Added Karatsuba's multiplication algorithm

Author: adesh2756

src/main/java/com/thealgorithms/divideandconquer/KaratsubaMultiplication.java

@@ -0,0 +1,47 @@
+import java.util.Scanner;
+
+public class KaratsubaMultiplication {
+
+    // Karatsuba multiplication function
+    public static long karatsuba(long x, long y) {
+        // Base case for recursion
+        if (x < 10 || y < 10) {
+            return x * y;
+        }
+
+        // Calculate the size of the numbers
+        int n = Math.max(Long.toString(x).length(), Long.toString(y).length());
+        int m = n / 2;
+
+        // Split the digit sequences about the middle
+        long high1 = x / (long) Math.pow(10, m);
+        long low1 = x % (long) Math.pow(10, m);
+        long high2 = y / (long) Math.pow(10, m);
+        long low2 = y % (long) Math.pow(10, m);
+
+        // 3 recursive calls
+        long z0 = karatsuba(low1, low2);
+        long z1 = karatsuba(low1 + high1, low2 + high2);
+        long z2 = karatsuba(high1, high2);
+
+        // Combine the results
+        return (z2 * (long) Math.pow(10, 2 * m)) + ((z1 - z2 - z0) * (long) Math.pow(10, m)) + z0;
+    }
+
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+
+        System.out.print("Enter first number: ");
+        long num1 = sc.nextLong();
+
+        System.out.print("Enter second number: ");
+        long num2 = sc.nextLong();
+
+        long result = karatsuba(num1, num2);
+
+        System.out.println("Product: " + result);
+
+        sc.close();
+    }
+}
+