Problem Statement:
Given an array a of n integers find all possible Pythagorean triplets from the array.
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. this formula is derived from Pythagoras theorem: “For every right angle triangle with side lengths a, b, and c=> a2 + b2 = c2“.
Pythagorean Triplet
Solution:
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Problem Statement:
Given a set S of n integers find all possible subsets(a,b,c) such that a + b + c = 0.
Solution:
Brute force approach is of O(n^4) but we can solve it in O(n^2) by using the approach in Non duplicate pairs that sum to S.
First sort the array(Order O(nlogn)), than finding a, b, c pairs is equal to finding=> For every element a in the array, if there exists a pair with sum equal to -a. As explained in Non duplicate pairs that sum to S, we can get the pair with sum -a in O(n) and we have to repeat this exercise n times so order of complexity will be O(n^2).
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 2 of 2013 hacker cup. only top 100 contestants will be moved to Round 3.
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.
The first line contains an integer T, T ≤ 20, followed by T test cases. Each test case begins with an integer N, N ≤ 1000, 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.
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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.
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:
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!).
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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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.
“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:
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.
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.
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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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.
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:
For example: let m = 3, l = 2
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).
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.
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.
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.
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.
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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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.
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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