Permutations with some identical elements: Difference between revisions

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Line 31: *   [[Permutations/Derangements]] <br><br> =={{header\|11l}}== {{trans\|Nim}} <syntaxhighlight lang="11l">F shouldSwap(s, start, curr) L(i) start .< curr I s[i] == s[curr] R 0B R 1B F findPerms(ss, index, n, &res) I index >= n res.append(ss) R V s = copy(ss) L(i) index .< n I shouldSwap(s, index, i) swap(&s[index], &s[i]) findPerms(s, index + 1, n, &res) swap(&s[index], &s[i]) F createSlice(nums, charSet) V result = ‘’ L(n) nums V i = L.index L 0 .< n result ‘’= charSet[i] R result [String] res1, res2, res3 V nums = [2, 1] V s = createSlice(nums, ‘12’) findPerms(s, 0, s.len, &res1) print(res1.join(‘ ’)) print() nums = [2, 3, 1] s = createSlice(nums, ‘123’) findPerms(s, 0, s.len, &res2) L(val) res2 print(val, end' I (L.index + 1) % 10 == 0 {"\n"} E ‘ ’) print() s = createSlice(nums, ‘ABC’) findPerms(s, 0, s.len, &res3) L(val) res3 print(val, end' I (L.index + 1) % 10 == 0 {"\n"} E ‘ ’)</syntaxhighlight> {{out}} <pre> 112 121 211 112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 122231 122321 122312 123221 123212 123122 132221 132212 132122 131222 211223 211232 211322 212123 212132 212213 212231 212321 212312 213221 213212 213122 221123 221132 221213 221231 221321 221312 222113 222131 222311 223121 223112 223211 231221 231212 231122 232121 232112 232211 312221 312212 312122 311222 321221 321212 321122 322121 322112 322211 AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCBA ABBCAB ABCBBA ABCBAB ABCABB ACBBBA ACBBAB ACBABB ACABBB BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCBA BABCAB BACBBA BACBAB BACABB BBAABC BBAACB BBABAC BBABCA BBACBA BBACAB BBBAAC BBBACA BBBCAA BBCABA BBCAAB BBCBAA BCABBA BCABAB BCAABB BCBABA BCBAAB BCBBAA CABBBA CABBAB CABABB CAABBB CBABBA CBABAB CBAABB CBBABA CBBAAB CBBBAA </pre> =={{header\|C++}}== <syntaxhighlight lang="cpp">#include <algorithm> #include <iostream> int main() { std::string str("AABBBC"); int count = 0; do { std::cout << str << (++count % 10 == 0 ? '\n' : ' '); } while (std::next_permutation(str.begin(), str.end())); }</syntaxhighlight> {{out}} <pre> AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCAB ABBCBA ABCABB ABCBAB ABCBBA ACABBB ACBABB ACBBAB ACBBBA BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCAB BABCBA BACABB BACBAB BACBBA BBAABC BBAACB BBABAC BBABCA BBACAB BBACBA BBBAAC BBBACA BBBCAA BBCAAB BBCABA BBCBAA BCAABB BCABAB BCABBA BCBAAB BCBABA BCBBAA CAABBB CABABB CABBAB CABBBA CBAABB CBABAB CBABBA CBBAAB CBBABA CBBBAA </pre> =={{header\|Dart}}== {{trans\|Tailspin}} <~~lang~~syntaxhighlight lang="dart"> import 'dart:io'; Line 74 ⟶ 164: yield* perms(elements); } </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 82 ⟶ 172: =={{header\|Factor}}== Removing duplicates from the list of all permutations: <~~lang~~syntaxhighlight lang="factor">USING: arrays grouping math math.combinatorics prettyprint sequences sets ; Line 89 ⟶ 179: members ; { 2 3 1 } distinct-permutations 10 group simple-table.</~~lang~~syntaxhighlight> {{out}} <pre> Line 101 ⟶ 191: Generating distinct permutations directly (more efficient in time and space): {{trans\|Go}} <~~lang~~syntaxhighlight lang="factor">USING: arrays io kernel locals math math.ranges sequences ; IN: rosetta-code.distinct-permutations Line 131 ⟶ 221: [ .distinct-permutations ] 2tri@ ; MAIN: main</~~lang~~syntaxhighlight> {{out}} <pre> Line 141 ⟶ 231: =={{header\|Go}}== This is based on the C++ code [https://www.geeksforgeeks.org/distinct-permutations-string-set-2/ here]. <~~lang~~syntaxhighlight lang="go">package main import "fmt" Line 196 ⟶ 286: findPerms(s, 0, len(s), &res3) fmt.Println(res3) }</~~lang~~syntaxhighlight> {{out}} Line 205 ⟶ 295: [AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCBA ABBCAB ABCBBA ABCBAB ABCABB ACBBBA ACBBAB ACBABB ACABBB BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCBA BABCAB BACBBA BACBAB BACABB BBAABC BBAACB BBABAC BBABCA BBACBA BBACAB BBBAAC BBBACA BBBCAA BBCABA BBCAAB BBCBAA BCABBA BCABAB BCAABB BCBABA BCBAAB BCBBAA CABBBA CABBAB CABABB CAABBB CBABBA CBABAB CBAABB CBBABA CBBAAB CBBBAA] </pre> =={{header\|Haskell}}== <syntaxhighlight lang="haskell">permutationsSomeIdentical :: [(a, Int)] -> [[a]] permutationsSomeIdentical [] = [[]] permutationsSomeIdentical xs = [ x : ys \| (x, xs_) <- select xs, ys <- permutationsSomeIdentical xs_ ] where select [] = [] select ((x, n) : xs) = (x, xs_) : [ (y, (x, n) : cs) \| (y, cs) <- select xs ] where xs_ \| 1 == n = xs \| otherwise = (x, pred n) : xs main :: IO () main = do print $ permutationsSomeIdentical [(1, 2), (2, 1)] print $ permutationsSomeIdentical [(1, 2), (2, 3), (3, 1)] print $ permutationsSomeIdentical [('A', 2), ('B', 3), ('C', 1)]</syntaxhighlight> {{out}} <pre> [[1,1,2],[1,2,1],[2,1,1]] [[1,1,2,2,2,3],[1,1,2,2,3,2],[1,1,2,3,2,2],[1,1,3,2,2,2],[1,2,1,2,2,3],[1,2,1,2,3,2],[1,2,1,3,2,2],[1,2,2,1,2,3],[1,2,2,1,3,2],[1,2,2,2,1,3],[1,2,2,2,3,1],[1,2,2,3,1,2],[1,2,2,3,2,1],[1,2,3,1,2,2],[1,2,3,2,1,2],[1,2,3,2,2,1],[1,3,1,2,2,2],[1,3,2,1,2,2],[1,3,2,2,1,2],[1,3,2,2,2,1],[2,1,1,2,2,3],[2,1,1,2,3,2],[2,1,1,3,2,2],[2,1,2,1,2,3],[2,1,2,1,3,2],[2,1,2,2,1,3],[2,1,2,2,3,1],[2,1,2,3,1,2],[2,1,2,3,2,1],[2,1,3,1,2,2],[2,1,3,2,1,2],[2,1,3,2,2,1],[2,2,1,1,2,3],[2,2,1,1,3,2],[2,2,1,2,1,3],[2,2,1,2,3,1],[2,2,1,3,1,2],[2,2,1,3,2,1],[2,2,2,1,1,3],[2,2,2,1,3,1],[2,2,2,3,1,1],[2,2,3,1,1,2],[2,2,3,1,2,1],[2,2,3,2,1,1],[2,3,1,1,2,2],[2,3,1,2,1,2],[2,3,1,2,2,1],[2,3,2,1,1,2],[2,3,2,1,2,1],[2,3,2,2,1,1],[3,1,1,2,2,2],[3,1,2,1,2,2],[3,1,2,2,1,2],[3,1,2,2,2,1],[3,2,1,1,2,2],[3,2,1,2,1,2],[3,2,1,2,2,1],[3,2,2,1,1,2],[3,2,2,1,2,1],[3,2,2,2,1,1]] ["AABBBC","AABBCB","AABCBB","AACBBB","ABABBC","ABABCB","ABACBB","ABBABC","ABBACB","ABBBAC","ABBBCA","ABBCAB","ABBCBA","ABCABB","ABCBAB","ABCBBA","ACABBB","ACBABB","ACBBAB","ACBBBA","BAABBC","BAABCB","BAACBB","BABABC","BABACB","BABBAC","BABBCA","BABCAB","BABCBA","BACABB","BACBAB","BACBBA","BBAABC","BBAACB","BBABAC","BBABCA","BBACAB","BBACBA","BBBAAC","BBBACA","BBBCAA","BBCAAB","BBCABA","BBCBAA","BCAABB","BCABAB","BCABBA","BCBAAB","BCBABA","BCBBAA","CAABBB","CABABB","CABBAB","CABBBA","CBAABB","CBABAB","CBABBA","CBBAAB","CBBABA","CBBBAA"] </pre> =={{header\|J}}== <syntaxhighlight lang="j"> ~.@(A.~ i.@!@#) (# i.@#) 2 1 0 0 1 0 1 0 1 0 0 (; {&'ABC') ~.@(A.~ i.@!@#) (# i.