69. Sqrt(x)

Implement int sqrt(int x).

Compute and return the square root of x.

Solution:

Method 1: Binary Search

Implementation is straightforward.

One tricky part is we use mid < x / mid instead of mid * mid < x just in case of Integer overflow.



Code:

public class Solution {
    public int mySqrt(int x) {
        if (x == 0) {
            return 0;
        }
        int start = 1;
        int end = x;
        while (start + 1 < end) {
            int mid = start + (end - start) / 2;
            if (mid < x / mid) {
                start = mid;
            }
            else {
                end = mid;
            }
        }
        if (end <= x / end) {
            return end;
        }
        return start;
    }
}

Method 2: Newton's Method