(:)(a())a:()a)a():(
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+():)((()():(:())))::aa((((:(((:)))::a:(:))()a)):(a):::((()a((a(aa(():))(():())((::a)a)):)()
+a(a)::(((::)))())((a)(:((:a())):((::(:()(a)))i am trapped in a test case generator :(:(a(:::))
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+a()(())(())(:)(:((:aa)()(a(():()()a)a()():(((:))()(()(a:(:aa)())))(:::()((::aa)))))(:)(((()())
+()((:(:)()((:aa)()(():))((a)(:(a(()))((()()a):()())aa)((:())a()(:)a()))a)aaaa)((a(()(a)a(()))))
+a(a)(a)::(a:()a()a)():)(:)aaa)(((a:(())()a):)(()))()(a)aa)a(:)()):a(:((a())a)()(a):a)a(():)
+()(((:(a(():a()((a)()a)a)a(:()))()(a(((:))())(a:)(aa(:a():()():(((a)a)(:a(a(:())a)():)()(())
+aa:((:((a()(()()a(:)::)(:)a)(()a((a(aa((((((()aaa)):()aa):))))()()(((a))))()a)(()()))a())()
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+a(:(((()a)()()a(()()aa(a(a:::aaa(:):)a(a:a((a(())((()((:))))(a()(())():()()(a(()()a)((:)(a))))))))
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+:::)(()::))a:):::()(a(:)(a)a)())::)()(()a)a(a)may the best hacker win:aa:)a()(())aa:::)(:())aa
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+(a())(::)(a))():(((a(()(:))a(:)))(:(:(:((():)(a))(:))(a)():(:(()aa):)(a((())a)a((a):)()(:(
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+::)(a()(::)):):)((()((:)::a:(((:a))(a(:():))a))i love jello:aaaa:(:a:)(:a:(()::(::aa)a)):(:())
+a((aa)(:a()a())()(()((()((a:(a)()aaa()(:::(a()):((:())(()))(((aa:(:a)):):(():)))((a()(()(())))
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+::((:))(((:)(aaa)(a())()(a:)(:)(:)()):)a())aa)())(():a):()::):)a()())a()):):(:a)a):()(a)(a)
+(:a()a)(a)a(aa(()(::)())(:a(a):()a(a()a(()():)))this is a min cost max flow problem(a)((a(()a)))a

2013/quals/balanced_smileys.md ADDED Viewed

	@@ -0,0 +1,36 @@

+Your friend John uses a lot of emoticons when you talk to him on Messenger. In
+addition to being a person who likes to express himself through emoticons, he
+hates unbalanced parenthesis so much that it makes him go :(
+Sometimes he puts emoticons within parentheses, and you find it hard to tell
+if a parenthesis really is a parenthesis or part of an emoticon.
+A message has balanced parentheses if it consists of one of the following:
+  * \- An empty string ""
+  * \- One or more of the following characters: 'a' to 'z', ' ' (a space) or ':' (a colon)
+  * \- An open parenthesis '(', followed by a message with balanced parentheses, followed by a close parenthesis ')'.
+  * \- A message with balanced parentheses followed by another message with balanced parentheses.
+  * \- A smiley face ":)" or a frowny face ":("
+Write a program that determines if there is a way to interpret his message
+while leaving the parentheses balanced.
+## Input
+The first line of the input contains a number **T **(1 ≤ **T** ≤ 50), the
+number of test cases.
+The following **T** lines each contain a message of length **s** that you got
+from John.
+## Output
+For each of the test cases numbered in order from 1 to **T**, output "Case #i:
+" followed by a string stating whether or not it is possible that the message
+had balanced parentheses. If it is, the string should be "YES", else it should
+be "NO" (all quotes for clarity only)
+## Constraints
+  * 1 ≤ length of **s** ≤ 100

2013/quals/balanced_smileys.out ADDED Viewed

	@@ -0,0 +1,62 @@

+Case #1: YES
+Case #2: NO
+Case #3: NO
+Case #4: YES
+Case #5: YES
+Case #6: NO
+Case #7: YES
+Case #8: YES
+Case #9: YES
+Case #10: YES
+Case #11: YES
+Case #12: YES
+Case #13: YES
+Case #14: YES
+Case #15: YES
+Case #16: YES
+Case #17: YES
+Case #18: YES
+Case #19: YES
+Case #20: YES
+Case #21: YES
+Case #22: NO
+Case #23: NO
+Case #24: NO
+Case #25: YES
+Case #26: YES
+Case #27: YES
+Case #28: NO
+Case #29: NO
+Case #30: NO
+Case #31: YES
+Case #32: YES
+Case #33: NO
+Case #34: YES
+Case #35: YES
+Case #36: NO
+Case #37: YES
+Case #38: YES
+Case #39: YES
+Case #40: YES
+Case #41: YES
+Case #42: NO
+Case #43: YES
+Case #44: YES
+Case #45: YES
+Case #46: NO
+Case #47: YES
+Case #48: YES
+Case #49: YES
+Case #50: NO
+Case #51: YES
+Case #52: NO
+Case #53: NO
+Case #54: NO
+Case #55: YES
+Case #56: YES
+Case #57: YES
+Case #58: NO
+Case #59: YES
+Case #60: YES
+Case #61: YES
+Case #62: YES

2013/quals/beautiful_strings.html ADDED Viewed

	@@ -0,0 +1,19 @@

+<p>When John was a little kid he didn't have much to do. There was no internet, no Facebook, and no programs to hack on. So he did the only thing he could... he evaluated the beauty of strings in a quest to discover the most beautiful string in the world.</p>
+<p>Given a string <b>s</b>, little Johnny defined the beauty of the string as the sum of the beauty of the letters in it.</p>
+<p>The beauty of each letter is an integer between 1 and 26, inclusive, and no two letters have the same beauty. Johnny doesn't care about whether letters are uppercase or lowercase, so that doesn't affect the beauty of a letter. (Uppercase 'F' is exactly as beautiful as lowercase 'f', for example.)</p>
+<p>You're a student writing a report on the youth of this famous hacker. You found the string that Johnny considered most beautiful. What is the maximum possible beauty of this string?</p>
+<p><h2>Input</h2>
+The input file consists of a single integer <strong>m</strong> followed by <strong>m</strong> lines.</p>
+<p><h2>Output</h2>
+Your output should consist of, for each test case, a line containing the string "Case #<strong>x</strong>: <strong>y</strong>" where <strong>x</strong> is the case number (with 1 being the first case in the input file, 2 being the second, etc.) and <strong>y</strong> is the maximum beauty for that test case.
+</p>
+<p><h2>Constraints</h2>
+5 &le; <strong>m</strong> &le; 50</strong><br/>
+2 &le; length of <strong>s</strong> &le; 500<br/>
+</p>

