Optimize power() using exponentiation by squaring (O(log n)) - Vinayak

Author: Vinayak-v12

src/main/java/com/thealgorithms/maths/PowerUsingRecursion.java

@@ -2,21 +2,44 @@
 
 /**
  * calculate Power using Recursion
- * @author Bama Charan Chhandogi (https://github.com/BamaCharanChhandogi)
+ * @author Vinayak (https://github.com/Vinayak-v12)
  */
 
 public final class PowerUsingRecursion {
     private PowerUsingRecursion() {
     }
 
+    /**
+     * Computes base raised to the given exponent.
+     *
+     * @param base the number to be raised
+     * @param exponent the power (can be negative)
+     * @return base^exponent
+     */
+    
     public static double power(double base, int exponent) {
-        // Base case: anything raised to the power of 0 is 1
+
+        // Handle negative exponent: a^-n = 1 / (a^n)
+        if (exponent < 0) {
+            return 1.0 / power(base, -exponent);
+        }
+
+        // Base cases
         if (exponent == 0) {
-            return 1;
+            return 1.0;
+        }
+        if (exponent == 1) {
+            return base;
+        }
+
+        // Exponentiation by Squaring
+        // If exponent is even: a^n = (a^(n/2))^2
+        if (exponent % 2 == 0) {
+            double half = power(base, exponent / 2);
+            return half * half;
         }
 
-        // Recursive case: base ^ exponent = base * base ^ (exponent - 1)
-        // Recurse with a smaller exponent and multiply with base
+        // If exponent is odd: a^n = a * a^(n-1)
         return base * power(base, exponent - 1);
     }
 }