0633-sum-of-square-numbers

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Description

Given a non-negative integer c, decide whether there're two integers a and b such that a2 + b2 = c.

 

Example 1:

Input: c = 5
Output: true
Explanation: 1 * 1 + 2 * 2 = 5

Example 2:

Input: c = 3
Output: false

 

Constraints:

• 0 <= c <= 231 - 1

Solution(Python)

class Solution(object):
    def judgeSquareSum(self, c):
        def binary_search(s, e, n):
            if s > e:
                return False
            mid = s + (e - s) // 2
            if mid * mid == n:
                return True
            elif mid * mid > n:
                return binary_search(s, mid - 1, n)
            else:
                return binary_search(mid + 1, e, n)

        for a in range(
            int(c**0.5) + 1
        ):  # equivalent to `for (long a = 0; a * a <= c; a++)` in Java
            b = c - a * a
            if binary_search(0, b, b):
                return True
        return False