Task

Write a program that generates all   permutations   of   n   different objects.   (Practically numerals!)



Related tasks
 
   Find the missing permutation
   Permutations/Derangements



 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



 
/* hopper-JAMBO - a flavour of Amazing Hopper! */
 
#include <jambo.h>
Main
  leng=0
  Void(lista)
  Set("la realidad","escapa","a los sentidos"), Apnd list(lista)
  Length(lista), Move to(leng)
  Toksep(" ")
  Printnl( lista )
  Set(1) Gosub(Permutar)
End-Return
 
Subrutines
 
Define( Permutar, pos )
    If ( Sub(leng, pos) Isgeq(1) )
       i=pos
       Loop if( Less( i, leng ) )
          Plusone(pos), Gosub(Permutar)
          Set( pos ),   Gosub(Rotate)
          Printnl( lista )
          ++i
       Back
      Plusone(pos), Gosub(Permutar)
      Set( pos ),   Gosub(Rotate)
   End If
Return
 
Define ( Rotate, pos )
    c=0, [pos] Get(lista), Move to(c)
    [ Plusone(pos): leng ] Cget(lista)
    [ pos: Minusone(leng) ] Cput(lista)
    Set(c), [ leng ] Cput(lista)
Return
 