2013/quals/beautiful_strings.in ADDED Viewed

	@@ -0,0 +1,51 @@

+50
+ABbCcc
+Good luck in the Facebook Hacker Cup this year!
+Ignore punctuation, please :)
+Sometimes test cases are hard to make up.
+So I just go consult Professor Dalves
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2013/quals/beautiful_strings.md ADDED Viewed

	@@ -0,0 +1,33 @@

+When John was a little kid he didn't have much to do. There was no internet,
+no Facebook, and no programs to hack on. So he did the only thing he could...
+he evaluated the beauty of strings in a quest to discover the most beautiful
+string in the world.
+Given a string **s**, little Johnny defined the beauty of the string as the
+sum of the beauty of the letters in it.
+The beauty of each letter is an integer between 1 and 26, inclusive, and no
+two letters have the same beauty. Johnny doesn't care about whether letters
+are uppercase or lowercase, so that doesn't affect the beauty of a letter.
+(Uppercase 'F' is exactly as beautiful as lowercase 'f', for example.)
+You're a student writing a report on the youth of this famous hacker. You
+found the string that Johnny considered most beautiful. What is the maximum
+possible beauty of this string?
+## Input
+The input file consists of a single integer **m** followed by **m** lines.
+## Output
+Your output should consist of, for each test case, a line containing the
+string "Case #**x**: **y**" where **x** is the case number (with 1 being the
+first case in the input file, 2 being the second, etc.) and **y** is the
+maximum beauty for that test case.
+## Constraints
+5 ≤ **m** ≤ 50**
+2 ≤ length of **s** ≤ 500

2013/quals/beautiful_strings.out ADDED Viewed

	@@ -0,0 +1,50 @@

+Case #1: 152
+Case #2: 754
+Case #3: 491
+Case #4: 729
+Case #5: 646
+Case #6: 1581
+Case #7: 1526
+Case #8: 5991
+Case #9: 5113
+Case #10: 6469
+Case #11: 3558
+Case #12: 3555
+Case #13: 6004
+Case #14: 1336
+Case #15: 3897
+Case #16: 1657
+Case #17: 2475
+Case #18: 1653
+Case #19: 4566
+Case #20: 2802
+Case #21: 4877
+Case #22: 2589
+Case #23: 5433
+Case #24: 5982
+Case #25: 3958
+Case #26: 5749
+Case #27: 1784
+Case #28: 348
+Case #29: 2108
+Case #30: 3593
+Case #31: 4266
+Case #32: 2138
+Case #33: 3974
+Case #34: 1169
+Case #35: 1358
+Case #36: 2962
+Case #37: 3695
+Case #38: 5510
+Case #39: 6059
+Case #40: 2081
+Case #41: 3056
+Case #42: 3191
+Case #43: 5495
+Case #44: 2348
+Case #45: 1811
+Case #46: 6097
+Case #47: 3559
+Case #48: 3953
+Case #49: 2254
+Case #50: 5873

2013/quals/find_the_min.html ADDED Viewed

	@@ -0,0 +1,26 @@

+<p> After sending smileys, John decided to play with arrays. Did you know that hackers enjoy playing with arrays? John has a zero-based index array, <b>m</b>, which contains <b>n</b> non-negative integers. However, only the first <b>k</b> values of the array are known to him, and he wants to figure out the rest. </p>
+<p> John knows the following: for each index <b>i</b>, where <b>k</b> &le; <b>i</b> &lt; <b>n, m</b>[<b>i</b>] is the minimum non-negative integer which is *not* contained in the previous *<b>k</b>* values of <b>m</b>. </p>
+<p> For example, if <b>k</b> = 3, <b>n</b> = 4 and the known values of <b>m</b> are [2, 3, 0], he can figure out that <b>m</b>[3] = 1. </p>
+<p> John is very busy making the world more open and connected, as such, he doesn't have time to figure out the rest of the array. It is your task to help him. </p>
+<p> Given the first <b>k</b> values of <b>m</b>, calculate the <b>n</b><sup>th</sup> value of this array. (i.e. <b>m</b>[<b>n</b> - 1]). </p>
+<p> Because the values of <b>n</b> and <b>k</b> can be very large, we use a pseudo-random number generator to calculate the first <b>k</b> values of <b>m</b>.
+Given non-negative integers <b>a</b>, <b>b</b>, <b>c</b> and positive integer <b>r</b>, the known values of <b>m</b> can be calculated as follows: </p>
+<ul>
+<li><b>m</b>[0] = <b>a</b></li>
+<li><b>m</b>[<b>i</b>] = (<b>b</b> * <b>m</b>[<b>i</b> - 1] + <b>c</b>) % <b>r</b>, 0 &lt; <b>i</b> &lt; <b>k</b></li>
+</ul>
+<p><h3>Input</h3>
+The first line contains an integer <b>T</b> (<b>T</b> &le; 20), the number of test cases.<br/>
+This is followed by <b>T</b> test cases, consisting of 2 lines each.<br/>
+The first line of each test case contains 2 space separated integers, <b>n</b>, <b>k</b> (1 &le; <b>k</b> &le; 10<sup>5</sup>, <b>k</b> &lt; <b>n</b> &le;10<sup>9</sup>).<br/>
+The second line of each test case contains 4 space separated integers <b>a</b>, <b>b</b>, <b>c</b>, <b>r</b> (0 &le; <b>a</b>, <b>b</b>, <b>c</b> &le; 10<sup>9</sup>, 1 &le; <b>r</b> &le; 10<sup>9</sup>). </p>
+<p><h3>Output</h3>
+For each test case, output a single line containing the case number and the <b>n</b><sup>th</sup> element of <b>m</b>. </p>

2013/quals/find_the_min.in ADDED Viewed

	@@ -0,0 +1,73 @@

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+1 1 0 2
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+100000 1 0 1000000000
+1000000000 100000
+1 1 1 1000000000
+1000000000 100000
+999999999 1 999999999 1000000000
+1000000000 100000
+99999 1 99999 100000
+1000000000 1
+12 7 74 12

