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x 的平方根

Sqrt(x)

专题
Algorithmic Programming / 算法编程
难度
L2
来源
Citadel

题目详情

问题：x 的平方根

考察：二分查找

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/sqrtx/

Given a non-negative integer x, return the square root of x rounded down to the nearest integer. The returned integer should be non-negative as well.

You must not use any built-in exponent function or operator.

  • For example, do not use pow(x, 0.5) in c++ or x ** 0.5 in python.

 

Example 1:

Input: x = 4
Output: 2
Explanation: The square root of 4 is 2, so we return 2.

Example 2:

Input: x = 8
Output: 2
Explanation: The square root of 8 is 2.82842..., and since we round it down to the nearest integer, 2 is returned.

 

Constraints:

  • 0 <= x <= 231 - 1
解析

思路：在 0 到 x 之间二分整数平方根。用 mid <= x / mid 判断避免 mid * mid 溢出，最终返回最大满足平方不超过 x 的整数。

复杂度：时间 O(log x)，空间 O(1)。