@#) 2 3 1 ┌───────────┬──────┐ │0 0 1 1 1 2│AABBBC│ │0 0 1 1 2 1│AABBCB│ │0 0 1 2 1 1│AABCBB│ │0 0 2 1 1 1│AACBBB│ │0 1 0 1 1 2│ABABBC│ │0 1 0 1 2 1│ABABCB│ │0 1 0 2 1 1│ABACBB│ │0 1 1 0 1 2│ABBABC│ │0 1 1 0 2 1│ABBACB│ │0 1 1 1 0 2│ABBBAC│ │0 1 1 1 2 0│ABBBCA│ │0 1 1 2 0 1│ABBCAB│ │0 1 1 2 1 0│ABBCBA│ │0 1 2 0 1 1│ABCABB│ │0 1 2 1 0 1│ABCBAB│ │0 1 2 1 1 0│ABCBBA│ │0 2 0 1 1 1│ACABBB│ │0 2 1 0 1 1│ACBABB│ │0 2 1 1 0 1│ACBBAB│ │0 2 1 1 1 0│ACBBBA│ │1 0 0 1 1 2│BAABBC│ │1 0 0 1 2 1│BAABCB│ │1 0 0 2 1 1│BAACBB│ │1 0 1 0 1 2│BABABC│ │1 0 1 0 2 1│BABACB│ │1 0 1 1 0 2│BABBAC│ │1 0 1 1 2 0│BABBCA│ │1 0 1 2 0 1│BABCAB│ │1 0 1 2 1 0│BABCBA│ │1 0 2 0 1 1│BACABB│ │1 0 2 1 0 1│BACBAB│ │1 0 2 1 1 0│BACBBA│ │1 1 0 0 1 2│BBAABC│ │1 1 0 0 2 1│BBAACB│ │1 1 0 1 0 2│BBABAC│ │1 1 0 1 2 0│BBABCA│ │1 1 0 2 0 1│BBACAB│ │1 1 0 2 1 0│BBACBA│ │1 1 1 0 0 2│BBBAAC│ │1 1 1 0 2 0│BBBACA│ │1 1 1 2 0 0│BBBCAA│ │1 1 2 0 0 1│BBCAAB│ │1 1 2 0 1 0│BBCABA│ │1 1 2 1 0 0│BBCBAA│ │1 2 0 0 1 1│BCAABB│ │1 2 0 1 0 1│BCABAB│ │1 2 0 1 1 0│BCABBA│ │1 2 1 0 0 1│BCBAAB│ │1 2 1 0 1 0│BCBABA│ │1 2 1 1 0 0│BCBBAA│ │2 0 0 1 1 1│CAABBB│ │2 0 1 0 1 1│CABABB│ │2 0 1 1 0 1│CABBAB│ │2 0 1 1 1 0│CABBBA│ │2 1 0 0 1 1│CBAABB│ │2 1 0 1 0 1│CBABAB│ │2 1 0 1 1 0│CBABBA│ │2 1 1 0 0 1│CBBAAB│ │2 1 1 0 1 0│CBBABA│ │2 1 1 1 0 0│CBBBAA│ └───────────┴──────┘</syntaxhighlight> =={{header\|jq}}== {{ works with\|jq}} '''Works with gojq, the Go implementation of jq''' First, we present the filters for generating the distinct permutations, and then some functions for pretty printing a solution for the task. <syntaxhighlight lang="jq"># Given an array of counts of the nonnegative integers, produce an array reflecting the multiplicities: # e.g. [3,1] => [0,0,0,1] def items: . as $in \| reduce range(0;length) as $i ([]; . + [range(0;$in[$i])\|$i]); # distinct permutations of the input array, via insertion def distinct_permutations: # Given an array as input, generate a stream by inserting $x at different positions to the left def insert($x): ((index([$x]) // length) + 1) as $ix \| range(0; $ix) as $pos \| .[0:$pos] + [$x] + .[$pos:]; if length <= 1 then . else .[0] as $first \| .[1:] \| distinct_permutations \| insert($first) end;</syntaxhighlight> For pretty-printing the results: <syntaxhighlight lang="jq"># Input: an array # Output: a stream of arrays def nwise($n): def w: if length <= $n then . else .[:$n], (.[$n:]\|w) end; w; def to_table: nwise(10) \| join(" ");</syntaxhighlight> The task: <syntaxhighlight lang="jq">[2,3,1] \| items \| [distinct_permutations \| join("")] \| to_table</syntaxhighlight> {{out}} <pre>001112 010112 100112 011012 101012 110012 011102 101102 110102 111002 011120 101120 110120 111020 111200 001121 010121 100121 011021 101021 110021 011201 101201 110201 112001 011210 101210 110210 112010 112100 001211 010211 100211 012011 102011 120011 012101 102101 120101 121001 012110 102110 120110 121010 121100 002111 020111 200111 021011 201011 210011 021101 201101 210101 211001 021110 201110 210110 211010 211100 </pre> =={{header\|Julia}}== ====With the Combinatorics package, create all permutations and filter out the duplicates==== <~~lang~~syntaxhighlight lang="julia">using Combinatorics catlist(spec) = mapreduce(i -> repeat([i], spec[i]), vcat, 1:length(spec)) Line 223 ⟶ 462: testpermwithident([2, 3, 1]) </~~lang~~syntaxhighlight>{{out}} <pre> Testing [2, 3, 1] yielding: Line 236 ⟶ 475: ====Generate directly==== {{trans\|Tailspin}} <~~lang~~syntaxhighlight lang="julia"> alpha(s, v) = map(i -> s[i], v) Line 255 ⟶ 494: println(map(p -> join(alpha("ABC", p), ""), distinctPerms([2, 3, 1]))) </syntaxhighlight> ~~</lang>~~ {{out}} <pre> ["AABBBC", "AABBCB", "AABCBB", "AACBBB", "ABABBC", "ABABCB", "ABACBB", "ABBABC", "ABBACB", "ABBBAC", "ABBBCA", "ABBCAB", "ABBCBA", "ABCABB", "ABCBAB", "ABCBBA", "ACABBB", "ACBABB", "ACBBAB", "ACBBBA", "BAABBC", "BAABCB", "BAACBB", "BABABC", "BABACB", "BABBAC", "BABBCA", "BABCAB", "BABCBA", "BACABB", "BACBAB", "BACBBA", "BBAABC", "BBAACB", "BBABAC", "BBABCA", "BBACAB", "BBACBA", "BBBAAC", "BBBACA", "BBBCAA", "BBCAAB", "BBCABA", "BBCBAA", "BCAABB", "BCABAB", "BCABBA", "BCBAAB", "BCBABA", "BCBBAA", "CAABBB", "CABABB", "CABBAB", "CABBBA", "CBAABB", "CBABAB", "CBABBA", "CBBAAB", "CBBABA", "CBBBAA"] </pre> =={{header\|Mathematica}}/{{header\|Wolfram Language}}== <syntaxhighlight lang="mathematica">ClearAll[PermsFromFrequencies] PermsFromFrequencies[l_List] := Module[{digs}, digs = Flatten[MapIndexed[ReverseApplied[ConstantArray], l]]; Permutations[digs] ] PermsFromFrequencies[{2, 3, 1}] // Column</syntaxhighlight> {{out}} <pre>{1,1,2,2,2,3} {1,1,2,2,3,2} {1,1,2,3,2,2} {1,1,3,2,2,2} {1,2,1,2,2,3} {1,2,1,2,3,2} {1,2,1,3,2,2} {1,2,2,1,2,3} {1,2,2,1,3,2} {1,2,2,2,1,3} {1,2,2,2,3,1} {1,2,2,3,1,2} {1,2,2,3,2,1} {1,2,3,1,2,2} {1,2,3,2,1,2} {1,2,3,2,2,1} {1,3,1,2,2,2} {1,3,2,1,2,2} {1,3,2,2,1,2} {1,3,2,2,2,1} {2,1,1,2,2,3} {2,1,1,2,3,2} {2,1,1,3,2,2} {2,1,2,1,2,3} {2,1,2,1,3,2} {2,1,2,2,1,3} {2,1,2,2,3,1} {2,1,2,3,1,2} {2,1,2,3,2,1} {2,1,3,1,2,2} {2,1,3,2,1,2} {2,1,3,2,2,1} {2,2,1,1,2,3} {2,2,1,1,3,2} {2,2,1,2,1,3} {2,2,1,2,3,1} {2,2,1,3,1,2} {2,2,1,3,2,1} {2,2,2,1,1,3} {2,2,2,1,3,1} {2,2,2,3,1,1} {2,2,3,1,1,2} {2,2,3,1,2,1} {2,2,3,2,1,1} {2,3,1,1,2,2} {2,3,1,2,1,2} {2,3,1,2,2,1} {2,3,2,1,1,2} {2,3,2,1,2,1} {2,3,2,2,1,1} {3,1,1,2,2,2} {3,1,2,1,2,2} {3,1,2,2,1,2} {3,1,2,2,2,1} {3,2,1,1,2,2} {3,2,1,2,1,2} {3,2,1,2,2,1} {3,2,2,1,1,2} {3,2,2,1,2,1} {3,2,2,2,1,1}</pre> =={{header\|MiniZinc}}== <syntaxhighlight lang="minizinc"> ~~<lang MiniZinc>~~ %Permutations with some identical elements. Nigel Galloway, September 9th., 2019 include "count.mzn"; Line 268 ⟶ 576: array [1..6] of var N: G; constraint count(G,A,2) /\ count(G,C,1); output [show(G)] </syntaxhighlight> ~~</lang>~~ {{out}} minizinc --all-solutions produces: Line 395 ⟶ 703: </pre> =={{header\|~~Perl~~Nim}}== {{~~libheader~~trans\|~~ntheory~~Go}} <syntaxhighlight lang="nim">import strutils ~~<lang perl>use ntheory qw<formultiperm>;~~ func shouldSwap(s: string; start, curr: int): bool = for i in start..<curr: if s[i] == s[curr]: return false return true func findPerms(s: string; index, n: int; res: var seq[string]) = if index >= n: res.add s return var s = s for i in index..<n: if s.shouldSwap(index, i): swap s[index], s[i] findPerms(s, index+1, n, res) swap s[index], s[i] func createSlice(nums: openArray[int]; charSet: string): string = for i, n in nums: for _ in 1..n: result.add charSet[i] when isMainModule: var res1, res2, res3: seq[string] var nums = @[2, 1] var s = createSlice(nums, "12") s.findPerms(0, s.len, res1) echo res1.join(" ") echo() nums = @[2, 3, 1] s = createSlice(nums, "123") findPerms(s, 0, s.len, res2) for i, val in res2: stdout.write val, if (i + 1) mod 10 == 0: '\n' else: ' ' echo() s = createSlice(nums, "ABC") findPerms(s, 0, s.len, res3) for i, val in res3: stdout.write val, if (i + 1) mod 10 == 0: '\n' else: ' '</syntaxhighlight> ~~formultiperm { print join('',@_) . ' ' } [<1 1 2>]; print "\n\n";~~ ~~formultiperm { print join('',@_) . ' ' } [<1 1 2 2 2 3>]; print "\n\n";~~ ~~formultiperm { print join('',@_) . ' ' } [split //,'AABBBC']; print "\n";</lang>~~ {{out}} <pre>112 121 211 112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 122231 122312 122321 123122 123212 123221 131222 132122 132212 