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



SUB perms (n)
    DIM a(0 TO n - 1), c(0 TO n - 1)
 
    FOR j = 0 TO n - 1
        a(j) = j + 1
        PRINT a(j);
    NEXT j
    PRINT
 
    i = 0
    WHILE i < n
        IF c(i) < i THEN
            IF (i AND 1) = 0 THEN
                SWAP a(0), a(i)
            ELSE
                SWAP a(c(i)), a(i)
            END IF
            FOR j = 0 TO n - 1
                PRINT a(j);
            NEXT j
            PRINT
            c(i) = c(i) + 1
            i = 0
        ELSE
            c(i) = 0
            i = i + 1
        END IF
    WEND
END SUB
 
perms(4)