Leetcode #1925: Count Square Sum Triples
In this guide, we solve Leetcode #1925 Count Square Sum Triples in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Math, Enumeration
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
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
The time complexity is , where is the given integer. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.