Niuke.com Brushing Questions-Find the Square Root

Problem Description

Implement the function int sqrt(int x).
Calculate and return the square root of x (rounded down)

Example

Example 1

Input
2

Output
1

Solutions

Ideas

1. Dichotomy: three situations

mid * mid <= x && (mid + 1)*(mid + 1)> x: The square root meets the condition (because mid is an integer down here)
mid * mid <x: Take the left measurement space
mid * mid> x: Take the right measurement space

Code

// 思路1
public class Solution {
    
      
    public int mySqrt(int x) {
    
    
        int left = 1; int right = x;
        while (true) {
    
    
            int mid = (left + right) / 2;
            if (mid <= x / mid && (mid + 1) > x / (mid + 1)) {
    
    
                return mid;
            } else if (mid < x / mid) {
    
    
                left = mid + 1;
            } else {
    
    
                right = mid - 1;
            }
        }
    }
}

Time complexity analysis:
O(lgN): dichotomy to traverse the array

Space complexity analysis:
O(1): No extra space is used

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Find the square root