chore(Java): add square root using binary search (#826)

algorithms/Java/Maths/square-root.java

@@ -0,0 +1,49 @@
+// Calculating Square root of a number which is not necessarily perfect square
+// using Binary Search i.e. is using decrease and conquer approach
+// Time: O(log(n))
+public class BinarySearchSQRT {
+    public static void main(String[] args) {
+        int n = 40; // number whose square root is to be calculated
+        int p = 3; // decimal precision required
+
+        System.out.printf("%.3f", sqrt(n, p));
+    }
+    static double sqrt(int n, int p) {
+        int s = 0;
+        int e = n;
+
+        double root = 0.0;
+
+        while (s <= e) {
+            int m = s + (e - s) / 2; //this method of calculating middle element avoids integer overflow
+
+            if (m * m == n) { //the middle element is the required sqrt
+                return m;
+            }
+            else if (m * m > n) { //sqrt lies on the left part
+                e = m - 1;
+            }
+            else { // sqrt lies in the right part
+                s = m + 1;
+                root = m;
+            }
+        }
+        //now the root contains the nearest integer to the required square root
+        //now we need to add decimal precision to the root so that we can get as close to the exact sqrt
+        double incr = 0.1; //initialise
+        for (int i = 0; i < p; i++) {
+            while (root * root <= n) { //if the square of the root we have is less than the number
+                root += incr; //we will add incr decimal point each time
+            }
+            root -= incr;
+            incr /= 10; //here we increase the decimal point
+        }
+
+        return root; //here we have root up to p decimal point
+    }
+}
+
+/*
+Output -
+6.324
+*/

algorithms/Java/README.md

@@ -33,6 +33,7 @@
 - [Catalan Numbers](Maths/catalan-numbers.java)
 - [Nth Geek Onacci Number](Maths/nth-geek-onacci-number.java)
 - [Random Node in Linked List](Maths/algorithms_random_node.java)
+- [Square Root using BinarySearch](Maths/square-root.java)
 
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