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



next.perm <- function(a) {
  n <- length(a)
  i <- n
  while (i > 1 && a[i - 1] >= a[i]) i <- i - 1
  if (i == 1) {
    NULL
  } else {
    j <- i
    k <- n
    while (j < k) {
      s <- a[j]
      a[j] <- a[k]
      a[k] <- s
      j <- j + 1
      k <- k - 1
    }
    s <- a[i - 1]
    j <- i
    while (a[j] <= s) j <- j + 1
    a[i - 1] <- a[j]
    a[j] <- s
    a
  }
}
 
perm <- function(n) {
  e <- NULL
  a <- 1:n
  repeat {
    e <- cbind(e, a)
    a <- next.perm(a)
    if (is.null(a)) break
  }
  unname(e)
}