2013/quals/find_the_min.md ADDED Viewed

	@@ -0,0 +1,42 @@

+After sending smileys, John decided to play with arrays. Did you know that
+hackers enjoy playing with arrays? John has a zero-based index array, **m**,
+which contains **n** non-negative integers. However, only the first **k**
+values of the array are known to him, and he wants to figure out the rest.
+John knows the following: for each index **i**, where **k** ≤ **i** < **n,
+m**[**i**] is the minimum non-negative integer which is *not* contained in the
+previous ***k*** values of **m**.
+For example, if **k** = 3, **n** = 4 and the known values of **m** are [2, 3,
+0], he can figure out that **m**[3] = 1.
+John is very busy making the world more open and connected, as such, he
+doesn't have time to figure out the rest of the array. It is your task to help
+him.
+Given the first **k** values of **m**, calculate the **n**th value of this
+array. (i.e. **m**[**n** \- 1]).
+Because the values of **n** and **k** can be very large, we use a pseudo-
+random number generator to calculate the first **k** values of **m**. Given
+non-negative integers **a**, **b**, **c** and positive integer **r**, the
+known values of **m** can be calculated as follows:
+  * **m**[0] = **a**
+  * **m**[**i**] = (**b** * **m**[**i** \- 1] + **c**) % **r**, 0 < **i** < **k**
+### Input
+The first line contains an integer **T** (**T** ≤ 20), the number of test
+cases.
+This is followed by **T** test cases, consisting of 2 lines each.
+The first line of each test case contains 2 space separated integers, **n**,
+**k** (1 ≤ **k** ≤ 105, **k** < **n** ≤109).
+The second line of each test case contains 4 space separated integers **a**,
+**b**, **c**, **r** (0 ≤ **a**, **b**, **c** ≤ 109, 1 ≤ **r** ≤ 109).
+### Output
+For each test case, output a single line containing the case number and the
+**n**th element of **m**.

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+Case #1: 8
+Case #2: 38
+Case #3: 41
+Case #4: 40
+Case #5: 12
+Case #6: 30
+Case #7: 12
+Case #8: 0
+Case #9: 76
+Case #10: 0
+Case #11: 26
+Case #12: 34
+Case #13: 42
+Case #14: 54
+Case #15: 6
+Case #16: 2
+Case #17: 29
+Case #18: 19
+Case #19: 58
+Case #20: 38
+Case #21: 18389
+Case #22: 3860
+Case #23: 21563
+Case #24: 30023
+Case #25: 19906
+Case #26: 9502
+Case #27: 44581
+Case #28: 25824
+Case #29: 44944
+Case #30: 573
+Case #31: 90002
+Case #32: 90001
+Case #33: 90001
+Case #34: 90001
+Case #35: 9999
+Case #36: 0

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+<p>John is playing a game with his friends. The game's rules are as follows: There is deck of <strong>N</strong> cards from which each person is dealt a hand of <strong>K</strong> cards. Each card has an integer value representing its strength. A hand's strength is determined by the value of the highest card in the hand. The person with the strongest hand wins the round. Bets are placed before each player reveals the strength of their hand.</p>
+<p>John needs your help to decide when to bet. He decides he wants to bet when the strength of his hand is higher than the average hand strength. Hence John wants to calculate the average strength of ALL possible sets of hands. John is very good at division, but he needs your help in calculating the sum of the strengths of all possible hands.</p>
+<h2>Problem</h2>
+<p>You are given an array <strong>a</strong> with <strong>N &le; 10,000</strong> different integer numbers and a number, <strong>K</strong>, where <strong>1 &le; K &le; N</strong>. For all possible subsets of <strong>a</strong> of size <strong>K</strong> find the sum of their maximal elements modulo <strong>1,000,000,007</strong>.</p>
+<h2>Input</h2>
+<p>The first line contains the number of test cases <strong>T</strong>, where <strong> 1 &le; T &le; 25 </strong></p>
+<p>Each case begins with a line containing integers <strong>N</strong> and <strong>K</strong>. The next line contains <strong>N</strong> space-separated numbers <strong>0 &le; a [i] &le; 2,000,000,000</strong>, which describe the array <strong>a</strong>.</p>
+<h2>Output</h2>
+<p>For test case <strong>i</strong>, numbered from <strong>1</strong> to <strong>T</strong>, output "Case #i: ", followed by a single integer, the sum of maximal elements for all subsets of size <strong>K</strong> modulo 1,000,000,007.</p>
+<h2>Example</h2>
+For <strong>a = [3, 6, 2, 8]</strong> and <strong>N = 4</strong> and <strong>K = 3</strong>, the maximal numbers among all triples are <strong>6, 8, 8, 8</strong> and the sum is <strong>30</strong>.

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2013/round1/card_game.md ADDED Viewed

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+John is playing a game with his friends. The game's rules are as follows:
+There is deck of **N** cards from which each person is dealt a hand of **K**
+cards. Each card has an integer value representing its strength. A hand's
+strength is determined by the value of the highest card in the hand. The
+person with the strongest hand wins the round. Bets are placed before each
+player reveals the strength of their hand.
+John needs your help to decide when to bet. He decides he wants to bet when
+the strength of his hand is higher than the average hand strength. Hence John
+wants to calculate the average strength of ALL possible sets of hands. John is
+very good at division, but he needs your help in calculating the sum of the
+strengths of all possible hands.
+## Problem
+You are given an array **a** with **N ≤ 10,000** different integer numbers and
+a number, **K**, where **1 ≤ K ≤ N**. For all possible subsets of **a** of
+size **K** find the sum of their maximal elements modulo **1,000,000,007**.
+## Input
+The first line contains the number of test cases **T**, where ** 1 ≤ T ≤ 25 **
+Each case begins with a line containing integers **N** and **K**. The next
+line contains **N** space-separated numbers **0 ≤ a [i] ≤ 2,000,000,000**,
+which describe the array **a**.
+## Output
+For test case **i**, numbered from **1** to **T**, output "Case #i: ",
+followed by a single integer, the sum of maximal elements for all subsets of
+size **K** modulo 1,000,000,007.
+## Example
+For **a = [3, 6, 2, 8]** and **N = 4** and **K = 3**, the maximal numbers
+among all triples are **6, 8, 8, 8** and the sum is **30**.

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+Case #1: 30
+Case #2: 400
+Case #3: 103
+Case #4: 1122
+Case #5: 2621483
+Case #6: 408515
+Case #7: 1004580
+Case #8: 40755786
+Case #9: 999929
+Case #10: 530567225
+Case #11: 322338625
+Case #12: 221309511
+Case #13: 600929371
+Case #14: 754869952
+Case #15: 50004993
+Case #16: 670107979
+Case #17: 283588254
+Case #18: 493922435
+Case #19: 607347357
+Case #20: 712376460
+Case #21: 313254333
+Case #22: 335296073
+Case #23: 915868532
+Case #24: 460246520
+Case #25: 514894931
+Case #26: 526863429
+Case #27: 464198425
+Case #28: 260278457
+Case #29: 794655996
+Case #30: 855587163
+Case #31: 584262053
+Case #32: 633477677
+Case #33: 681471440
+Case #34: 120711485
+Case #35: 90889566
+Case #36: 947249559
+Case #37: 190955579
+Case #38: 610605848
+Case #39: 832615581
+Case #40: 130056877
+Case #41: 707469732
+Case #42: 705325059
+Case #43: 490200453
+Case #44: 724934349
+Case #45: 624738998
+Case #46: 850880749
+Case #47: 150608471
+Case #48: 180665000
+Case #49: 216384039
+Case #50: 159672993

