Finding Square root using Binary Search

Today we are going to see how we can find the square root of any number without using the inbuilt method.

public class BinarySearchSQRT{
    public static void main(String[] args) {
        int n = 40;

        //this p is precesion it means till how many decimal points we want our answer to be
        int p = 3;

        System.out.printf("%.3f",SQRT(n,p));
        
    }

    static double SQRT(int n, int p){

//As we are going to search in sorted numbers so we will use binary search
        int s = 1;
        int e = n/2;

        double root = 0.0;

        while(s <= e){
            int m = s + (e-s)/2;

            if(m*m == n){
                return m;
            }
            else if(m*m < n){
                s = m+1;
            }
            else{
                e = m-1;
            }
        }

        root = e;
        double incr = 0.1;

        //now get the precision
        for(int i = 0; i < p; i++){
            while(root*root <= n){
                root += incr;
            }
            root -= incr;

            incr /= 10;
        }

        return root;
    }
}

Time complexity:- O(log n)

Space complexity:- O(1)

Thank you for reading. If you have any queries then, please let me know in the comment section. I will surely be responsive toward it.