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



 
n=3
dim a(n+1)  '+1 needed due to bug in LB that checks loop condition
    '   until (i=0) or (a(i)<a(i+1))
    'before executing i=i-1 in loop body.
for i=1 to n: a(i)=i: next
do
  for i=1 to n: print a(i);: next: print
  i=n
  do
    i=i-1
  loop until (i=0) or (a(i)<a(i+1))
  j=i+1
  k=n
  while j<k
    'swap a(j),a(k)
    tmp=a(j): a(j)=a(k): a(k)=tmp
    j=j+1
    k=k-1
  wend
  if i>0 then
    j=i+1
    while a(j)<a(i)
      j=j+1
    wend
    'swap a(i),a(j)
    tmp=a(j): a(j)=a(i): a(i)=tmp
  end if
loop until i=0
 