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+<p>John's friend Peter purchases a new high resolution monitor with dimension <b>W</b> * <b>H</b> where <b>W</b> is the number of pixels in each row (i.e. width) and <b>H</b> is the number of pixels in each column (i.e. height).</p>
+<p>However, there are <b>N</b> dead pixels on the monitor. The <b>i</b>-th dead pixel is located at (<b>x</b>[<b>i</b>], <b>y</b>[<b>i</b>]). (0, 0) is the top-left pixel and (<b>W</b> - 1, <b>H</b> - 1) is the bottom-right pixel. The locations of the dead pixels could be generated by 6 given integers <b>X</b>, <b>Y</b>, <b>a</b>, <b>b</b>, <b>c</b> and <b>d</b> by the following rules. If 2 pixels are at the same location, they are considered the same. It is possible that there are less than <b>N</b> <strong>distinct</strong> dead pixels.</p>
+<p>
+<li><b>x</b>[0] = <b>X</b></li>
+<li><b>y</b>[0] = <b>Y</b></li>
+<li><b>x</b>[<b>i</b>] = (<b>x</b>[<b>i</b> - 1] * <b>a</b> + <b>y</b>[<b>i</b> - 1] * <b>b</b> + 1) % <b>W</b> (for 0 &lt; <b>i</b> &lt; <b>N</b>)</li>
+<li><b>y</b>[<b>i</b>] = (<b>x</b>[<b>i</b> - 1] * <b>c</b> + <b>y</b>[<b>i</b> - 1] * <b>d</b> + 1) % <b>H</b> (for 0 &lt; <b>i</b> &lt; <b>N</b>)</li>
+</p>
+<p>Peter connects his monitor to his computer and opens an image with dimension <b>P</b> (width) * <b>Q</b> (height). How many unique positions can the image be placed so that it can be displayed perfectly (i.e. all pixels of the picture are shown on the monitor)? The image cannot be rotated.</p>
+<h3>Input</h3>
+<p>
+The first line contains an integer <b>T</b>, which is the number of test cases.
+Then <b>T</b> test cases follow.
+Each test case contains 11 integers <b>W</b>, <b>H</b>, <b>P</b>, <b>Q</b>, <b>N</b>, <b>X</b>, <b>Y</b>, <b>a</b>, <b>b</b>, <b>c</b>, <b>d</b>.
+</p>
+<h3>Output</h3><p>
+For each of the test cases numbered in order from 1 to <b>T</b>,
+output "Case #", followed by the case number (with 1 being the first test case), followed by ": ", followed by an integer which is the number of different possible positions for the poster.
+</p>
+<h3>Constraints</h3>
+<li>1 &le; <b>T</b> &le; 20</li>
+<li>1 &le; <b>W</b>, <b>H</b> &le; 40 000</li>
+<li>1 &le; <b>P</b> &le; <b>W</b></li>
+<li>1 &le; <b>Q</b> &le; <b>H</b></li>
+<li>1 &le; <b>N</b> &le; min(1 000 000, <b>W</b> * <b>H</b>)</li>
+<li>1 &le; <b>a</b>, <b>b</b>, <b>c</b>, <b>d</b> &le; <b>100</b></li>
+<li> 0 &le; <b> X </b> &lt; <b> W </b></li>
+<li> 0 &le; <b> Y </b> &lt; <b> H </b></li>
+<p>&nbsp;</p>

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+40
+4 4 2 2 1 0 2 1 2 3 4
+4 4 1 1 3 1 1 2 2 2 2
+6 10 3 2 2 0 0 5 4 3 2
+16 18 5 1 5 10 8 21 27 29 87
+14 15 12 4 4 3 5 84 74 53 68
+196 827 117 730 108 131 477 41 72 11 66
+703 687 125 343 321 68 78 38 8 2 66
+943 715 356 144 449 893 533 86 24 28 90
+192 223 29 170 28 25 108 89 74 40 51
+490 844 318 332 275 241 434 79 99 34 80
+1163 9027 94 86 1000000 1054 6993 92 90 59 19
+1078 5052 143 146 1000000 857 568 15 20 2 7
+9870 591 100 109 1000000 46 313 37 25 63 70
+6503 8478 146 197 1000000 332 8138 33 8 90 43
+5726 4567 144 121 1000000 454 3685 99 81 46 52
+4886 4367 95 87 1000000 3493 4363 2 66 19 64
+5134 2621 141 183 1000000 2309 282 36 56 66 26
+8497 2343 94 193 1000000 5999 1852 70 15 92 16
+4718 7077 134 115 1000000 3964 4597 7 20 29 77
+9883 7515 100 76 1000000 9567 1921 35 86 77 52
+35510 11125 1346 1407 395 35248 9485 18 91 26 9
+28557 13495 1138 1991 385 23252 10801 56 19 77 36
+21995 37911 1150 1245 833 47 23529 19 74 87 95
+24576 30148 1171 1922 740 19787 13047 34 74 34 11
+20133 29990 1305 1623 603 7664 19517 81 90 36 9
+39724 39430 20919 20227 3 7295 34728 28 46 33 14
+39491 39608 20414 20014 3 22564 17425 7 17 95 40
+39078 39880 20882 20735 3 22243 24336 53 36 6 40
+39843 39881 20522 20114 3 11897 5279 74 89 96 58
+39353 39838 20565 20767 3 35517 37854 90 60 17 84
+38850 37146 6 132 1443 28733 35729 1 38 55 58
+35277 38250 2 199 1349 28136 16549 49 90 40 96
+36598 39593 9 164 1449 27518 12034 65 2 51 34
+37637 35252 131 4 1326 1844 2265 72 38 3 79
+38095 39579 180 6 1507 11485 32227 86 32 39 26
+36478 39536 170 1 1442 22516 31242 4 70 37 6
+36402 39273 278 35 1000000 11371 25106 51 98 33 54
+39527 38179 294 327 1000000 12899 20050 56 52 99 46
+35728 35276 139 460 1000000 14745 27690 33 97 8 69
+39954 39461 443 17 1000000 34349 36388 60 98 69 44

