Derangements

[FedericoStra]

Add a function to generate all derangements:

julia> map(join, derangements("abbac"))
4-element Vector{String}:
 "baacb"
 "bacba"
 "bcaba"
 "caabb"

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.22%. Comparing base (edb9c2c) to head (4944526).
Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #150   +/-   ##
=======================================
  Coverage   97.22%   97.22%           
=======================================
  Files           8        8           
  Lines         828      829    +1     
=======================================
+ Hits          805      806    +1     
  Misses         23       23           

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[inkydragon]

Can we make this error message better?
Maybe we could tell people to use a typed vector.

julia> collect(derangements([]))
ERROR: MethodError: no method matching multiset_permutations(::Vector{Any}, ::Vector{Any}, ::Int64)
The function `multiset_permutations` exists, but no method is defined for this combination of argument types.

[FedericoStra]

Can we make this error message better? Maybe we could tell people to use a typed vector.

julia> collect(derangements([]))
ERROR: MethodError: no method matching multiset_permutations(::Vector{Any}, ::Vector{Any}, ::Int64)
The function `multiset_permutations` exists, but no method is defined for this combination of argument types.

• I fixed a type instability in multiset_permutations that allows to call it with a=[]. Now the local variable f is always a Vector{Int}. Without the type annotation ::Int Julia wasn't able to infer that sum(<iterator of booleans>) returns an Int.

• I added also a test collect(derangements([])) == [[]].

[FedericoStra]

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.

[FedericoStra]

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.