Count Square Sum Triples

A square triple (a,b,c) is a triple where a, b, and c are integers and a2 + b2 = c2.

Given an integer n, return the number of square triples such that 1 <= a, b, c <= n.

 

Example 1:

Input: n = 5
Output: 2
Explanation: The square triples are (3,4,5) and (4,3,5).

Example 2:

Input: n = 10
Output: 4
Explanation: The square triples are (3,4,5), (4,3,5), (6,8,10), and (8,6,10).

 

Constraints:

  • 1 <= n <= 250
SOLUTION:
class Solution:
    def countTriples(self, n: int) -> int:
        exists = set()
        for c in range(1, n + 1):
            exists.add(c * c)
        ctr = 0
        for a in range(1, n + 1):
            for b in range(a, n + 1):
                if (a * a + b * b) in exists:
                    ctr += 2
        return ctr

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