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+John's friend Peter purchases a new high resolution monitor with dimension
+**W** * **H** where **W** is the number of pixels in each row (i.e. width) and
+**H** is the number of pixels in each column (i.e. height).
+However, there are **N** dead pixels on the monitor. The **i**-th dead pixel
+is located at (**x**[**i**], **y**[**i**]). (0, 0) is the top-left pixel and
+(**W** \- 1, **H** \- 1) is the bottom-right pixel. The locations of the dead
+pixels could be generated by 6 given integers **X**, **Y**, **a**, **b**,
+**c** and **d** by the following rules. If 2 pixels are at the same location,
+they are considered the same. It is possible that there are less than **N**
+**distinct** dead pixels.
+* **x**[0] = **X**
+* **y**[0] = **Y**
+* **x**[**i**] = (**x**[**i** \- 1] * **a** \+ **y**[**i** \- 1] * **b** \+ 1) % **W** (for 0 < **i** < **N**)
+* **y**[**i**] = (**x**[**i** \- 1] * **c** \+ **y**[**i** \- 1] * **d** \+ 1) % **H** (for 0 < **i** < **N**)
+Peter connects his monitor to his computer and opens an image with dimension
+**P** (width) * **Q** (height). How many unique positions can the image be
+placed so that it can be displayed perfectly (i.e. all pixels of the picture
+are shown on the monitor)? The image cannot be rotated.
+### Input
+The first line contains an integer **T**, which is the number of test cases.
+Then **T** test cases follow. Each test case contains 11 integers **W**,
+**H**, **P**, **Q**, **N**, **X**, **Y**, **a**, **b**, **c**, **d**.
+### Output
+For each of the test cases numbered in order from 1 to **T**, output "Case #",
+followed by the case number (with 1 being the first test case), followed by ":
+", followed by an integer which is the number of different possible positions
+for the poster.
+### Constraints
+* 1 ≤ **T** ≤ 20
+* 1 ≤ **W**, **H** ≤ 40 000
+* 1 ≤ **P** ≤ **W**
+* 1 ≤ **Q** ≤ **H**
+* 1 ≤ **N** ≤ min(1 000 000, **W** * **H**)
+* 1 ≤ **a**, **b**, **c**, **d** ≤ **100**
+* 0 ≤ ** X ** < ** W **
+* 0 ≤ ** Y ** < ** H **

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+Case #1: 7
+Case #2: 15
+Case #3: 32
+Case #4: 197
+Case #5: 16
+Case #6: 0
+Case #7: 0
+Case #8: 0
+Case #9: 174
+Case #10: 0
+Case #11: 5143976
+Case #12: 0
+Case #13: 234800
+Case #14: 137
+Case #15: 0
+Case #16: 7117142
+Case #17: 0
+Case #18: 0
+Case #19: 0
+Case #20: 18323862
+Case #21: 51269087
+Case #22: 35640189
+Case #23: 186206173
+Case #24: 63069325
+Case #25: 58918133
+Case #26: 96242184
+Case #27: 18068400
+Case #28: 86716522
+Case #29: 187837304
+Case #30: 236760710
+Case #31: 1436707606
+Case #32: 1341788941
+Case #33: 1440614287
+Case #34: 1321395055
+Case #35: 1498870465
+Case #36: 1435268809
+Case #37: 1082989958
+Case #38: 8231724
+Case #39: 373470264
+Case #40: 1202810198

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+<p>You are designing a new encryption system that works in the following way:<p/>
+<p>For server-client communication you need a key <strong>k</strong>, composed of <strong>m</strong> sections, each of length <strong>l</strong>, and the key consists only of lowercase characters in the set {a, b, c, d, e, f}. The server has a key <strong>k1</strong> and the client has a key <strong>k2</strong> where:<p/>
+<ul>
+ <li>k1 = f(k). <strong>f</strong> is a function that receives a key and replace some random letters by ? indicating that those characters can be any lowercase letter of the set described before.</li>
+ <li>k2 = f(g(k)). <strong>g</strong> is a function that takes a key and produces a random permutation of its m sections. And <strong>f</strong> is the function defined above.</li>
+</ul>
+<p>For example: let m = 3, l = 2</p>
+<ul>
+ <li>f('abacbc') = '?ba??c'</li>
+ <li>g('abacbc') = 'acbcab' (each section was moved one place to the left).</li>
+</ul>
+<p>Your task is given <strong>k1</strong> and <strong>k2</strong>, find key <strong>k</strong>. If there are several solutions, print the lexicographically smallest key. And if there is no solution at all, print "IMPOSSIBLE" (without the quotes).</p>
+<h2>Input description:</h2>
+<p>The first line has a single integer <strong>T</strong>, which corresponds to the number of test cases. <strong>T</strong> test cases follows: the first line of the test case corresponds to the integer <strong>m</strong>, the second line contains the string <strong>k1</strong> and the third line contains the string <strong>k2</strong>.</p>
+<h2>Constraints:</h2>
+<p>
+ <ul>
+  <li>T &le; 20</li>
+  <li>0 &lt; |k1| &le; 100</li>
+  <li>0 &lt; m &le; 50</li>
+  <li>|k2| = |k1|</li>
+  <li>It is guaranteed that m is always a divisor of |k1|</li>
+  <li>k1 and k2 consist of {a, b, c, d, e, f, ?}</li>
+ </ul>
+<p/>
+<h2>Output description:</h2>
+<p>For test case <strong>i</strong>, numbered from <strong>1</strong> to <strong>T</strong>, output "Case #i: ", followed by the lexicographically smallest key or "IMPOSSIBLE".</p>

2013/round1/security.in ADDED Viewed

	@@ -0,0 +1,322 @@

+107
+2
+abcd
+c?ab
+3
+ab?c?c
+ac?c??
+3
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+2
+aa
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+abcd
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+50
+????????????????????????????????????????????????????????????????????????????????????????????????????
+ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+50
+????????????????????????????????????????????????????????????????????????????????????????????????????
+ffffffffaffffffffbffffafffffffcffffffdffffffbfffffffefffffdfffffffaffffffbffffffaffffffffcffffffffff
+46
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2013/round1/security.md ADDED Viewed

	@@ -0,0 +1,40 @@

+You are designing a new encryption system that works in the following way:
+For server-client communication you need a key **k**, composed of **m**
+sections, each of length **l**, and the key consists only of lowercase
+characters in the set {a, b, c, d, e, f}. The server has a key **k1** and the
+client has a key **k2** where:
+  * k1 = f(k). **f** is a function that receives a key and replace some random letters by ? indicating that those characters can be any lowercase letter of the set described before.
+  * k2 = f(g(k)). **g** is a function that takes a key and produces a random permutation of its m sections. And **f** is the function defined above.
+For example: let m = 3, l = 2
+  * f('abacbc') = '?ba??c'
+  * g('abacbc') = 'acbcab' (each section was moved one place to the left).
+Your task is given **k1** and **k2**, find key **k**. If there are several
+solutions, print the lexicographically smallest key. And if there is no
+solution at all, print "IMPOSSIBLE" (without the quotes).
+## Input description:
+The first line has a single integer **T**, which corresponds to the number of
+test cases. **T** test cases follows: the first line of the test case
+corresponds to the integer **m**, the second line contains the string **k1**
+and the third line contains the string **k2**.
+## Constraints:
+  * T ≤ 20
+  * 0 < |k1| ≤ 100
+  * 0 < m ≤ 50
+  * |k2| = |k1|
+  * It is guaranteed that m is always a divisor of |k1|
+  * k1 and k2 consist of {a, b, c, d, e, f, ?}
+## Output description:
+For test case **i**, numbered from **1** to **T**, output "Case #i: ",
+followed by the lexicographically smallest key or "IMPOSSIBLE".

