// Helene Martin, CSE 143
// Demonstrates using recursive backtracking to identify and print all possible dice roll 
// values for a given number of dice and all rolls that add up to a given sum.
import java.util.*;

// diceSum(3, 7);
// - no pruning: 259 calls
// - pruning: 133 calls

// diceSum(5, 7);
// - no pruning: 9331
// - pruning: 343

public class Dice {
	public static void main(String[] args) {
		diceRoll(3);
		// diceSum(3, 7);
	}

	// Prints all possible outcomes of rolling the given
	// number of six-sided dice in [#, #, #] format.
	// pre: dice >= 0
	public static void diceRoll(int dice) {
		diceRoll(dice, new ArrayList<Integer>());
	}

	private static void diceRoll(int dice, List<Integer> soFar) {
		if (dice == 0) {
			System.out.println(soFar);
		} else {
			System.out.println("> " + soFar); // beginning of a new call
			// set a value for first die
			// remove a die
			// recurse
			for (int i = 1; i <= 6; i++) {
				soFar.add(i);
				diceRoll(dice - 1, soFar);
				soFar.remove(soFar.size() - 1);
			}
		}
	}

	// Prints all possible outcomes of rolling the given
	// number of six-sided dice that add up to exactly
	// the given sum, in [#, #, #] format.
	public static void diceSum(int dice, int sum) {
		diceSum(dice, sum, new ArrayList<Integer>(), 0);
	}

	private static void diceSum(int dice, int sum, List<Integer> soFar,
			int sumSoFar) {
		// int sumSoFar = 0;
		// for (int value : soFar) {
		// sumSoFar += value;
		// }
		if (dice == 0) {
			if (sumSoFar == sum) {
				System.out.println(soFar);
			}
		} else if (sumSoFar + dice <= sum && sumSoFar + dice * 6 >= sum) {
			for (int i = 1; i <= 6; i++) {
				soFar.add(i);
				diceSum(dice - 1, sum, soFar, sumSoFar + i);
				soFar.remove(soFar.size() - 1);
			}
		}
	}
}