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
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1
)
…
(
n
−
k
+
1
)


k
(
k
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1
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…
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
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1
)
⋅
(
n
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2
)
⋯
(
n
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k
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)


{\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
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1



C

k


=



(
n
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!


(
n
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!
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



  [ stack ]                     is perms.min    (       --> [ )
 
  [ stack ]                     is perms.max    (       --> [ )
 
                        forward is (perms)
 
  [ over size
    perms.min share > if
      [ over temp take
        swap nested join
        temp put ]
    over size
    perms.max share < if
      [ dup size times
         [ 2dup i^ pluck
           rot swap nested join
           swap (perms) ] ]
    2drop ]               resolves (perms)      (   [ [ -->    )
 
  [ perms.max put
    1 - perms.min put
    [] temp put
    [] swap (perms)
    temp take
    perms.min release
    perms.max release ]         is perms        ( [ a b --> [ )
 
  [ dup size dup perms ]        is permutations (     [ --> [ )
 
  ' [ 1 2 3 ] permutations echo cr
  $ "quack" permutations 60 wrap$
  $ "quack" 3 4 perms 46 wrap$