Count Square Sum Triples — LeetCode 1925 Python Solution

The problem

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

Input

n = 5

Output

2

Explanation

The square triples are (3,4,5) and (4,3,5).

Python solution

class Solution:
    def countTriples(self, n: int) -> int:
        ans = 0
        for a in range(1, n):
            for b in range(1, n):
                x = a * a + b * b
                c = int(sqrt(x))
                if c <= n and c * c == x:
                    ans += 1
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1925. Count Square Sum Triples is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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