Find square root of a number using binary search algorithm

Given a positive number, find square root of it. If the number is not a perfect square, then return floor of its square root.


For example,

Input: x = 12
Output: 3

Input: x = 16
Output: 4

Naive solution is to consider all positive numbers starting from 1, and find the first number i for which i*i is greater than the given number x. Then, i-1 would be the floor of square root of x.


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The time complexity of above solution is O(√x). We can improve the time complexity to O(log(x)) with the help of binary search algorithm. The algorithm can be implemented as follows in C:


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Recursive solution to this problem:

int sqrt(int num, int so_far, int s, int e){
if( s <= e){
int mid = (s+e)/2;
if( mid * mid == num) return mid;
else if(mid*mid < num){
so_far = mid;
return sqrt(num,so_far,mid+1, e);
}else return sqrt(num, so_far,s, mid-1);
return so_far;