Cube Sum Pairs

Easy

0/40

Average time to solve is 15m

111 upvotes

Asked in companies

Problem statement

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.

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line of the input contains an integer T denoting the number of test cases.

The first and only line of each test case consists of a single positive integer N.

Output Format:

For each test case, print an integer that denotes the count of the number of ways of representing N as a sum of cubes of 2 integers (A and B) in a separate line.

Note:

You don't have to print anything, it has already been taken care of. Just Implement the given function.

Constraints:

1 <= T <= 10^3
1 <= N <= 10^8
Time Limit: 1 sec.

Sample Input 1:

1
9

Sample Output 1:

Explanation For Sample Input 1:

There are 2 ways to represent N in the (A^3 + B^3) form ie. {(1, 2), (2, 1)}.
Eg. 1^3 + 2^3 = 9 and 2^3 + 1^3 = 9.

Sample Input 2:

1
27

Sample Output 2:

Explanation For Sample Input 2:

There is only 1 way to represent N in the (A^3 + B^3) form ie. {(3, 0)}.
Eg. 3^3 + 0^3 = 27.

Console