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



 
class
	APPLICATION
 
create
	make
 
feature {NONE}
 
	make
		do
			test := <<2, 5, 1>>
			permute (test, 1)
		end
 
	test: ARRAY [INTEGER]
 
	permute (a: ARRAY [INTEGER]; k: INTEGER)
			-- All permutations of 'a'.
		require
			count_positive: a.count > 0
			k_valid_index: k > 0
		local
			t: INTEGER
		do
			if k = a.count then
				across
					a as ar
				loop
					io.put_integer (ar.item)
				end
				io.new_line
			else
				across
					k |..| a.count as c
				loop
					t := a [k]
					a [k] := a [c.item]
					a [c.item] := t
					permute (a, k + 1)
					t := a [k]
					a [k] := a [c.item]
					a [c.item] := t
				end
			end
		end
 
end
 
 