2013/round1/security.out ADDED Viewed

	@@ -0,0 +1,107 @@

+Case #1: abcd
+Case #2: abacac
+Case #3: IMPOSSIBLE
+Case #4: IMPOSSIBLE
+Case #5: abcd
+Case #6: ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+Case #7: afafafafbfcfdfeffbfbfcfdffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+Case #8: abaccfcccdeefffeffffbbfccbbfbedaffbefcdcfafcfe
+Case #9: IMPOSSIBLE
+Case #10: debbafdfacdfeccedfaddfaacfdadeeffeeceabccbdfdabafbceefbabeadffffeabaaebccebbdb
+Case #11: IMPOSSIBLE
+Case #12: ececbdbabcdadfecaaeaaecdcfacbdabbfbebdaecdcb
+Case #13: IMPOSSIBLE
+Case #14: aecbfaabfbddbaddcadcdcedbcebecefebddbbefbacffaebdacbfaaafbeabbcbaccbbcefddeefbcbceec
+Case #15: IMPOSSIBLE
+Case #16: cadebfbecfbdebfcabcbbfbfceadafeecedadec
+Case #17: IMPOSSIBLE
+Case #18: ddcbaaacaddadcdbdbebfcaeadaffbecdfcfecfbc
+Case #19: afeedbfcaabfeababddffddcfbfbdcaeeecf
+Case #20: aaadfacfefdffdbbefcaccebcccadfeccbbecbbdbecaadfacffaebeacddedcaddbceacdeeffffacdacedcdfbdee
+Case #21: IMPOSSIBLE
+Case #22: bcbcbabcacdefebdeaafeecebaebbebbfbadafefaabbccafd
+Case #23: IMPOSSIBLE
+Case #24: afffebaafdbebeadfbacadfbfecbefddbacdbaefeddb
+Case #25: IMPOSSIBLE
+Case #26: adedfedbddeeacbbfbaadfbfbadfcadbeacffdabd
+Case #27: IMPOSSIBLE
+Case #28: dbffabaaabefbccaeddaaefabcbfcefeeefefdababecafecababafaee
+Case #29: IMPOSSIBLE
+Case #30: ebfefbbbbedafccbfbcfcdededaaeb
+Case #31: cbbfbfabfebaafabefabbeddeccfccaabdeccbbfddadfec
+Case #32: beeefdacdfeacfbdfceecbfdfcbddbbeadfedbdabfecfccabbccedfeebffaadcfeadadcfbcbeeeaf
+Case #33: IMPOSSIBLE
+Case #34: addecbcafdfabaffacacfbfcdcaefaffbefefbaafceadedbfefebe
+Case #35: IMPOSSIBLE
+Case #36: affbefadfbeafbccdfbbafbdcbaaddadebadabbeaaaeeaeaddaccb
+Case #37: IMPOSSIBLE
+Case #38: bafdabecbaacaccaceadaafacdceeaceeebcefcadcaeecba
+Case #39: IMPOSSIBLE
+Case #40: afbbfaeadbdecbabeedaaebefeafcebadeddddbaebdebbaceaacdaebfdcbdcfcbaaecaccccffdefaebdeaabfccacfacfeabe
+Case #41: IMPOSSIBLE
+Case #42: aaccbceaadddcdeaeafbcfcbddfbbadabfaeaadeeeaeebbaacadeeaeeecfdfafcaedbbffceebabbebedcaeebffdadedbdffb
+Case #43: cdefaabdaaaaebcfbddefaecdaceeafced
+Case #44: ffbacbbc
+Case #45: IMPOSSIBLE
+Case #46: bbbdcfabbacbcbfcddfcbfbcfbdbaeabadcdddefeffbefdfedddfffcfddfdfdaaeaeaafbdcefedbbaeee
+Case #47: IMPOSSIBLE
+Case #48: ccdbdcefeffbfbaebbaffbecceffdaeacded
+Case #49: IMPOSSIBLE
+Case #50: eaacceefdefdacfebbbeeedd
+Case #51: IMPOSSIBLE
+Case #52: daacfdcdcafaffcbffdcacabdcaacffdbcaadaccbdcfacadadecdcdeecabedddacecabeabadecdceecfebdcafcadbddbbd
+Case #53: IMPOSSIBLE
+Case #54: cfbaafcaabdaafaeafffeabbdfdddcbeadba
+Case #55: IMPOSSIBLE
+Case #56: ecbfaebfebedbbbdeafacdcdfadeddfacadaafccedbeadebddabeadabdccafcdfbdacacbfabc
+Case #57: IMPOSSIBLE
+Case #58: daabacaacfabeebadaadaadaefabdaaecafaaeaebadbdbdeedbffa
+Case #59: aabcfedcaaffafacadaaaaadaacefaeafaccfadbaaddaabfbdbdbbabcaabbecdebdfbdcceaaecbbdfcafbc
+Case #60: addaaaeaaaaaaaadfadeaadaafeaaaaecdbabaafdbccaaacdbadbe
+Case #61: aeaeaaaacbbbfcaaadadcaacadabecbbaccaedfaafdbfafddfcd
+Case #62: aadebacdbeaacddededbdafbccaeaaccaffcecbabafaddafdeacda
+Case #63: IMPOSSIBLE
+Case #64: adfadadadabeadeabaebaeaacabbceacbadacfccbbeafadcdfcafefcdaeafbbadedaaaceeefaecefabbaddeaafafafda
+Case #65: aaaaaaebacbaaaeadaaeabdceaeaabcaafabadfaeddaaffccfecafffcfefcdecdbbdfadddeedfabeaeec
+Case #66: adbecbbeeabdaaeefbfefaafefcbceaaaaaadaaa
+Case #67: adeabdaddaaaacabeadafbdcbcfdedebaacbcceefadcefebbfbe
+Case #68: aadbdffecbdaadaaaaaaeaadaaaaddaaeafcaebdaabcadfaacafa
+Case #69: IMPOSSIBLE
+Case #70: afaeaaaaaacaaaaaeadacbaaaebdedafccaeccaaaffafdfbeefbdfbde
+Case #71: IMPOSSIBLE
+Case #72: aadaeacabcaacaaaaafcacabadadefcebdfa
+Case #73: IMPOSSIBLE
+Case #74: adadaeaacafecbdaafaadaacaa
+Case #75: IMPOSSIBLE
+Case #76: aaeaaaeaaaabcaafcf
+Case #77: dedcacafccfaedcbaabfaeecbaadfe
+Case #78: babaeaacaaaaaabeaaaaaaeecaacecccdedfffeef
+Case #79: aecacbcabcbafddbdabfaadfebedfaea
+Case #80: baaadceaaaaacabaacbaadbcfffaaaaaabfbadcbacadbceadbafaeafcfdadacfeadaedfcde
+Case #81: IMPOSSIBLE
+Case #82: daadaaadacafdabacaaaaacabbbddf
+Case #83: badacadcaadadfedcddafbadaaadfaefdcdcceadaeedc
+Case #84: ccaaaaaaacdcdecccaaafcaaaaddabcadaebeaaaaaaaaacaaadabaaaaaaaaacfabfedbaaaaafcafbceeeeeaddbbbaafd
+Case #85: IMPOSSIBLE
+Case #86: abaafeaacfafaaaabddae
+Case #87: fcadacdadbbcaededffaaf
+Case #88: eafaaaabaaaabaaaeaeaaaaaaaaafaaaaaafaacaaaafafaaffaaaaaaafaafbeceabaaaaacaebadebbadbbaadbaaaebbdbeaa
+Case #89: facfaabeadaaecabaaaaaffaacacafcaeadaababaefa
+Case #90: aaabadaaaaaaaaaaaaaaaaaaaaaaaeaaadabaaabcfadaaae
+Case #91: afeaaacfaaaaaaeabaaeaaabadaaaaefcbbaaeadabaaeaaafbddadcaffbeaeaaafcabafeaeeabcccafcfb
+Case #92: aaaaaaaaacaaabdaaaaaaaaaaaaabaaacadaaaacfafdbaaaaaafafaaacfeaabaafaaaaaadafb
+Case #93: adfaaaaaaaefacaabcaaaacdaaaaeacaaeffaaaaddadaaaaaabebbbbcfbeabcdfbda
+Case #94: aaacaacaaaeaaaaaaadabfd
+Case #95: addaaaaaaaebacaacaaaaaaaabacfcfeadaf
+Case #96: aaaaaaaebaaaaaaaabadafafea
+Case #97: IMPOSSIBLE
+Case #98: ecaecdaafaccfdcaeacddeaedfdcffbbeffbedaeeaffaac
+Case #99: IMPOSSIBLE
+Case #100: fdfeefaaafeccbdddecefbfaaeccffcbbbbe
+Case #101: IMPOSSIBLE
+Case #102: ebdafbbcdbfcfabeadfadedcaeebcfbed
+Case #103: IMPOSSIBLE
+Case #104: dfecfcbfabbeaaefdddadfbecadaafadcfbcafbefbabcbfebbfddbfaabfeecdfdbaccadbdbacdebcceaaccdb
+Case #105: IMPOSSIBLE
+Case #106: eeafbebdeebbcccefedfbaceadbfabaf
+Case #107: IMPOSSIBLE

