// CSE 143, Summer 2012
// Uses recursive backtracking to print all sets of dice
// roll values for a given number of dice, and all rolls of dice that
// add up to a given sum.

import java.util.*;

public class Dice {
	public static void main(String[] args) {
		diceRoll(2);
		System.out.println();
		diceSum(3, 7);
	}
	
	// Prints all possible outcomes of rolling the given
	// number of six-sided dice in [#, #, #] format.
	public static void diceRoll(int dice) {
		ArrayList<Integer> list = new ArrayList<Integer>();
		diceRoll(dice, list);
	}

	// Private recursive helper to implement diceRoll logic.
	// Adds a 'chosen' parameter of a list representing
	// what dice values have been chosen so far.
	private static void diceRoll(int dice, ArrayList<Integer> chosen) {
		if (dice == 0) {
			// Base case: nothing left to roll.  Print what we chose.
			System.out.println(chosen);
		} else {
			// Recursive case: dice >= 1.
			// Try choosing all possible values for the next 1 die.
			for (int i = 1; i <= 6; i++) {
				chosen.add(i);  //choose
				diceRoll(dice - 1, chosen);  //explore
				chosen.remove(chosen.size() - 1);  //un-choose
			}
		}
	}
	
	// Prints all possible outcomes of rolling the given
	// number of six-sided dice that add up to exactly
	// the given sum, in [#, #, #] format.
	// Example: diceSum(3, 10) will print [1, 5, 4], [3, 4, 4], ...
	public static void diceSum(int dice, int n) {
		ArrayList<Integer> list = new ArrayList<Integer>();
		diceSum(dice, n, list, 0);
	}

	// Private recursive helper to implement diceSum logic.
	// Adds a 'chosen' parameter of a list representing what dice values
	// have been chosen so far, and a 'sumSoFar' parameter for the sum of
	// all the dice rolls made so far.
	// (The sumSoFar parameter avoids having to re-compute similar sums.)
	private static void diceSum(int dice, int n, ArrayList<Integer> chosen, int sumSoFar) {
		if (dice == 0) {
			// Base case; nothing left to roll.  Maybe print what we chose.
			if (sumSoFar == n) {
				System.out.println(chosen);
			}
		} else if (sumSoFar < n && sumSoFar + 6 * dice >= n){
			// Recursive case: dice >= 1, and it is possible
			// to get the desired sum with this many dice; 
			// try choosing all possible values for the next 1 die
			for (int i = 1; i <= 6; i++) {
				//choose
				chosen.add(i);
				sumSoFar += i;
				//explore
				diceSum(dice - 1, n, chosen, sumSoFar);
				//unchoose
				chosen.remove(chosen.size() - 1);
				sumSoFar -= i;
			}
		}
	}
}