Cube Sum Pairs

Posted: 29 Dec, 2020
Difficulty: Easy

PROBLEM STATEMENT

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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.
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.
Approach 1
  1. Maintain a counter which will count possible pairs (A, B).
  2. Iterate over all possible ‘A’ values.
    • Possible ‘A’ values are in the range 1 to N.
  3. For each ‘A’ value iterate over all possible values of ‘B’
    • Possible ‘B’ values are in the range 0 to N.
  4. If ‘A’^3 + ‘B’^3 comes to be N, then increment the counter.
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