132221 211223 211232 211322 212123 212132 212213 212231 212312 212321 213122 213212 213221 221123 221132 221213 221231 221312 221321 222113 222131 222311 223112 223121 223211 231122 231212 231221 232112 232121 232211 311222 312122 312212 312221 321122 321212 321221 322112 322121 322211 122231 122321 122312 123221 123212 123122 132221 132212 132122 131222 211223 211232 211322 212123 212132 212213 212231 212321 212312 213221 213212 213122 221123 221132 221213 221231 221321 221312 222113 222131 222311 223121 223112 223211 231221 231212 231122 232121 232112 232211 312221 312212 312122 311222 321221 321212 321122 322121 322112 322211 AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCAB ABBCBA ABCABB ABCBAB ABCBBA ACABBB ACBABB ACBBAB ACBBBA BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCAB BABCBA BACABB BACBAB BACBBA BBAABC BBAACB BBABAC BBABCA BBACAB BBACBA BBBAAC BBBACA BBBCAA BBCAAB BBCABA BBCBAA BCAABB BCABAB BCABBA BCBAAB BCBABA BCBBAA CAABBB CABABB CABBAB CABBBA CBAABB CBABAB CBABBA CBBAAB CBBABA CBBBAA</pre> ABBBCA ABBCBA ABBCAB ABCBBA ABCBAB ABCABB ACBBBA ACBBAB ACBABB ACABBB BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCBA BABCAB BACBBA BACBAB BACABB BBAABC BBAACB BBABAC BBABCA BBACBA BBACAB BBBAAC BBBACA BBBCAA BBCABA BBCAAB BBCBAA BCABBA BCABAB BCAABB BCBABA BCBAAB BCBBAA CABBBA CABBAB CABABB CAABBB CBABBA CBABAB CBAABB CBBABA CBBAAB CBBBAA</pre> =={{header\|Pascal}}== modified version to get permutations of different lenght.<BR> Most time consuming is appending to the stringlist.So I limited that to 10000<BR> One can use the string directly in EvaluatePerm. <syntaxhighlight lang="pascal">program PermWithRep;//of different length {$IFDEF FPC} {$mode Delphi} {$Optimization ON,All} {$ELSE} {$APPTYPE CONSOLE} {$ENDIF} uses sysutils,classes {for stringlist}; const cTotalSum = 16; cMaxCardsOnDeck = cTotalSum; CMaxCardsUsed = cTotalSum; type ~~=={{header\|Perl 6}}==~~ tDeckIndex = 0..cMaxCardsOnDeck-1; ~~{{works with\|Rakudo\|2019.07}}~~ tSequenceIndex = 0..CMaxCardsUsed; tDiffCardCount = Byte;//A..Z tSetElem = packed record ~~<lang perl6>sub permutations-with-some-identical-elements ( @elements, @reps = () ) {~~ Elemcount : tDeckIndex; ~~with @elements { (@reps ?? flat $_ Zxx @reps !! flat .keys.map(+1) Zxx .values).permutations».join.unique }~~ Elem : tDiffCardCount; } end; tRemSet = array [low(tDeckIndex)..High(tDeckIndex)] of tSetElem; ~~for (<2 1>,), (<2 3 1>,), (<A B C>, <2 3 1>), (<🦋 ⚽ 🙄>, <2 2 1>) {~~ tpRemSet = ^tRemSet; ~~put permutations-with-some-identical-elements \|$_;~~ tRemainSet = array [low(tSequenceIndex)..High(tSequenceIndex)] of tRemSet; ~~say '';~~ tCardSequence = array [low(tSequenceIndex)..High(tSequenceIndex)] of tDiffCardCount; ~~}</lang>~~ var {$ALIGN 32} RemainSets : tRemainSet; CardString : AnsiString; CS : pchar; sl :TStringList; gblMaxCardsUsed, gblMaxUsedIdx, gblPermCount : NativeInt; //**************************************************************************** procedure Out_SL(const sl:TStringlIst;colCnt:NativeInt); var j,i : NativeInt; begin j := colCnt; For i := 0 to sl.count-1 do Begin write(sl[i],' '); dec(j); if j= 0 then Begin writeln; j := colCnt; end; end; if j <> colCnt then writeln; end; procedure SetClear(var ioSet:tRemSet); begin fillChar(ioSet[0],SizeOf(ioSet),#0); end; procedure SetInit(var ioSet:tRemSet;const inSet:tRemSet); var i,j,k,sum : integer; begin ioSet := inSet; sum := 0; k := 0; write('Initial set : '); For i := Low(ioSet) to High(ioSet) do Begin j := inSet[i].ElemCount; if j <> 0 then inc(k); sum += j; For j := j downto 1 do write(chr(inSet[i].Elem)); end; gblMaxCardsUsed := sum; gblMaxUsedIdx := k; writeln(' lenght: ',sum,' different elements : ',k); end; procedure EvaluatePerm; Begin //append maximal 10000 strings if gblPermCount < 10000 then sl.append(CS); end; procedure Permute(depth,MaxCardsUsed:NativeInt); var pSetElem : tpRemSet;//^tSetElem; i : NativeInt; begin i := 0; pSetElem := @RemainSets[depth]; repeat if pSetElem^[i].Elemcount > 0 then begin //take one of the same elements of the stack //insert in result here string CS[depth] := chr(pSetElem^[i].Elem); //done one permutation IF depth = MaxCardsUsed then begin inc(gblpermCount); EvaluatePerm; end else begin RemainSets[depth+1]:=RemainSets[depth]; //remove one element dec(RemainSets[depth+1][i].ElemCount); Permute(depth+1,MaxCardsUsed); end; end; //move on to the next Elem inc(i); until i >= gblMaxUsedIdx; end; procedure Permutate(MaxCardsUsed:NativeInt); Begin gblpermCount := 0; if MaxCardsUsed > gblMaxCardsUsed then MaxCardsUsed := gblMaxCardsUsed; if MaxCardsUsed>0 then Begin setlength(CardString,MaxCardsUsed); CS := @CardString[1]; permute(0,MaxCardsUsed-1) end; end; var Manifolds : tRemSet; j :nativeInt; Begin SetClear(Manifolds); with Manifolds[0] do begin Elemcount := 2; Elem := Ord('A'); end; with Manifolds[1] do begin Elemcount := 3; Elem := Ord('B'); end; with Manifolds[2] do begin Elemcount := 1; Elem := Ord('C'); end; try sl := TStringList.create; SetInit(RemainSets[0], Manifolds); j := gblMaxCardsUsed; writeln('Count of elements: ',j); while j > 1 do begin sl.clear; Permutate(j); writeln('Length ',j:2,' Permutations ',gblpermCount:7); Out_SL(sl,80 DIV (Length(CS)+1)); writeln; dec(j); end; //change to 1,2,3 Manifolds[0].Elem := Ord('1'); Manifolds[1].Elem := Ord('2'); Manifolds[2].Elem := Ord('3'); SetInit(RemainSets[0], Manifolds); j := gblMaxCardsUsed; writeln('Count of elements: ',j); while j > 1 do begin sl.clear; Permutate(j); writeln('Length ',j:2,' Permutations ',gblpermCount:7); Out_SL(sl,80 DIV (Length(CS)+1)); writeln; dec(j); end; //extend by 3 more elements with Manifolds[3] do begin Elemcount := 2; Elem := Ord('4'); end; with Manifolds[4] do begin Elemcount := 3; Elem := Ord('5'); end; with Manifolds[5] do begin Elemcount := 1; Elem := Ord('6'); end; SetInit(RemainSets[0], Manifolds); j := gblMaxCardsUsed; writeln('Count of elements: ',j); sl.clear; Permutate(j); writeln('Length ',j:2,' Permutations ',gblpermCount:7); //Out_SL(sl,80 DIV (Length(CS)+1)); writeln; except writeln(' Stringlist Error '); end; sl.free; end.