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



program permutations
 
  implicit none
  integer, parameter :: value_min = 1
  integer, parameter :: value_max = 3
  integer, parameter :: position_min = value_min
  integer, parameter :: position_max = value_max
  integer, dimension (position_min : position_max) :: permutation
 
  call generate (position_min)
 
contains
 
  recursive subroutine generate (position)
 
    implicit none
    integer, intent (in) :: position
    integer :: value
 
    if (position > position_max) then
      write (*, *) permutation
    else
      do value = value_min, value_max
        if (.not. any (permutation (: position - 1) == value)) then
          permutation (position) = value
          call generate (position + 1)
        end if
      end do
    end if
 
  end subroutine generate
 
end program permutations