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RoboElection solution: Facebook hacker cup 2013 Round 2

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the second question(Carried 35 marks out of 100) for the Round 2 of 2013 hacker cup. only top 100 contestants will be moved to Round 3.

Problem Statement

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:

  • – Every robot can cast at most one vote per round of voting and the votes are anonymous.
  • – The only option on the ballot is the vote for reelection of the emperor.
  • – If at least P percent of the population cast votes for the emperor he becomes reelected for the next millennium.
  • – Otherwise the emperor declares the vote void, disassembles K 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.

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!).

Problem

Given N – the initial population size, K – the number of robots disassembled after an unsuccessful vote and P – the required percentage of votes.

Compute the number of times the vote will take place.
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Cake Cutting solution: Facebook hacker cup 2013 Round 2

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the first question(Carried 20 marks out of 100) for the Round 2 of 2013 hacker cup.

Problem Statement

“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?
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Dead Pixels solution: Facebook hacker cup 2013 Round 1

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the third question(Carried 45 marks out of 100) for the Round 1 of 2013 hacker cup. only top 500 contestants will be moved to Round 2.

Problem Statement

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.
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Security problem solution: Facebook hacker cup 2013 Round 1

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the second question(Carried 35 marks out of 100) for the Round 1 of 2013 hacker cup. only top 500 contestants will be moved to Round 2.

Problem Statement

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:

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Card Game solution: Facebook hacker cup 2013 Round1

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the first question(Carried 20 marks out of 100) for the Round 1 of 2013 hacker cup. only top 500 contestants will be moved to Round 2.

Problem Statement

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

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Find the Min solution: Facebook hacker Cup 2013 Qual Round

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the third question(Carried 45 marks out of 100) for the qualification round 2013 hacker cup.

Problem Statement

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.
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Balanced Smileys solution: Facebook hacker Cup 2013 Qual Round

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the second question((Carried 35 marks out of 100) for the qualification round 2013 hacker cup.

Problem Statement

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:
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Beautiful Strings solution: Facebook hacker Cup 2013 Qual Round

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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the first question in the qualification round of 2013 hacker cup.

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?

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