public class SimpleRecursion {

	/*
	 * method for recursively computing n!
	 * @param n
	 * precondition: n>=0
	 * postcondition: returns n!	
	 */
	public int factorial(int n){
		if (n==0) {
			System.out.println("BASE CASE:   factorial(0) = 1");
			return 1;
		}
		else {
			int result = factorial(n-1) * n;
			System.out.println("current n: " + n + " current result: " + result);
			return result;
		}
	}

	
	public int max(int [] list){
		return recursiveMax(list, 0);
	}

	/*
	 * recursive method for computing the maximum element in part of an array
	 * that starts at a given index
	 * @param list - an array of integers
	 * @param start - the starting index
	 * precondition:   0 <= start < list.length
	 * postcondition:  returns the maximum in list[start],...,list[list.length - 1]
	 */
	public int recursiveMax(int [] list, int start){
		if (start == list.length - 1) {
			return list[start];
		}
		else {
			return Math.max(list[start], recursiveMax(list, start + 1));
		}
	}


	public static void main(String[] args) {

		SimpleRecursion rec = new SimpleRecursion();

		for(int i=1; i<8; i++){
			System.out.println("computing factorial("+ i +")");
			System.out.println("factorial("+i+")=" + rec.factorial(i));
		}
		
		int [] list = { 1, 5, 2, 3};
		System.out.println("maximum in the list: " + rec.max(list));
		
		}
}