</syntaxhighlight> {{out}} <pre>~~112 121 211~~ Initial set : AABBBC lenght: 6 Count of elements: 6 Length 6 Permutations 60 AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCAB ABBCBA ABCABB ABCBAB ABCBBA ACABBB ACBABB ACBBAB ACBBBA BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCAB BABCBA BACABB BACBAB BACBBA BBAABC BBAACB BBABAC BBABCA BBACAB BBACBA BBBAAC BBBACA BBBCAA BBCAAB BBCABA BBCBAA BCAABB BCABAB BCABBA BCBAAB BCBABA BCBBAA CAABBB CABABB CABBAB CABBBA CBAABB CBABAB CBABBA CBBAAB CBBABA CBBBAA Length 5 Permutations 60 112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 122231 122312 122321 123122 123212 123221 131222 132122 132212 132221 211223 211232 211322 212123 212132 212213 212231 212312 212321 213122 213212 213221 221123 221132 221213 221231 221312 221321 222113 222131 222311 223112 223121 223211 231122 231212 231221 232112 232121 232211 311222 312122 312212 312221 321122 321212 321221 322112 322121 322211 AABBB AABBC AABCB AACBB ABABB ABABC ABACB ABBAB ABBAC ABBBA ABBBC ABBCA ABBCB ABCAB ABCBA ABCBB ACABB ACBAB ACBBA ACBBB BAABB BAABC BAACB BABAB BABAC BABBA BABBC BABCA BABCB BACAB BACBA BACBB BBAAB BBAAC BBABA BBABC BBACA BBACB BBBAA BBBAC BBBCA BBCAA BBCAB BBCBA BCAAB BCABA BCABB BCBAA BCBAB BCBBA CAABB CABAB CABBA CABBB CBAAB CBABA CBABB CBBAA CBBAB CBBBA Length 4 Permutations 38 AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCAB ABBCBA ABCABB ABCBAB ABCBBA ACABBB ACBABB ACBBAB ACBBBA BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCAB BABCBA BACABB BACBAB BACBBA BBAABC BBAACB BBABAC BBABCA BBACAB BBACBA BBBAAC BBBACA BBBCAA BBCAAB BBCABA BBCBAA BCAABB BCABAB BCABBA BCBAAB BCBABA BCBBAA CAABBB CABABB CABBAB CABBBA CBAABB CBABAB CBABBA CBBAAB CBBABA CBBBAA AABB AABC AACB ABAB ABAC ABBA ABBB ABBC ABCA ABCB ACAB ACBA ACBB BAAB BAAC BABA BABB BABC BACA BACB BBAA BBAB BBAC BBBA BBBC BBCA BBCB BCAA BCAB BCBA BCBB CAAB CABA CABB CBAA CBAB CBBA CBBB Length 3 Permutations 19 🦋🦋⚽⚽🙄 🦋🦋⚽🙄⚽ 🦋🦋🙄⚽⚽ 🦋⚽🦋⚽🙄 🦋⚽🦋🙄⚽ 🦋⚽⚽🦋🙄 🦋⚽⚽🙄🦋 🦋⚽🙄🦋⚽ 🦋⚽🙄⚽🦋 🦋🙄🦋⚽⚽ 🦋🙄⚽🦋⚽ 🦋🙄⚽⚽🦋 ⚽🦋🦋⚽🙄 ⚽🦋🦋🙄⚽ ⚽🦋⚽🦋🙄 ⚽🦋⚽🙄🦋 ⚽🦋🙄🦋⚽ ⚽🦋🙄⚽🦋 ⚽⚽🦋🦋🙄 ⚽⚽🦋🙄🦋 ⚽⚽🙄🦋🦋 ⚽🙄🦋🦋⚽ ⚽🙄🦋⚽🦋 ⚽🙄⚽🦋🦋 🙄🦋🦋⚽⚽ 🙄🦋⚽🦋⚽ 🙄🦋⚽⚽🦋 🙄⚽🦋🦋⚽ 🙄⚽🦋⚽🦋 🙄⚽⚽🦋🦋 AAB AAC ABA ABB ABC ACA ACB BAA BAB BAC BBA BBB BBC BCA BCB CAA CAB CBA CBB Length 2 Permutations 8 AA AB AC BA BB BC CA CB Initial set : 112223 lenght: 6 Count of elements: 6 Length 6 Permutations 60 112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 122231 122312 122321 123122 123212 123221 131222 132122 132212 132221 211223 211232 211322 212123 212132 212213 212231 212312 212321 213122 213212 213221 221123 221132 221213 221231 221312 221321 222113 222131 222311 223112 223121 223211 231122 231212 231221 232112 232121 232211 311222 312122 312212 312221 321122 321212 321221 322112 322121 322211 Length 5 Permutations 60 11222 11223 11232 11322 12122 12123 12132 12212 12213 12221 12223 12231 12232 12312 12321 12322 13122 13212 13221 13222 21122 21123 21132 21212 21213 21221 21223 21231 21232 21312 21321 21322 22112 22113 22121 22123 22131 22132 22211 22213 22231 22311 22312 22321 23112 23121 23122 23211 23212 23221 31122 31212 31221 31222 32112 32121 32122 32211 32212 32221 Length 4 Permutations 38 1122 1123 1132 1212 1213 1221 1222 1223 1231 1232 1312 1321 1322 2112 2113 2121 2122 2123 2131 2132 2211 2212 2213 2221 2223 2231 2232 2311 2312 2321 2322 3112 3121 3122 3211 3212 3221 3222 Length 3 Permutations 19 112 113 121 122 123 131 132 211 212 213 221 222 223 231 232 311 312 321 322 Length 2 Permutations 8 11 12 13 21 22 23 31 32 Initial set : 112223445556 lenght: 12 Count of elements: 12 Length 12 Permutations 3326400 </pre> =={{header\|Perl}}== {{libheader\|ntheory}} <syntaxhighlight lang="perl">use ntheory qw<formultiperm>; formultiperm { print join('',@_) . ' ' } [<1 1 2>]; print "\n\n"; formultiperm { print join('',@_) . ' ' } [<1 1 2 2 2 3>]; print "\n\n"; formultiperm { print join('',@_) . ' ' } [split //,'AABBBC']; print "\n";</syntaxhighlight> {{out}} <pre>112 121 211 112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 122231 122312 122321 123122 123212 123221 131222 132122 132212 132221 211223 211232 211322 212123 212132 212213 212231 212312 212321 213122 213212 213221 221123 221132 221213 221231 221312 221321 222113 222131 222311 223112 223121 223211 231122 231212 231221 232112 232121 232211 311222 312122 312212 312221 321122 321212 321221 322112 322121 322211 AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCAB ABBCBA ABCABB ABCBAB ABCBBA ACABBB ACBABB ACBBAB ACBBBA BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCAB BABCBA BACABB BACBAB BACBBA BBAABC BBAACB BBABAC BBABCA BBACAB BBACBA BBBAAC BBBACA BBBCAA BBCAAB BBCABA BBCBAA BCAABB BCABAB BCABBA BCBAAB BCBABA BCBBAA CAABBB CABABB CABBAB CABBBA CBAABB CBABAB CBABBA CBBAAB CBBABA CBBBAA</pre> =={{header\|Phix}}== {{trans\|Go}} <!--<syntaxhighlight lang="phix">(phixonline)--> ~~<lang Phix>function shouldSwap(string s, integer start, curr)~~ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> ~~for i=start to curr-1 do~~ <span style="color: #008080;">function</span> <span style="color: #000000;">shouldSwap</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">curr</span><span style="color: #0000FF;">)</span> ~~if s[i] == s[curr] then~~ <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">start</span> <span style="color: #008080;">to</span> <span style="color: #000000;">curr</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> ~~return false~~ <span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">curr</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> ~~end if~~ <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> ~~end for~~ <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> ~~return true~~ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> ~~end function~~ <span style="color: #008080;">return</span> <span style="color: #004600;">true</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> ~~function findPerms(string s, integer i=1, sequence res={})~~ ~~if i>length(s) then~~ <span style="color: #008080;">function</span> <span style="color: #000000;">findPerms</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">={})</span> ~~res = append(res, s)~~ <span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> ~~else~~ <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> ~~for j=i to length(s) do~~ <span style="color: #008080;">else</span> ~~if shouldSwap(s, i, j) then~~ <span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> ~~{s[i], s[j]} = {s[j], s[i]}~~ <span style="color: #008080;">if</span> <span style="color: #000000;">shouldSwap</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> ~~res = findPerms(s, i+1, res)~~ <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">si</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sj</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}</span> ~~{s[i], s[j]} = {s[j], s[i]}~~ <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sj</span> ~~end if~~ <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">si</span> ~~end for~~ <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">findPerms</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> ~~end if~~ <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">si</span> ~~return res~~ <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sj</span> ~~end function~~ <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> ~~function createSlice(sequence nums, string charSet)~~ <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> ~~string chars = ""~~ <span style="color: #008080;">return</span> <span style="color: #000000;">res</span> ~~for i=1 to length(nums) do~~ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> ~~chars &= repeat(charSet[i],nums[i])~~ ~~end for~~ <span style="color: #008080;">function</span> <span style="color: #000000;">createSlice</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">nums</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">charSet</span><span style="color: #0000FF;">)</span> ~~return chars~~ <span style="color: #004080;">string</span> <span style="color: #000000;">chars</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span> ~~end function~~ <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nums</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">chars</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">charSet</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">nums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> ~~pp(findPerms(createSlice({2,1}, "12"))) -- (=== findPerms("112"))~~ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> ~~pp(findPerms(createSlice({2,3,1}, "123"))) -- (=== findPerms("112223"))~~ <span style="color: #008080;">return</span> <span style="color: #000000;">chars</span> ~~pp(findPerms(createSlice({2,3,1}, "ABC"))) -- (=== findPerms("AABBBC"))</lang>~~ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">findPerms</span><span style="color: #0000FF;">(</span><span style="color: #000000;">createSlice</span><span style="color: #0000FF;">({</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span> <span style="color: #008000;">"12"</span><span style="color: #0000FF;">)))</span> <span style="color: #000080;font-style:italic;">-- (=== findPerms("112"))</span> <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">findPerms</span><span style="color: #0000FF;">(</span><span style="color: #000000;">createSlice</span><span style="color: #0000FF;">({</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span> <span style="color: #008000;">"123"</span><span style="color: #0000FF;">)))</span> <span style="color: #000080;font-style:italic;">-- (=== findPerms("112223"))</span> <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">findPerms</span><span style="color: #0000FF;">(</span><span style="color: #000000;">createSlice</span><span style="color: #0000FF;">({</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span> <span style="color: #008000;">"ABC"</span><span style="color: #0000FF;">)))</span> <span style="color: #000080;font-style:italic;">-- (=== findPerms("AABBBC"))</span> <!--</syntaxhighlight>--> {{out}} <pre> Line 489 ⟶ 1,130: `CBAABB`, `CBBABA`, `CBBAAB`, `CBBBAA`} </pre> ~~The~~You ~~following~~can ~~(createSlice~~also ~~omitted~~use ~~for~~a ~~brevity)~~builtin function ~~produces~~to produce exactly the same output, ~~but~~(createSlice ~~may~~omitted befor ~~significantly slower on large sets.~~clarity) <!--<syntaxhighlight lang="phix">(phixonline)--> ~~<lang Phix>function permutes(string s)~~ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> ~~sequence res = {}~~ <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> ~~for i=1 to factorial(length(s)) do~~ <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">permutes</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"112"</span><span style="color: #0000FF;">))</span> ~~res = append(res,permute(i,s))~~ <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">permutes</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"112223"</span><span style="color: #0000FF;">))</span> ~~end for~~ <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">permutes</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"AABBBC"</span><span style="color: #0000FF;">))</span> ~~return unique(res)~~ <!--</syntaxhighlight>--> ~~end function~~ =={{header\|Python}}== ~~pp(permutes("112"))~~ Set filters out unique permutations ~~pp(permutes("112223"))~~ <syntaxhighlight lang="python"> ~~pp(permutes("AABBBC"))</lang>~~ #Aamrun, 5th October 2021 from itertools import permutations numList = [2,3,1] baseList = [] for i in numList: for j in range(0,i): baseList.append(i) stringDict = {'A':2,'B':3,'C':1} baseString="" for i in stringDict: for j in range(0,stringDict[i]): baseString+=i print("Permutations for " + str(baseList) + " : ") [print(i) for i in set(permutations(baseList))] print("Permutations for " + baseString + " : ") [print(i) for i in set(permutations(baseString))] </syntaxhighlight> {{out}} <pre> Permutations for [2, 2, 3, 3, 3, 1] : (2, 1, 3, 2, 3, 3) (3, 2, 3, 3, 1, 2) (3, 2, 3, 1, 2, 3) (3, 3, 1, 2, 2, 3) (3, 3, 2, 2, 3, 1) (3, 1, 3, 3, 2, 2) (3, 1, 3, 2, 3, 2) (2, 3, 3, 3, 1, 2) (3, 3, 1, 3, 2, 2) (3, 1, 2, 3, 2, 3) (3, 2, 2, 1, 3, 3) (3, 2, 3, 2, 1, 3) (3, 1, 3, 2, 2, 3) (2, 3, 1, 3, 2, 3) (3, 2, 1, 2, 3, 3) (2, 3, 3, 2, 1, 3) (2, 3, 1, 3, 3, 2) (3, 3, 2, 3, 2, 1) (3, 3, 2, 2, 1, 3) (2, 2, 3, 3, 3, 1) (2, 3, 1, 2, 3, 3) (3, 3, 2, 3, 1, 2) (3, 3, 3, 2, 2, 1) (2, 1, 2, 3, 3, 3) (2, 3, 2, 3, 3, 1) (2, 1, 3, 3, 3, 2) (2, 2, 3, 3, 1, 3) (3, 1, 2, 2, 3, 3) (2, 3, 2, 1, 3, 3) (3, 2, 1, 3, 3, 2) (1, 3, 3, 3, 2, 2) (3, 3, 3, 2, 1, 2) (2, 3, 2, 3, 1, 3) (3, 2, 2, 3, 3, 1) (1, 3, 2, 2, 3, 3) (2, 1, 3, 3, 2, 3) (3, 2, 1, 3, 2, 3) (1, 3, 3, 2, 2, 3) (1, 3, 3, 2, 3, 2) (1, 2, 3, 3, 3, 2) (2, 3, 3, 1, 3, 2) (3, 3, 2, 1, 3, 2) (1, 2, 3, 2, 3, 3) (3, 3, 2, 1, 2, 3) (3, 2, 3, 3, 2, 1) (1, 3, 2, 3, 3, 2) (1, 2, 3, 3, 2, 3) (2, 3, 3, 1, 2, 3) (3, 2, 2, 3, 1, 3) (1, 3, 2, 3, 2, 3) (3, 1, 2, 3, 3, 2) (2, 3, 3, 2, 3, 1) (3, 3, 1, 2, 3, 2) (2, 2, 3, 1, 3, 3) (3, 3, 3, 1, 2, 2) (1, 2, 2, 3, 3, 3) (3, 2, 3, 1, 3, 2) (2, 2, 1, 3, 3, 3) (2, 3, 3, 3, 2, 1) (3, 2, 3, 2, 3, 1) Permutations for AABBBC : ('B', 'B', 'A', 'C', 'B', 'A') ('B', 'C', 'B', 'A', 'B', 'A') ('A', 'B', 'A', 'B', 'B', 'C') ('B', 'A', 'B', 'B', 'C', 'A') ('C', 'B', 'A', 'B', 'B', 'A') ('A', 'A', 'B', 'C', 'B', 'B') ('A', 'B', 'B', 'C', 'A', 'B') ('B', 'C', 'B', 'B', 'A', 'A') ('B', 'B', 'A', 'A', 'C', 'B') ('A', 'B', 'C', 'B', 'B', 'A') ('A', 'C', 'A', 'B', 'B', 'B') ('B', 'B', 'B', 'A', 'A', 'C') ('C', 'B', 'B', 'A', 'B', 'A') ('A', 'A', 'C', 'B', 'B', 'B') ('C', 'A', 'A', 'B', 'B', 'B') ('B', 'C', 'A', 'A', 'B', 'B') ('A', 'B', 'B', 'A', 'C', 'B') ('B', 'B', 'C', 'A', 'B', 'A') ('A', 'A', 'B', 'B', 'B', 'C') ('C', 'B', 'B', 'B', 'A', 'A') ('B', 'C', 'A', 'B', 'B', 'A') ('C', 'A', 'B', 'A', 'B', 'B') ('B', 'A', 'A', 'B', 'C', 'B') ('B', 'B', 'B', 'C', 'A', 'A') ('B', 'B', 'C', 'B', 'A', 'A') ('B', 'A', 'B', 'C', 'A', 'B') ('A', 'C', 'B', 'B', 'B', 'A') ('B', 'B', 'A', 'A', 'B', 'C') ('C', 'B', 'A', 'A', 'B', 'B') ('C', 'A', 'B', 'B', 'A', 'B') ('B', 'A', 'A', 'C', 'B', 'B') ('B', 'C', 'B', 'A', 'A', 'B') ('B', 'B', 'A', 'B', 'A', 'C') ('A', 'B', 'B', 'A', 'B', 'C') ('B', 'A', 'A', 'B', 'B', 'C') ('A', 'B', 'B', 'C', 'B', 'A') ('B', 'A', 'C', 'B', 