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



#NoEnv
StringCaseSense On
 
o := str := "Hello"
 
Loop
{
   str := perm_next(str)
   If !str
   {
      MsgBox % clipboard := o
      break
   }
   o.= "`n" . str
}
 
perm_Next(str){
   p := 0, sLen := StrLen(str)
   Loop % sLen
   {
      If A_Index=1
         continue
      t := SubStr(str, sLen+1-A_Index, 1)
      n := SubStr(str, sLen+2-A_Index, 1)
      If ( t < n )
      {
         p := sLen+1-A_Index, pC := SubStr(str, p, 1)
         break
      }
   }
   If !p
      return false
   Loop
   {
      t := SubStr(str, sLen+1-A_Index, 1)
      If ( t > pC )
      {
         n := sLen+1-A_Index, nC := SubStr(str, n, 1)
         break
      }
   }
   return SubStr(str, 1, p-1) . nC . Reverse(SubStr(str, p+1, n-p-1) . pC .  SubStr(str, n+1))
}
 
Reverse(s){
   Loop Parse, s
      o := A_LoopField o
   return o
}