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 TestPermutations;
 
{$APPTYPE CONSOLE}
 
type
  TItem = Integer;                // declare ordinal type for array item
  TArray = array[0..3] of TItem;
 
const
  Source: TArray = (1, 2, 3, 4);
 
procedure Permutation(K: Integer; var A: TArray);
var
  I, J: Integer;
  Tmp: TItem;
 
begin
  for I:= Low(A) + 1 to High(A) + 1 do begin
    J:= K mod I;
    Tmp:= A[J];
    A[J]:= A[I - 1];
    A[I - 1]:= Tmp;
    K:= K div I;
  end;
end;
 
var
  A: TArray;
  I, K, Count: Integer;
  S, S1, S2: ShortString;
 
begin
  Count:= 1;
  I:= Length(A);
  while I > 1 do begin
    Count:= Count * I;
    Dec(I);
  end;
 
  S:= '';
  for K:= 0 to Count - 1 do begin
    A:= Source;
    Permutation(K, A);
    S1:= '';
    for I:= Low(A) to High(A) do begin
      Str(A[I]:1, S2);
      S1:= S1 + S2;
    end;
    S:= S + '  ' + S1;
    if Length(S) > 40 then begin
      Writeln(S);
      S:= '';
    end;
  end;
 
  if Length(S) > 0 then Writeln(S);
  Readln;
end.