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


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=

n



C

k


=



n
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n
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…
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k
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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


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n
⋅
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n
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⋅
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2
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⋯
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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








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C

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!


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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



 
{def inject
 {lambda {:x :a}
  {if {A.empty? :a}
   then {A.new {A.new :x}}  
   else {let { {:c {{lambda {:a :b} {A.cons {A.first :a} :b}} :a}}
               {:d {inject :x {A.rest :a}}}
               {:e {A.cons :x :a}}
             } {A.cons :e {A.map :c :d}}}}}} 
-> inject
 
{def permut
 {lambda {:a}
  {if {A.empty? :a}
   then {A.new :a}
   else {let { {:c {{lambda {:a :b} {inject {A.first :a} :b}} :a}}
               {:d {permut {A.rest :a}}}
             } {A.reduce A.concat {A.map :c :d}}}}}}
-> permut
 
{permut {A.new 1 2 3}}
-> [[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]]
 
{permut {A.new 1 2 3 4}}
-> 
[[1,2,3,4],[2,1,3,4],[2,3,1,4],[2,3,4,1],[1,3,2,4],[3,1,2,4],[3,2,1,4],[3,2,4,1],[1,3,4,2],[3,1,4,2],[3,4,1,2],[3,4,2,1],[1,2,4,3],[2,1,4,3],[2,4,1,3],[2,4,3,1],[1,4,2,3],[4,1,2,3],[4,2,1,3],[4,2,3,1],[1,4,3,2],[4,1,3,2],[4,3,1,2],[4,3,2,1]]
 