2013/round2/cake_cutting.html ADDED Viewed

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+<p>"Happy birthday to you... Happy birthday to you... Happy birthday to Grovyle... Happy birthday to you..."</p>
+<p>Today is Grovyle's birthday and he is going to invite his friends to his birthday party.
+To have an awesome party, each of the attendants should get one piece of cake.
+Your job is to help Grovyle invite as many friends as you can.
+</p>
+<p>
+However, Grovyle's parents are very mean, and make him use the following rules when cutting his cake:
+<li>There is only ONE cylindrical cake.
+<li>Grovyle cuts the cake <b>N</b> times, each cut being perpendicular to the surface of the cake.
+<li>The <b>i</b>-th cut is a broken line with <b>a</b>[<b>i</b>] vertices.
+<li>The knife is only allowed to intersect the edge of the cylindrical cake at the start and end of the cut.
+</p>
+<p>
+What is the maximum number of pieces Grovyle could get?
+</p>
+<h3>Input</h3>
+<p>
+The first line contains an integer <b>T</b>, <b>T</b> &le; 50, indicating the number of test cases.
+Each test case begins with an integer <b>N</b>, 1 &le; <b>N</b> &le; 100, followed by <b>N</b> integers <b>a</b>[<b>i</b>], 0 &le; <b>a</b>[<b>i</b>] &lt; 400, which indicate the number of vertices in the <b>i</b>-th cut.
+</p>
+<h3>Output</h3>
+<p>
+For each test case, output "Case #i: " followed by the maximum number of pieces of cake Grovyle can cut.
+</p>

2013/round2/cake_cutting.in ADDED Viewed

	@@ -0,0 +1,51 @@

+50
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+"Happy birthday to you... Happy birthday to you... Happy birthday to
+Grovyle... Happy birthday to you..."
+Today is Grovyle's birthday and he is going to invite his friends to his
+birthday party. To have an awesome party, each of the attendants should get
+one piece of cake. Your job is to help Grovyle invite as many friends as you
+can.
+However, Grovyle's parents are very mean, and make him use the following rules
+when cutting his cake:
+* There is only ONE cylindrical cake.
+* Grovyle cuts the cake **N** times, each cut being perpendicular to the surface of the cake.
+* The **i**-th cut is a broken line with **a**[**i**] vertices.
+* The knife is only allowed to intersect the edge of the cylindrical cake at the start and end of the cut.
+What is the maximum number of pieces Grovyle could get?
+### Input
+The first line contains an integer **T**, **T** ≤ 50, indicating the number of
+test cases. Each test case begins with an integer **N**, 1 ≤ **N** ≤ 100,
+followed by **N** integers **a**[**i**], 0 ≤ **a**[**i**] < 400, which
+indicate the number of vertices in the **i**-th cut.
+### Output
+For each test case, output "Case #i: " followed by the maximum number of
+pieces of cake Grovyle can cut.

2013/round2/cake_cutting.out ADDED Viewed

	@@ -0,0 +1,50 @@

+Case #1: 7
+Case #2: 7
+Case #3: 10
+Case #4: 14
+Case #5: 63
+Case #6: 1051
+Case #7: 682
+Case #8: 1006
+Case #9: 1342
+Case #10: 481
+Case #11: 73970
+Case #12: 84716
+Case #13: 83486
+Case #14: 78656
+Case #15: 80651
+Case #16: 71303
+Case #17: 72060
+Case #18: 45803
+Case #19: 44303
+Case #20: 63953
+Case #21: 2812106
+Case #22: 3290995
+Case #23: 3438853
+Case #24: 2886103
+Case #25: 3376201
+Case #26: 3475666
+Case #27: 3311551
+Case #28: 3186650
+Case #29: 3257728
+Case #30: 3337336
+Case #31: 52516036
+Case #32: 47244220
+Case #33: 43082563
+Case #34: 47672890
+Case #35: 73732456
+Case #36: 54637991
+Case #37: 50205370
+Case #38: 49955170
+Case #39: 45063431
+Case #40: 31343563
+Case #41: 225027705
+Case #42: 213924470
+Case #43: 203465078
+Case #44: 155734976
+Case #45: 185657015
+Case #46: 229933490
+Case #47: 212850228
+Case #48: 698389451
+Case #49: 741991703
+Case #50: 782437661

