Software Engineer

You are given a positive integer N, and you have to find the number of ways to represent N as a sum of cubes of two integers(let’s say A and B), such that:

N = A^3 + B^3.

Note:

1. A should be greater than or equal to one (A>=1).
2. B should be greater than or equal to zero (B>=0).
3. (A, B) and (B, A) should be considered different solutions, if A is not equal to B, i.e (A, B) and (B, A) will not be distinct if A=B.

You are given 'N' stones labeled from 1 to 'N'. The 'i-th' stone has the weight W[i]. There are 'M' colors labeled by integers from 1 to 'M'. The 'i-th' stone has the color C[i] which is an integer between 1 to 'M', both inclusive.

You have been required to fill a Knapsack with these stones. The Knapsack can hold a total weight of 'X'.

You are required to select exactly 'M' stones; one of each color. The sum of the weights of the stones must not exceed 'X'. Since you paid a premium for a Knapsack with capacity 'X', you are required to fill the Knapsack as much as possible.

Write a program to calculate the best way to fill the Knapsack - that is, the unused capacity should be minimized.

Ninja is learning a new but strange language known as Alien Language. Alien language possesses the same alphabets as of English language, but their order is different. The order of letters are given as ‘ORDER’ string. Ninja has ‘N’ words in the ‘WORDS’ array. Ninja’s task is to check whether the words of ‘WORDS’ are sorted lexicographically in this alien language or not.

Note: ‘ORDER’ consists of all 26 letters of English alphabet.

For Example

If ‘WORDS’ = ["word","world","row"], ‘ORDER’ = "worldabcefghijkmnpqstuvxyz",the answer will be ‘NO’ as first and second words are not lexicographically sorted as ‘l’ comes before ‘d’ in alien language.

You have been given ‘N’ courses and some courses may have prerequisites. Now consider a matrix ‘PREREQUISITES’ of size 'M' x 2 which represents that you must complete the course 'PREREQUISITES[i][1]' before the course 'PREREQUISITES[i][0]'.

Your task is to return the order of courses you should take to finish all courses.

Note:

If it is impossible to finish all courses, return an empty array. If there are multiple answers, return any one.

For example:

Input:
3 2
1 2
2 3

There are three courses to take. To start with, First course 3 is taken. Then course 2 is taken for which course 3 must be completed. 

At last course 1 is taken for which course 2 must be completed. So the correct course order is [3,2,1].    

You are given a string 'S'. Your task is to partition 'S' such that every substring of the partition is a palindrome. You need to return all possible palindrome partitioning of 'S'.

Note: A substring is a contiguous segment of a string.

For Example:

For a given string “BaaB”
3 possible palindrome partitioning of the given string are:
{“B”, “a”, “a”, “B”}
{“B”, “aa”, “B”}
{“BaaB”}
Every substring of all the above partitions of “BaaB” is a palindrome.