'B', 'A') ('C', 'B', 'A', 'B', 'A', 'B') ('B', 'A', 'B', 'A', 'C', 'B') ('A', 'B', 'A', 'B', 'C', 'B') ('A', 'B', 'C', 'A', 'B', 'B') ('B', 'B', 'B', 'A', 'C', 'A') ('A', 'B', 'B', 'B', 'A', 'C') ('B', 'B', 'A', 'C', 'A', 'B') ('A', 'B', 'C', 'B', 'A', 'B') ('C', 'A', 'B', 'B', 'B', 'A') ('A', 'A', 'B', 'B', 'C', 'B') ('B', 'A', 'B', 'B', 'A', 'C') ('A', 'B', 'A', 'C', 'B', 'B') ('A', 'C', 'B', 'A', 'B', 'B') ('B', 'A', 'C', 'A', 'B', 'B') ('B', 'B', 'A', 'B', 'C', 'A') ('B', 'C', 'A', 'B', 'A', 'B') ('C', 'B', 'B', 'A', 'A', 'B') ('B', 'A', 'B', 'A', 'B', 'C') ('B', 'A', 'B', 'C', 'B', 'A') ('B', 'A', 'C', 'B', 'A', 'B') ('A', 'B', 'B', 'B', 'C', 'A') ('B', 'B', 'C', 'A', 'A', 'B') ('A', 'C', 'B', 'B', 'A', 'B') </pre> Alternatively, generalized to accept any iterable. <syntaxhighlight lang="python">"""Permutations with some identical elements. Requires Python >= 3.7.""" from itertools import chain from itertools import permutations from itertools import repeat from typing import Iterable from typing import Tuple from typing import TypeVar T = TypeVar("T") def permutations_repeated( duplicates: Iterable[int], symbols: Iterable[T], ) -> Iterable[Tuple[T, ...]]: """Return distinct permutations for `symbols` repeated `duplicates` times.""" iters = (repeat(sym, dup) for sym, dup in zip(symbols, duplicates)) return sorted( set( permutations( chain.from_iterable(iters), ), ), ) def main() -> None: print(permutations_repeated([2, 3, 1], range(1, 4))) # 1-based print(permutations_repeated([2, 3, 1], range(3))) # 0-based print(permutations_repeated([2, 3, 1], ["A", "B", "C"])) # letters if __name__ == "__main__": main() </syntaxhighlight> {{out}} <pre style="font-size:85%"> [(1, 1, 2, 2, 2, 3), (1, 1, 2, 2, 3, 2), (1, 1, 2, 3, 2, 2), (1, 1, 3, 2, 2, 2), (1, 2, 1, 2, 2, 3), (1, 2, 1, 2, 3, 2), (1, 2, 1, 3, 2, 2), (1, 2, 2, 1, 2, 3), (1, 2, 2, 1, 3, 2), (1, 2, 2, 2, 1, 3), (1, 2, 2, 2, 3, 1), (1, 2, 2, 3, 1, 2), (1, 2, 2, 3, 2, 1), (1, 2, 3, 1, 2, 2), (1, 2, 3, 2, 1, 2), (1, 2, 3, 2, 2, 1), (1, 3, 1, 2, 2, 2), (1, 3, 2, 1, 2, 2), (1, 3, 2, 2, 1, 2), (1, 3, 2, 2, 2, 1), (2, 1, 1, 2, 2, 3), (2, 1, 1, 2, 3, 2), (2, 1, 1, 3, 2, 2), (2, 1, 2, 1, 2, 3), (2, 1, 2, 1, 3, 2), (2, 1, 2, 2, 1, 3), (2, 1, 2, 2, 3, 1), (2, 1, 2, 3, 1, 2), (2, 1, 2, 3, 2, 1), (2, 1, 3, 1, 2, 2), (2, 1, 3, 2, 1, 2), (2, 1, 3, 2, 2, 1), (2, 2, 1, 1, 2, 3), (2, 2, 1, 1, 3, 2), (2, 2, 1, 2, 1, 3), (2, 2, 1, 2, 3, 1), (2, 2, 1, 3, 1, 2), (2, 2, 1, 3, 2, 1), (2, 2, 2, 1, 1, 3), (2, 2, 2, 1, 3, 1), (2, 2, 2, 3, 1, 1), (2, 2, 3, 1, 1, 2), (2, 2, 3, 1, 2, 1), (2, 2, 3, 2, 1, 1), (2, 3, 1, 1, 2, 2), (2, 3, 1, 2, 1, 2), (2, 3, 1, 2, 2, 1), (2, 3, 2, 1, 1, 2), (2, 3, 2, 1, 2, 1), (2, 3, 2, 2, 1, 1), (3, 1, 1, 2, 2, 2), (3, 1, 2, 1, 2, 2), (3, 1, 2, 2, 1, 2), (3, 1, 2, 2, 2, 1), (3, 2, 1, 1, 2, 2), (3, 2, 1, 2, 1, 2), (3, 2, 1, 2, 2, 1), (3, 2, 2, 1, 1, 2), (3, 2, 2, 1, 2, 1), (3, 2, 2, 2, 1, 1)] [(0, 0, 1, 1, 1, 2), (0, 0, 1, 1, 2, 1), (0, 0, 1, 2, 1, 1), (0, 0, 2, 1, 1, 1), (0, 1, 0, 1, 1, 2), (0, 1, 0, 1, 2, 1), (0, 1, 0, 2, 1, 1), (0, 1, 1, 0, 1, 2), (0, 1, 1, 0, 2, 1), (0, 1, 1, 1, 0, 2), (0, 1, 1, 1, 2, 0), (0, 1, 1, 2, 0, 1), (0, 1, 1, 2, 1, 0), (0, 1, 2, 0, 1, 1), (0, 1, 2, 1, 0, 1), (0, 1, 2, 1, 1, 0), (0, 2, 0, 1, 1, 1), (0, 2, 1, 0, 1, 1), (0, 2, 1, 1, 0, 1), (0, 2, 1, 1, 1, 0), (1, 0, 0, 1, 1, 2), (1, 0, 0, 1, 2, 1), (1, 0, 0, 2, 1, 1), (1, 0, 1, 0, 1, 2), (1, 0, 1, 0, 2, 1), (1, 0, 1, 1, 0, 2), (1, 0, 1, 1, 2, 0), (1, 0, 1, 2, 0, 1), (1, 0, 1, 2, 1, 0), (1, 0, 2, 0, 1, 1), (1, 0, 2, 1, 0, 1), (1, 0, 2, 1, 1, 0), (1, 1, 0, 0, 1, 2), (1, 1, 0, 0, 2, 1), (1, 1, 0, 1, 0, 2), (1, 1, 0, 1, 2, 0), (1, 1, 0, 2, 0, 1), (1, 1, 0, 2, 1, 0), (1, 1, 1, 0, 0, 2), (1, 1, 1, 0, 2, 0), (1, 1, 1, 2, 0, 0), (1, 1, 2, 0, 0, 1), (1, 1, 2, 0, 1, 0), (1, 1, 2, 1, 0, 0), (1, 2, 0, 0, 1, 1), (1, 2, 0, 1, 0, 1), (1, 2, 0, 1, 1, 0), (1, 2, 1, 0, 0, 1), (1, 2, 1, 0, 1, 0), (1, 2, 1, 1, 0, 0), (2, 0, 0, 1, 1, 1), (2, 0, 1, 0, 1, 1), (2, 0, 1, 1, 0, 1), (2, 0, 1, 1, 1, 0), (2, 1, 0, 0, 1, 1), (2, 1, 0, 1, 0, 1), (2, 1, 0, 1, 1, 0), (2, 1, 1, 0, 0, 1), (2, 1, 1, 0, 1, 0), (2, 1, 1, 1, 0, 0)] [('A', 'A', 'B', 'B', 'B', 'C'), ('A', 'A', 'B', 'B', 'C', 'B'), ('A', 'A', 'B', 'C', 'B', 'B'), ('A', 'A', 'C', 'B', 'B', 'B'), ('A', 'B', 'A', 'B', 'B', 'C'), ('A', 'B', 'A', 'B', 'C', 'B'), ('A', 'B', 'A', 'C', 'B', 'B'), ('A', 'B', 'B', 'A', 'B', 'C'), ('A', 'B', 'B', 'A', 'C', 'B'), ('A', 'B', 'B', 'B', 'A', 'C'), ('A', 'B', 'B', 'B', 'C', 'A'), ('A', 'B', 'B', 'C', 'A', 'B'), ('A', 'B', 'B', 'C', 'B', 'A'), ('A', 'B', 'C', 'A', 'B', 'B'), ('A', 'B', 'C', 'B', 'A', 'B'), ('A', 'B', 'C', 'B', 'B', 'A'), ('A', 'C', 'A', 'B', 'B', 'B'), ('A', 'C', 'B', 'A', 'B', 'B'), ('A', 'C', 'B', 'B', 'A', 'B'), ('A', 'C', 'B', 'B', 'B', 'A'), ('B', 'A', 'A', 'B', 'B', 'C'), ('B', 'A', 'A', 'B', 'C', 'B'), ('B', 'A', 'A', 'C', 'B', 'B'), ('B', 'A', 'B', 'A', 'B', 'C'), ('B', 'A', 'B', 'A', 'C', 'B'), ('B', 'A', 'B', 'B', 'A', 'C'), ('B', 'A', 'B', 'B', 'C', 'A'), ('B', 'A', 'B', 'C', 'A', 'B'), ('B', 'A', 'B', 'C', 'B', 'A'), ('B', 'A', 'C', 'A', 'B', 'B'), ('B', 'A', 'C', 'B', 'A', 'B'), ('B', 'A', 'C', 'B', 'B', 'A'), ('B', 'B', 'A', 'A', 'B', 'C'), ('B', 'B', 'A', 'A', 'C', 'B'), ('B', 'B', 'A', 'B', 'A', 'C'), ('B', 'B', 'A', 'B', 'C', 'A'), ('B', 'B', 'A', 'C', 'A', 'B'), ('B', 'B', 'A', 'C', 'B', 'A'), ('B', 'B', 'B', 'A', 'A', 'C'), ('B', 'B', 'B', 'A', 'C', 'A'), ('B', 'B', 'B', 'C', 'A', 'A'), ('B', 'B', 'C', 'A', 'A', 'B'), ('B', 'B', 'C', 'A', 'B', 'A'), ('B', 'B', 'C', 'B', 'A', 'A'), ('B', 'C', 'A', 'A', 'B', 'B'), ('B', 'C', 'A', 'B', 'A', 'B'), ('B', 'C', 'A', 'B', 'B', 'A'), ('B', 'C', 'B', 'A', 'A', 'B'), ('B', 'C', 'B', 'A', 'B', 'A'), ('B', 'C', 'B', 'B', 'A', 'A'), ('C', 'A', 'A', 'B', 'B', 'B'), ('C', 'A', 'B', 'A', 'B', 'B'), ('C', 'A', 'B', 'B', 'A', 'B'), ('C', 'A', 'B', 'B', 'B', 'A'), ('C', 'B', 'A', 'A', 'B', 'B'), ('C', 'B', 'A', 'B', 'A', 'B'), ('C', 'B', 'A', 'B', 'B', 'A'), ('C', 'B', 'B', 'A', 'A', 'B'), ('C', 'B', 'B', 'A', 'B', 'A'), ('C', 'B', 'B', 'B', 'A', 'A')] </pre> =={{header\|Quackery}}== This is Narayana Pandita’s algorithm to generate the lexicographically next permutation from a given permutation, described in गणित कौमुदी ("Ganita Kaumudi", Google translation "Math skills", literal translation "Moonlight of Mathematics") pub. CE1356. Starting with a list of characters (Initially in lexicographic order, <code>A < B < C < D < E < F etc.