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



code ChOut=8, CrLf=9;
def  N=4;                       \number of objects (letters)
char S0, S1(N);
 
proc Permute(D);                \Display all permutations of letters in S0
int D;                          \depth of recursion
int I, J;
[if D=N then
        [for I:= 0 to N-1 do ChOut(0, S1(I));
        CrLf(0);
        return;
        ];
for I:= 0 to N-1 do
        [for J:= 0 to D-1 do    \check if object (letter) already used
                if S1(J) = S0(I) then J:=100;
        if J<100 then
                [S1(D):= S0(I); \object (letter) not used so append it
                Permute(D+1);   \recurse next level deeper
                ];
        ];
];
 
[S0:= "rose ";                  \N different objects (letters)
Permute(0);                     \(space char avoids MSb termination)
]