Find square root of number upto given precision using binary search in C++

Suppose we have a positive number n, and precision p. We have to find square root of the number n up to p decimal places using binary search technique. So if the number is n = 50, and p = 3, then output is 7.071.

So solve this, we have to follow some steps −

Initialize start := 0 and end := n
Compare the square of mid integer, if this is equal to the number then integral part has found out, otherwise look for left or right as required.
Once we have completed the task for integral part, then do for the fractional part.
Initialize increment variable as 0.1, then compute fractional part up to p places. For each iteration increment changes to 1/10 th of its previous value.
Finally return the answer.

Example

Live Demo

#include<iostream>
using namespace std;
float sqrtBinarySearch(int num, int p) {
   int left = 0, right = num;
   int mid;
   float res;
   while (left <= right) {
      mid = (left + right) / 2;
      if (mid * mid == num) {
         res = mid;
         break;
      }
      if (mid * mid < num) {
         left = mid + 1;
         res = mid;
      } else {
         right = mid - 1;
      }
   }
   float incr = 0.1;
   for (int i = 0; i < p; i++) {
      while (res * res <= num) {
         res += incr;
      }
      res -= incr;
      incr /= 10;
   }
   return res;
}
int main() {
   int n = 50, p = 3;
   cout << "Square root of " << n << " up to precision " << p << " is: " << sqrtBinarySearch(50, 3) << endl;
}

Output

Square root of 50 up to precision 3 is: 7.071

Arnab Chakraborty

Published on 19-Dec-2019 12:12:20

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