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merged 5 commits into from
May 10, 2025
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Derangements #150

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fa90350
Add a function to generate all derangements.
FedericoStra Dec 15, 2023
d16ccf7
Add tests for `derangements`
FedericoStra Dec 15, 2023
6897953
Add doctest for `derangements`
FedericoStra May 2, 2025
82fc13d
Fix type stability in `multiset_permutations`
FedericoStra May 10, 2025
4944526
Remove unnecessary call to `collect`
FedericoStra May 10, 2025
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41 changes: 39 additions & 2 deletions src/permutations.jl
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Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
#Permutations

export
derangements,
levicivita,
multiset_permutations,
nthperm!,
Expand Down Expand Up @@ -136,6 +137,42 @@ function permutations(a, t::Integer)
return Permutations(a, t)
end

"""
derangements(a)

Generate all derangements of an indexable object `a` in lexicographic order.
Because the number of derangements can be very large, this function returns an iterator object.
Use `collect(derangements(a))` to get an array of all derangements.
Only works for `a` with defined length.

# Examples
```jldoctest
julia> derangements("julia") |> collect
44-element Vector{Vector{Char}}:
['u', 'j', 'i', 'a', 'l']
['u', 'j', 'a', 'l', 'i']
['u', 'l', 'j', 'a', 'i']
['u', 'l', 'i', 'a', 'j']
['u', 'l', 'a', 'j', 'i']
['u', 'i', 'j', 'a', 'l']
['u', 'i', 'a', 'j', 'l']
['u', 'i', 'a', 'l', 'j']
['u', 'a', 'j', 'l', 'i']
['u', 'a', 'i', 'j', 'l']
⋮
['a', 'j', 'i', 'l', 'u']
['a', 'l', 'j', 'u', 'i']
['a', 'l', 'u', 'j', 'i']
['a', 'l', 'i', 'j', 'u']
['a', 'l', 'i', 'u', 'j']
['a', 'i', 'j', 'u', 'l']
['a', 'i', 'j', 'l', 'u']
['a', 'i', 'u', 'j', 'l']
['a', 'i', 'u', 'l', 'j']
```
"""
derangements(a) = (d for d in multiset_permutations(a, length(a)) if all(t -> t[1] != t[2], zip(a, d)))


function nextpermutation(m, t, state)
perm = [m[state[i]] for i in 1:t]
Expand Down Expand Up @@ -249,8 +286,8 @@ julia> collect(multiset_permutations([1,1,2], 3))
```
"""
function multiset_permutations(a, t::Integer)
m = unique(collect(a))
f = [sum([c == x for c in a]) for x in m]
m = unique(a)
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This call to collect is unnecessary because unique already collects the items into a new vector.

Benchmark Benchmark improves to 
julia> @benchmark multiset_permutations($a)
BenchmarkTools.Trial: 10000 samples with 27 evaluations per sample.
 Range (min … max):  930.074 ns … 160.078 μs  ┊ GC (min … max):  0.00% … 98.59%
 Time  (median):     956.333 ns               ┊ GC (median):     0.00%
 Time  (mean ± σ):     1.094 μs ±   3.083 μs  ┊ GC (mean ± σ):  10.17% ±  4.00%

  ▅█▇▅▃▁     ▁                                                  ▂
  ███████▇▆▇████▇▆▇▅▅▅▅▄▄▁▁▃▃▃▄▁▁▄▁▃▄▃▃▁▅▅▁▃▄▅▄▇▇▆▅▃▅▅▆▅▅▅▅▄▅▅▄ █
  930 ns        Histogram: log(frequency) by time       1.75 μs <

 Memory estimate: 2.16 KiB, allocs estimate: 33.

f = [sum(c == x for c in a)::Int for x in m]
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Here I also removed the square brackets to turn the comprehension into a generator expression, which is ever so slightly more efficient, as can be verified by benchmarking.

Benchmark 
julia> a = repeat(1:10, 3);

With comprehension:

julia> @benchmark multiset_permutations($a)
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
 Range (min … max):  1.284 μs …  1.236 ms  ┊ GC (min … max):  0.00% … 99.62%
 Time  (median):     1.350 μs              ┊ GC (median):     0.00%
 Time  (mean ± σ):   1.921 μs ± 16.533 μs  ┊ GC (mean ± σ):  12.11% ±  1.41%

  ▆█▇▄▂                   ▁   ▁▂ ▁▂▂▁▁▂▃▂▁▂▂▂▁▁▁▁▁           ▁
  █████▇▆▅▅▄▅▇▇▇▅▆▄▅▅▇▆▅▅▇██▇█████████████████████████▇▇▇▇▆▅ █
  1.28 μs      Histogram: log(frequency) by time     3.07 μs <

 Memory estimate: 3.39 KiB, allocs estimate: 55.

With generator expression:

julia> @benchmark multiset_permutations($a)
BenchmarkTools.Trial: 10000 samples with 22 evaluations per sample.
 Range (min … max):  943.545 ns … 462.770 μs  ┊ GC (min … max):  0.00% … 99.37%
 Time  (median):     976.227 ns               ┊ GC (median):     0.00%
 Time  (mean ± σ):     1.251 μs ±   5.907 μs  ┊ GC (mean ± σ):  13.38% ±  3.54%

  ▇█▄▁   ▁              ▁ ▂▂▁▂▁▂▁▁▁                             ▂
  ████▇▇████▇▆▅▄▃▁▁▁▁▄▆▆█████████████▇▇▆▆▆▄▄▄▄▁▄▄▄▃▅▄▃▃▁▄▄▁▃▁▁▅ █
  944 ns        Histogram: log(frequency) by time       2.54 μs <

 Memory estimate: 2.45 KiB, allocs estimate: 35.

multiset_permutations(m, f, t)
end

Expand Down
12 changes: 12 additions & 0 deletions test/permutations.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -68,6 +68,18 @@ end
@test collect(multiset_permutations("", -1)) == Any[]
@test length(multiset_permutations("aaaaaaaaaaaaaaaaaaaaab", 21)) == 22

# derangements
@test length(collect(derangements(1:4))) == 9
@test length(collect(derangements(1:8))) == derangement(8) == 14833
@test collect(derangements([])) == [[]]
@test collect(derangements(Int[])) == [Int[]]
@test collect(derangements([1])) == Vector{Int}[]
@test collect(derangements([1, 1])) == Vector{Int}[]
@test collect(derangements([1, 1, 2])) == Vector{Int}[]
@test collect(derangements([1, 1, 2, 2])) == [[2, 2, 1, 1]]
@test map(join, derangements("aabbc")) == ["bbaca", "bbcaa", "bcaab", "cbaab"]
@test map(join, derangements("aaabbbc")) == ["bbbaaca", "bbbacaa", "bbbcaaa", "bbcaaab", "bcbaaab", "cbbaaab"]

#nthperm!
for n = 0:7, k = 1:factorial(n)
p = nthperm!([1:n;], k)
Expand Down
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