Sqrt(x)

description

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

submission

// binary search, we search the first number l that
// (l + 1) * (l + 1) > x
// then the answer is l
impl Solution {
    pub fn my_sqrt(x: i32) -> i32 {
        let (mut l, mut r) = (0, x);
        while l < r {
            // +1 here
            let mid = l + (r - l) / 2 + 1;
            // simple trick to avoid i64
            if mid <= x / mid {
                l = mid;
            } else {
                r = mid - 1;
            }
        }
        l
    }
}