2013/round2/permutations.html ADDED Viewed

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+<p>In this problem you need to count number of possible permutations <strong>p</strong> of the first <strong>N</strong> integers,
+given <strong>N-1</strong> constraints of the form <strong>p<sub>i</sub> &lt; p<sub>j</sub>.</strong><p>
+<h2>Input</h2>
+<p>The first line contains an integer <strong>T</strong>, <strong>T</strong> &le; 20, followed by <b>T</b> test cases. Each test case begins with an integer <strong>N</strong>, <strong>N</strong> &le; 1,000, which is the number of integers in the permutation. The next <strong>N - 1</strong> lines each contain a single constraint in the following format: "<b>i</b> <b>sign</b> <b>j</b>", where 0 &le; <strong>i</strong>, <strong>j</strong> &le; <strong>N - 1</strong> and <strong>sign</strong> is either "<strong>&lt;</strong>" or "<strong>&gt;</strong>", which denotes whether the <b>i</b>-th element of the permutation should be less than or greater than the <b>j</b>-th element.</p>
+<p>It is guaranteed that it is not possible to partition indices into two disjoint sets A and B such
+that there is no constraint involving elements from both A and B.</p>
+<h2>Output</h2>
+<p>For each test case, output one single line with the number of permutations that satisfy all the
+constraints, following the output format shown in the example. The answer may be very large, so you should give the result modulo <strong>1,000,000,007</strong>.</p>

2013/round2/permutations.in ADDED Viewed

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2013/round2/permutations.md ADDED Viewed

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+In this problem you need to count number of possible permutations **p** of the
+first **N** integers, given **N-1** constraints of the form **pi < pj.**
+## Input
+The first line contains an integer **T**, **T** ≤ 20, followed by **T** test
+cases. Each test case begins with an integer **N**, **N** ≤ 1,000, which is
+the number of integers in the permutation. The next **N - 1** lines each
+contain a single constraint in the following format: "**i** **sign** **j**",
+where 0 ≤ **i**, **j** ≤ **N - 1** and **sign** is either "**<**" or "**>**",
+which denotes whether the **i**-th element of the permutation should be less
+than or greater than the **j**-th element.
+It is guaranteed that it is not possible to partition indices into two
+disjoint sets A and B such that there is no constraint involving elements from
+both A and B.
+## Output
+For each test case, output one single line with the number of permutations
+that satisfy all the constraints, following the output format shown in the
+example. The answer may be very large, so you should give the result modulo
+**1,000,000,007**.

2013/round2/permutations.out ADDED Viewed

	@@ -0,0 +1,60 @@

+Case #1: 1
+Case #2: 1
+Case #3: 4
+Case #4: 6
+Case #5: 1
+Case #6: 764344399
+Case #7: 450800465
+Case #8: 898996475
+Case #9: 226501413
+Case #10: 598446060
+Case #11: 923158588
+Case #12: 311325632
+Case #13: 221028522
+Case #14: 976696890
+Case #15: 398503520
+Case #16: 702516736
+Case #17: 733724736
+Case #18: 402844675
+Case #19: 554181637
+Case #20: 407752774
+Case #21: 176111360
+Case #22: 578419130
+Case #23: 783121995
+Case #24: 110121107
+Case #25: 571247919
+Case #26: 333381309
+Case #27: 957059657
+Case #28: 74430116
+Case #29: 752981215
+Case #30: 605744922
+Case #31: 65130122
+Case #32: 11050467
+Case #33: 369696022
+Case #34: 386169919
+Case #35: 781872677
+Case #36: 286188750
+Case #37: 603564700
+Case #38: 682609757
+Case #39: 713083365
+Case #40: 954131631
+Case #41: 379666854
+Case #42: 316070471
+Case #43: 14401757
+Case #44: 158451693
+Case #45: 974926246
+Case #46: 373588671
+Case #47: 249001229
+Case #48: 348656138
+Case #49: 371822065
+Case #50: 730948093
+Case #51: 339234304
+Case #52: 472477039
+Case #53: 244180714
+Case #54: 471613032
+Case #55: 740830151
+Case #56: 230510055
+Case #57: 373748783
+Case #58: 408060198
+Case #59: 85824300
+Case #60: 892144422

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+<p>In the not so distant future the world is populated by robots and ruled by an evil robot emperor. Every robot in the world can be identified by a unique numeric ID, and the list of all the existing robot IDs is easily accessible to everyone.
+One day the emperor decided to call for a general election to preserve an illusion of democracy. He set it up in the following way:<p>
+<ul>
+<li> - Every robot can cast at most one vote per round of voting and the votes are anonymous.</li>
+<li> - The only option on the ballot is the vote for reelection of the emperor.</li>
+<li> - If at least <strong>P</strong> percent of the population cast votes for the emperor he becomes reelected for the next millennium.</li>
+<li> - Otherwise the emperor declares the vote void, disassembles <strong>K</strong> robots with the lowest ID numbers (who he finds to be the most rebellious), and then if there are any functional robots left he restarts the whole process.</li>
+</ul>
+<p>
+All the robots are perfectly logical but also rather lazy and prone to procrastination. That's why after figuring out the plan of the emperor, they will abstain from voting unless they have to vote to survive the election (including this round and all later rounds). If they will die whether or not they vote, they will vote in the hope that the emperor will spare them. (He won't, because he's evil!).
+</p>
+<h2>Problem</h2>
+<p>
+Given <strong>N</strong> - the initial population size, <strong>K</strong> - the number of robots disassembled after an unsuccessful vote and <strong>P</strong> - the required percentage of votes.</p><p> Compute the number of times the vote will take place. </p>
+<h2>Input</h2>
+<p>The first line contains the number of test cases <strong>T</strong>, where <strong> 1 &le; T &le; 100 </strong></p>
+<p>Each case is a single line with three space-separated integers <strong>N</strong> <strong>K</strong> <strong>P</strong></p>
+<p>0 &lt; <strong>K</strong> &le; <strong>N</strong> &le; 1,000,000,000,000 <br/>
+0 &lt; <strong>P</strong> &le; 100</p>
+<h2>Output</h2>
+<p>For test case <strong>i</strong>, numbered from <strong>1</strong> to <strong>T</strong>, output "Case #i: ", followed by a single integer, the number of times the emperor will have to call a vote before getting reelected.
+<h2>Example</h2>
+<p>In the first case we have three robots. Two of them are facing disassembly, so they will vote for the emperor. The third robot will survive even if he abstains in the first round, so he doesn't vote. But two out of three is not enough to reach the 75% minimum, so the election proceeds to a second round. The election ends when the single remaining robot casts a vote for the emperor.</p>
+<p>In the second case again two robots are in immediate danger, but the next two robots are forced to vote as well, otherwise they would end up in the same situation as in the first example case. Now with the 4 out of 5 casting the vote the election successfully ends.</p>