</code>, here we consider an arbitrary permutation in the middle of the sequence.) <pre>[ B C F E D A ]</pre> Scan from right to left to find the first character that is less than the previous character (N). <pre>[ B C F E D A ] ↑</pre> * If they are in reverse order <code>[ F E D C B A ]</code> that is the lexicographically last permutation. Scan from right to left to find the first one that is greater than N. <pre>[ B C F E D A ] ↑ ↑</pre> Exchange them. <pre>[ B D F E C A ] ↑ ↑</pre> Reverse the order of the characters to the right of the first found character. <pre>[ B D A C E F ] ↑</pre> This is the next permutation. * There is one permutation of the empty list, <code>[ ]</code>; it is the empty list, <code>[ ]</code>. The code presented here checks explicitly for this to avoid an array out of bounds error. * When the lexicographically last permutation is detected, the code presented here reverses the whole list and skips the rest of the steps, returning the lexicographically first permutation, so repeated calls to <code>nextperm</code> will cycle through the permutations forever. This means there is no requirement to start with the lexicographically first permutation, but you will need to either precompute the number of permutations (<code>countperms</code>) or compare each permutation returned by <code>nextperm</code> to the first permutation. <syntaxhighlight lang="Quackery"> [ dup [] = if done 0 over dup -1 peek over size times [ over i 1 - peek tuck > if [ rot drop i unrot conclude ] ] 2drop split swap dup [] = iff [ drop reverse ] done -1 pluck rot 0 unrot dup size times [ 2dup i peek < if [ rot drop i 1+ unrot conclude ] ] rot split swap -1 pluck dip [ unrot join join reverse ] swap join join ] is nextperm ( [ --> [ ) [ 1 swap times [ i^ 1+ * ] ] is ! ( n --> n ) [ 0 over witheach + ! swap witheach [ ! / ] ] is permcount ( [ --> n ) [ [] swap $ "" over witheach [ i^ char A + swap of join ] swap permcount times [ dup dip [ nested join ] nextperm ] drop 70 wrap$ ] is task ( [ --> ) ' [ 2 3 1 ] task</syntaxhighlight> {{out}} <pre>AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCAB ABBCBA ABCABB ABCBAB ABCBBA ACABBB ACBABB ACBBAB ACBBBA BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCAB BABCBA BACABB BACBAB BACBBA BBAABC BBAACB BBABAC BBABCA BBACAB BBACBA BBBAAC BBBACA BBBCAA BBCAAB BBCABA BBCBAA BCAABB BCABAB BCABBA BCBAAB BCBABA BCBBAA CAABBB CABABB CABBAB CABBBA CBAABB CBABAB CBABBA CBBAAB CBBABA CBBBAA </pre> '''Bonus code''' Counting the permutations of "senselessness". It would be more efficient to use the formula given in the task description, n!/(a1! × a2! ... × ak!), (implemented as <code>permcount</code>), which yields 180180. This confirms that computation. <syntaxhighlight lang="Quackery"> 0 $ "senselessness" dup [ rot 1+ unrot nextperm 2dup = until ] 2drop echo say " permutations generated"</syntaxhighlight> {{out}} <pre>180180 permutations generated</pre> =={{header\|Raku}}== (formerly Perl 6) {{works with\|Rakudo\|2019.07}} <syntaxhighlight lang="raku" line>sub permutations-with-some-identical-elements ( @elements, @reps = () ) { with @elements { (@reps ?? flat $_ Zxx @reps !! flat .keys.map(+1) Zxx .values).permutations».join.unique } } for (<2 1>,), (<2 3 1>,), (<A B C>, <2 3 1>), (<🦋 ⚽ 🙄>, <2 2 1>) { put permutations-with-some-identical-elements \|$_; say ''; }</syntaxhighlight> {{out}} <pre>112 121 211 112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 122231 122312 122321 123122 123212 123221 131222 132122 132212 132221 211223 211232 211322 212123 212132 212213 212231 212312 212321 213122 213212 213221 221123 221132 221213 221231 221312 221321 222113 222131 222311 223112 223121 223211 231122 231212 231221 232112 232121 232211 311222 312122 312212 312221 321122 321212 321221 322112 322121 322211 AABBBC AABBCB AABCBB AACBBB ABABBC ABABCB ABACBB ABBABC ABBACB ABBBAC ABBBCA ABBCAB ABBCBA ABCABB ABCBAB ABCBBA ACABBB ACBABB ACBBAB ACBBBA BAABBC BAABCB BAACBB BABABC BABACB BABBAC BABBCA BABCAB BABCBA BACABB BACBAB BACBBA BBAABC BBAACB BBABAC BBABCA BBACAB BBACBA BBBAAC BBBACA BBBCAA BBCAAB BBCABA BBCBAA BCAABB BCABAB BCABBA BCBAAB BCBABA BCBBAA CAABBB CABABB CABBAB CABBBA CBAABB CBABAB CBABBA CBBAAB CBBABA CBBBAA 🦋🦋⚽⚽🙄 🦋🦋⚽🙄⚽ 🦋🦋🙄⚽⚽ 🦋⚽🦋⚽🙄 🦋⚽🦋🙄⚽ 🦋⚽⚽🦋🙄 🦋⚽⚽🙄🦋 🦋⚽🙄🦋⚽ 🦋⚽🙄⚽🦋 🦋🙄🦋⚽⚽ 🦋🙄⚽🦋⚽ 🦋🙄⚽⚽🦋 ⚽🦋🦋⚽🙄 ⚽🦋🦋🙄⚽ ⚽🦋⚽🦋🙄 ⚽🦋⚽🙄🦋 ⚽🦋🙄🦋⚽ ⚽🦋🙄⚽🦋 ⚽⚽🦋🦋🙄 ⚽⚽🦋🙄🦋 ⚽⚽🙄🦋🦋 ⚽🙄🦋🦋⚽ ⚽🙄🦋⚽🦋 ⚽🙄⚽🦋🦋 🙄🦋🦋⚽⚽ 🙄🦋⚽🦋⚽ 🙄🦋⚽⚽🦋 🙄⚽🦋🦋⚽ 🙄⚽🦋⚽🦋 🙄⚽⚽🦋🦋 </pre> =={{header\|REXX}}== ===shows permutation list=== <~~lang~~syntaxhighlight lang="rexx">/REXX program computes and displays the permutations with some identical elements. / parse arg g /obtain optional arguments from the CL/ if g='' \| g="," then g= 2 3 1 /Not specified? Then use the defaults/ Line 526 ⟶ 1,497: say 'number of permutations: ' words($) say say strip(translate($, @, left(123456789, #) ) ) /display the translated string to term/</~~lang~~syntaxhighlight> {{out\|output\|text=  when using the inputs of:     <tt> 2   1 </tt>}} <pre> Line 542 ⟶ 1,513: ===only shows permutation count=== If any of the arguments is negative, the list of the permutations is suppressed, only the permutation count is shown. <~~lang~~syntaxhighlight lang="rexx">/REXX program computes and displays the permutations with some identical elements. / parse arg g /obtain optional arguments from the CL/ if g='' \| g="," then g= 2 3 1 /Not specified? Then use the defaults/ Line 570 ⟶ 1,541: say 'number of permutations: ' words($) /# perms with some identical elements./ say if show then say strip(translate($, @, left(123456789, #) ) ) /display translated str./</~~lang~~syntaxhighlight> {{out\|output\|text=  when using the inputs of:     <tt> -2   3   1   1   1 </tt>}} <pre> Line 590 ⟶ 1,561: <pre> number of permutations: 5040 </pre> =={{header\|RPL}}== Based on the algorithm used by the Quackery implementation. {{works with\|HP\|48G}} {\| class="wikitable" ≪ ! RPL code ! Comment \|- \| ≪ → a b ≪ DUP a GET OVER b GET ROT ROT b SWAP PUT a ROT PUT ≫ ≫ '<span style="color:blue">SWAPITEMS</span>' STO ≪ DUP SIZE → n ≪ '''IF''' n 1 > '''THEN''' 1 CF n '''WHILE''' 1 FC? OVER 1 > AND '''REPEAT''' DUP2 GET ROT ROT 1 - DUP2 GET '''IF''' 4 ROLL < '''THEN''' 1 SF '''END''' '''END''' '''IF''' 1 FC?C '''THEN''' DROP SORT '''ELSE''' SWAP n '''WHILE''' 1 FC? OVER AND '''REPEAT''' DUP2 GET '''IF''' 3 PICK 5 PICK GET > '''THEN''' 1 SF '''ELSE''' 1 - '''END''' '''END''' 3 PICK <span style="color:blue">SWAPITEMS</span> SWAP DUP2 1 SWAP SUB ROT ROT 1 + n SUB REVLIST + '''END''' '''END''' ≫ ≫ ‘<span style="color:blue">NEXTPERM</span>’ STO \| <span style="color:blue">SWAPITEMS</span> ''( {list} a b → {list} ) '' get list items at a and b positions swap them return new list <span style="color:blue">NEXTPERM</span> ''( {list} → {list} )'' check at least 2 items in the list flag 1 controls loop break loop j = end downto 2 get list[j] and list[j-1] exit loop if list[j-1]<list[j] end loop if no break, this is the last perm else loop k = end downto 2 look for list[k] > list[j] end loop swap list[j] and list[k] reverse list, starting from j+1 return next permutation \|} ≪ → s ≪ "" 1 s SIZE '''FOR''' j s j GET 64 + CHR + '''NEXT''' ≫ ≫ '<span style="color:blue">→ABC</span>' STO ≪ { } 1 3 PICK SIZE '''FOR''' j 