Task

Given non-negative integers    m    and    n,   generate all size    m    combinations   of the integers from    0   (zero)   to    n-1    in sorted order   (each combination is sorted and the entire table is sorted).



Example

3   comb    5      is:

0 1 2
0 1 3
0 1 4
0 2 3
0 2 4
0 3 4
1 2 3
1 2 4
1 3 4
2 3 4

If it is more "natural" in your language to start counting from    1   (unity) instead of    0   (zero),

the combinations can be of the integers from    1   to    n. 



See also


 The number of samples of size k from n objects.


With   combinations and permutations   generation tasks. 






 Order Unimportant

 Order Important


 Without replacement








(


n
k


)




=

n



C

k


=



n
(
n
−
1
)
…
(
n
−
k
+
1
)


k
(
k
−
1
)
…
1





{\displaystyle {\binom {n}{k}}=^{n}\operatorname {C} _{k}={\frac {n(n-1)\ldots (n-k+1)}{k(k-1)\dots 1}}}










n



P

k


=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋯
(
n
−
k
+
1
)


{\displaystyle ^{n}\operatorname {P} _{k}=n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}




Task: Combinations

Task: Permutations


 With replacement








(



n
+
k
−
1

k


)




=

n
+
k
−
1



C

k


=



(
n
+
k
−
1
)
!


(
n
−
1
)
!
k
!





{\displaystyle {\binom {n+k-1}{k}}=^{n+k-1}\operatorname {C} _{k}={(n+k-1)! \over (n-1)!k!}}








n

k




{\displaystyle n^{k}}




Task: Combinations with repetitions

Task: Permutations with repetitions



using System;
using System.Collections.Generic;
 
public class Program
{
    public static IEnumerable<int[]> Combinations(int m, int n)
    {
            int[] result = new int[m];
            Stack<int> stack = new Stack<int>();
            stack.Push(0);
 
            while (stack.Count > 0)
           {
                int index = stack.Count - 1;
                int value = stack.Pop();
 
                while (value < n) 
               {
                    result[index++] = ++value;
                    stack.Push(value);
 
                    if (index == m) 
                    {
                        yield return result;
                        break;
                    }
                }
            }
    }
 
    static void Main()
    {
        foreach (int[] c in Combinations(3, 5))
        {
            Console.WriteLine(string.Join(",", c));
            Console.WriteLine();
        }
    }
}