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



 
 <?php
 
$a=array(1,2,3,4,5);
$k=3;
$n=5;
$c=array_splice($a, $k);
$b=array_splice($a, 0, $k);
$j=$k-1;
print_r($b);
 
        while (1) {
 
       		$m=array_search($b[$j]+1,$c);
       	     if ($m!==false) {
	     	$c[$m]-=1; 
        	$b[$j]=$b[$j]+1;
               	print_r($b);	       
        }
       	if ($b[$k-1]==$n) {
	 $i=$k-1; 
	 while ($i >= 0) {
 
	 		if ($i == 0 && $b[$i] == $n-$k+1) break 2;
 
       		  $m=array_search($b[$i]+1,$c);
		  if ($m!==false) { 
		  	  $c[$m]=$c[$m]-1; 
			  $b[$i]=$b[$i]+1; 
 
			$g=$i;
		while ($g != $k-1) {
			array_unshift ($c, $b[$g+1]);
			$b[$g+1]=$b[$g]+1;
			$g++;
			}
			$c=array_diff($c,$b);
			print_r($b);
		 	     break;  
       			 }
	 	$i--;
 
		}
 
	}
 
 
}
 
?>
 