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



$ include "seed7_05.s7i";
 
const type: combinations is array array integer;
 
const func combinations: comb (in array integer: arr, in integer: k) is func
  result
    var combinations: combResult is combinations.value;
  local
    var integer: x is 0;
    var integer: i is 0;
    var array integer: suffix is 0 times 0;
  begin
    if k = 0 then
      combResult := 1 times 0 times 0;
    else
      for x key i range arr do
        for suffix range comb(arr[succ(i) ..], pred(k)) do
          combResult &:= [] (x) & suffix;
        end for;
      end for;
    end if;
  end func;
 
const proc: main is func
  local
    var array integer: aCombination is 0 times 0;
    var integer: element is 0;
  begin
    for aCombination range comb([] (0, 1, 2, 3, 4), 3) do
      for element range aCombination do
        write(element lpad 3);
      end for;
      writeln;
    end for;
  end func;