// In this exercise you receive n and k and write a code that
// iterates over  all k-uples (t_1,..., t_k) where
// t_1, ..., t_k are in {0,...,n-1} and t_1 <= ... <= t_k
//
// The idea here is: equal to the other exercise, I'll just change the
// next_tuple function to make sure that t_1 <= ... <= t_k.
//
// Notice that generating all n^k and verifying which are monotone
// is VERY inneficient, so you should avoid that solution.


#include "stdio.h"

int t[100]; // say k <= 100


// This function prints all the tuples.
void iterate_and_print (int n, int k) {
	int i;
	// initialize t = (0,...,0)
	for (i = 0; i < k; ++i) t[i] = 0;
	do {
		for (i = 0; i < k; ++i) printf("%d ", t[i]);
		printf("\n");
	} while (next_tuple(n,k));
}


// This function finds the next tuple. It does like in the example,
// it increments one variable, if it < n, I return. If it is n, I
// increment the other variable recursively. It returns false if there
// is no next permutation.
int next_tuple(int n, int k) {
	int i;
	for (i = 0; i < k; ++i) {
		t[i]++;

		if (i < k-1) {
			if (t[i] <= t[i+1]) return 1;
			else t[i] = 0;
		} else {
			if (t[i] < n) return 1;
			else t[i] = 0;
		}
	}
	return 0;
}

	
int main() {
	iterate_and_print(4,4);
}