Problem Statement
Implement the function boolean isPalindrome (int n);
Which will return true if the bit-wise representation of the integer
is a palindrome and false otherwise.
Algorithm
Sort the array in O(N)
Problem Statement
Given an integer array of length N, containing values in the range 1,2,3…N^2. Sort the array in O(N) time.
Solution
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Find a pythagorean triplet from an array
Problem Statement:
Given an array a of n integers find all possible Pythagorean triplets from the array.
What is Pythagorean triplet?
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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3 SUM problem
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).
Permutations solution: Facebook hacker cup 2013 Round 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.
Problem Statement
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 ≤ 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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Dead Pixels solution: Facebook hacker cup 2013 Round 1
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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