// CSE 143, Winter 2010, Marty Stepp
// This program demonstrates a recursive pow method that 
// performs exponentiation recursively.

public class Powers {
    public static void main(String[] args) {
        System.out.println(pow(3, 4));
        System.out.println(pow(2, 8));
        System.out.println(pow(2, 24));
        System.out.println(pow(10, 3));
    }
    
    // Returns (base) raised to the (exponent) power, recursively.
    // Precondition base >= 0 and exponent >= 0
    public static int pow(int base, int exponent) {
        if (exponent < 0) {
            throw new IllegalArgumentException();
        }
        
        if (exponent == 0) {
            // base case
            return 1;
        } else if (exponent % 2 == 0) {
            // recursive case 2
            // optimization: 3^12 == (3^2)^6
            return pow(base * base, exponent / 2);
        } else {
            // recursive case 1
            return base * pow(base, exponent - 1);
        }
    }

    // 7^4 == 7 * 7^3
    //     ==     7 * 7^2
    //     ==         7 * 7^1
    //     ==             7 * 7^0
    //     ==                 1
}