// CSE 143, Winter 2009, Marty Stepp
// This program demonstrates a recursive printBinary method that 
// prints the binary representation of an integer.
//
// We also wrote a recursive pow method today which is included below.

public class Binary {
    public static void main(String[] args) {
        printBinary(4);       // 100
        System.out.println();
        printBinary(12);      // 1100
        System.out.println();
        printBinary(21);      // 10101
        System.out.println();
        printBinary(42);      // 101010
        System.out.println();
        printBinary(69743);   // 10001000001101111
        System.out.println();
        
        System.out.println(pow(3, 4));
    }
    
    // Prints the binary representation of the given integer.
    // For example, printBinary(42) prints 101010.
    // Precondition: n >= 0
    public static void printBinary(int n) {
        if (n < 2) {
            // recursive case: n == 0 or n == 1
            // it has the same binary representation, so just print it
            System.out.print(n);
        } else {
            // recursive case: n >= 2
            // chop off last digit; use recursion for the rest
            printBinary(n / 2);
            printBinary(n % 2);
        }
    }
    
    // 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) {
            // base case: x^0 == 1 for all x
            return 1;
        } else if (exponent % 2 == 0) {
            // optimization: x^y == (x^2)^(y/2)  if y is even
            int half = pow(base, exponent / 2);
            return half * half;
        } else {
            // x^y == x * x^(y-1)
            return base * pow(base, exponent - 1);
        }
    }
}