1 3 PICK j GET '''START''' j + '''NEXT NEXT''' SWAP DROP → b ≪ { } b '''DO''' SWAP OVER <span style="color:blue">→ABC</span> + SWAP <span style="color:blue">NEXTPERM</span> '''UNTIL''' DUP b == END '''DROP''' ≫ ≫ '<span style="color:blue">TASK</span>' STO { 2 3 1 } <span style="color:blue">TASK</span> {{out}} <pre> 1: { "AABBBC" "AABBCB" "AABCBB" "AACBBB" "ABABBC" "ABABCB" "ABACBB" "ABBABC" "ABBACB" "ABBBAC" ABBBCA" "ABBCAB" "ABBCBA" "ABCABB" "ABCBAB" "ABCBBA" "ACABBB" "ACBABB" "ACBBAB" "ACBBBA" "BAABBC" "BAABCB" "BAACBB" "BABABC" "BABACB" "BABBAC" "BABBCA" "BABCAB" "BABCBA" "BACABB" "BACBAB" "BACBBA" "BBAABC" "BBAACB" "BBABAC" "BBABCA" "BBACAB" "BBACBA" "BBBAAC" "BBBACA" "BBBCAA" "BBCAAB" "BBCABA" "BBCBAA" "BCAABB" "BCABAB" "BCABBA" "BCBAAB" "BCBABA" "BCBBAA" "CAABBB" "CABABB" "CABBAB" "CABBBA" "CBAABB" "CBABAB" "CBABBA" "CBBAAB" "CBBABA" "CBBBAA"} </pre> =={{header\|Ruby}}== <syntaxhighlight lang="ruby">require 'set' # for older Ruby versions def permutations_with_identical_elements(reps, elements=nil) elements \|\|= (1..reps.size) all = elements.zip(reps).flat_map{\|el, r\| [el]r} all.permutation.inject(Set.new){\|s, perm\| s << perm.join} end permutations_with_identical_elements([2,3,1]).each_slice(10) {\|slice\| puts slice.join(" ")} p permutations_with_identical_elements([2,1], ["A", "B"])</syntaxhighlight> {{out}} <pre>112223 112232 112322 113222 121223 121232 121322 122123 122132 122213 122231 122312 122321 123122 123212 123221 131222 132122 132212 132221 211223 211232 211322 212123 212132 212213 212231 212312 212321 213122 213212 213221 221123 221132 221213 221231 221312 221321 222113 222131 222311 223112 223121 223211 231122 231212 231221 232112 232121 232211 311222 312122 312212 312221 321122 321212 321221 322112 322121 322211 #<Set: {"AAB", "ABA", "BAA"}> </pre> =={{header\|Sidef}}== Simple implementation, by filtering out the duplicated permutations. <~~lang~~syntaxhighlight lang="ruby">func permutations_with_some_identical_elements (reps) { reps.map_kv {\|k,v\| v.of(k+1)... }.permutations.uniq } say permutations_with_some_identical_elements([2,1]).map{.join}.join(' ') say permutations_with_some_identical_elements([2,3,1]).map{.join}.join(' ')</~~lang~~syntaxhighlight> {{out}} <pre> Line 607 ⟶ 1,682: More efficient approach, by generating the permutations without duplicates: <~~lang~~syntaxhighlight lang="ruby">func next_uniq_perm (array) { var k = array.end Line 620 ⟶ 1,695: if (array[i+1] > array[k]) { array = [array.~~slice~~first(0, i+1)..., array.slice(i+1, ).first(k).flip...] } Line 648 ⟶ 1,723: say "\nPermutations with array = #{a}#{b ? \" and reps = #{b}\" : ''}:" say unique_permutations(a,b).map{.join}.join(' ') }</~~lang~~syntaxhighlight> {{out}} <pre> Line 663 ⟶ 1,738: =={{header\|Tailspin}}== Creates lots of new arrays, which might be wasteful. <~~lang~~syntaxhighlight lang="tailspin"> templates distinctPerms templates perms when <[](1)> do $(1) ! <>otherwise def elements: $; 1..$::length -> \( def k: $; def tail: $elements -> \[i]( when <?($i <=$k>)> do $ -> \(<[](2..)> $(2..last)!\) ! <>otherwise $! \); $tail -> perms -> [$elements($k;1), $...] ! Line 683 ⟶ 1,758: def alpha: ['ABC'...]; [[2,3,1] -> distinctPerms -> '$alpha($)...;' ] -> !OUT::write </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 690 ⟶ 1,765: Work in place (slightly modified from the Go solution to preserve lexical order) {{trans\|Go}} <~~lang~~syntaxhighlight lang="tailspin"> templates distinctPerms templates shouldSwap@&{start:} when <?($@distinctPerms($start..~$) <~[<=$@distinctPerms($)>]>)> do $! end shouldSwap templates findPerms when <$@distinctPerms::length..> do $@distinctPerms ! <>otherwise def index: $; $index..$@distinctPerms::length -> shouldSwap@&{start: $index} -> \( @findPerms: $; Line 710 ⟶ 1,785: 1 -> findPerms ! end distinctPerms def alpha: ['ABC'...]; [[2,3,1] -> distinctPerms -> '$alpha($)...;' ] -> !OUT::write </syntaxhighlight> ~~</lang>~~ {{out}} <pre> [AABBBC, AABBCB, AABCBB, AACBBB, ABABBC, ABABCB, ABACBB, ABBABC, ABBACB, ABBBAC, ABBBCA, ABBCAB, ABBCBA, ABCABB, ABCBAB, ABCBBA, ACABBB, ACBABB, ACBBAB, ACBBBA, BAABBC, BAABCB, BAACBB, BABABC, BABACB, BABBAC, BABBCA, BABCAB, BABCBA, BACABB, BACBAB, BACBBA, BBAABC, BBAACB, BBABAC, BBABCA, BBACAB, BBACBA, BBBAAC, BBBACA, BBBCAA, BBCAAB, BBCABA, BBCBAA, BCAABB, BCABAB, BCABBA, BCBAAB, BCBABA, BCBBAA, CAABBB, CABABB, CABBAB, CABBBA, CBAABB, CBABAB, CBABBA, CBBAAB, CBBABA, CBBBAA] </pre> =={{header\|Wren}}== {{libheader\|Wren-perm}} <syntaxhighlight lang="wren">import "./perm" for Perm var createList = Fn.new { \|nums, charSet\| var chars = [] for (i in 0...nums.count) { for (j in 0...nums[i]) chars.add(charSet[i]) } return chars } var nums = [2, 1] var a = createList.call(nums, "12") System.print(Perm.listDistinct(a).map { \|p\| p.join() }.toList) System.print() nums = [2, 3, 1] a = createList.call(nums, "123") System.print(Perm.listDistinct(a).map { \|p\| p.join() }.toList) System.print() a = createList.call(nums, "ABC") System.print(Perm.listDistinct(a).map { \|p\| p.join() }.toList)</syntaxhighlight> {{out}} <pre> [112, 121, 211] [112223, 112232, 112322, 113222, 121223, 121232, 121322, 122123, 122132, 122213, 122231, 122321, 122312, 123221, 123212, 123122, 132221, 132212, 132122, 131222, 211223, 211232, 211322, 212123, 212132, 212213, 212231, 212321, 212312, 213221, 213212, 213122, 221123, 221132, 221213, 221231, 221321, 221312, 222113, 222131, 222311, 223121, 223112, 223211, 231221, 231212, 231122, 232121, 232112, 232211, 312221, 312212, 312122, 311222, 321221, 321212, 321122, 322121, 322112, 322211] [AABBBC, AABBCB, AABCBB, AACBBB, ABABBC, ABABCB, ABACBB, ABBABC, ABBACB, ABBBAC, ABBBCA, ABBCBA, ABBCAB, ABCBBA, ABCBAB, ABCABB, ACBBBA, ACBBAB, ACBABB, ACABBB, BAABBC, BAABCB, BAACBB, BABABC, BABACB, BABBAC, BABBCA, BABCBA, BABCAB, BACBBA, BACBAB, BACABB, BBAABC, BBAACB, BBABAC, BBABCA, BBACBA, BBACAB, BBBAAC, BBBACA, BBBCAA, BBCABA, BBCAAB, BBCBAA, BCABBA, BCABAB, BCAABB, BCBABA, BCBAAB, BCBBAA, CABBBA, CABBAB, CABABB, CAABBB, CBABBA, CBABAB, CBAABB, CBBABA, CBBAAB, CBBBAA] </pre> =={{header\|zkl}}== <~~lang~~syntaxhighlight lang="zkl"> // eg ( (2,3,1), "ABC" ) == permute "A","A","B","B","B","C" and remove duplicates // --> ( "AABBBC", "AABBCB" .. ) // this gets ugly lots sooner than it should Line 727 ⟶ 1,836: Utils.Helpers.permute(_) : Utils.Helpers.listUnique(_) .apply("concat") // ("A","A","B","B","B","C")-->"AABBCB" }</~~lang~~syntaxhighlight> <~~lang~~syntaxhighlight lang="zkl">permutationsWithSomeIdenticalElements(T(2,1),"123").println(); permutationsWithSomeIdenticalElements(T(2,1),L("\u2192","\u2191")).concat(" ").println(); Line 734 ⟶ 1,843: println(z.len()); z.pump(Void,T(Void.Read,9,False), // print rows of ten items fcn{ vm.arglist.concat(" ").println() });</~~lang~~syntaxhighlight> {{out}} <pre>