From bc3931fe8bacea458e0e5a2c041933f6c99a9d7c Mon Sep 17 00:00:00 2001
From: Federico Stra <stra.federico@gmail.com>
Date: Tue, 6 May 2025 14:43:07 +0200
Subject: [PATCH 1/4] perf: optimize `permutations` by implementing it via
 `multiset_permutations`

As it currently stands, `multiset_permutations` is more efficient than
`permutations`; see #151. We can exploit it to optimize `permutations`.
---
 src/permutations.jl | 54 ++++++++++++++++-----------------------------
 1 file changed, 19 insertions(+), 35 deletions(-)

diff --git a/src/permutations.jl b/src/permutations.jl
index b6ef788..f008849 100644
--- a/src/permutations.jl
+++ b/src/permutations.jl
@@ -14,42 +14,26 @@ struct Permutations{T}
     length::Int
 end
 
-function has_repeats(state::Vector{Int})
-    # This can be safely marked inbounds because of the type restriction in the signature.
-    # If the type restriction is ever loosened, please check safety of the `@inbounds`
-    @inbounds for outer in eachindex(state)
-        for inner in (outer+1):lastindex(state)
-            if state[outer] == state[inner]
-                return true
-            end
-        end
-    end
-    return false
-end
-
-function increment!(state::Vector{Int}, min::Int, max::Int)
-    state[end] += 1
-    for i in reverse(eachindex(state))[firstindex(state):end-1]
-        if state[i] > max
-            state[i] = min
-            state[i-1] += 1
-        end
-    end
-end
-
-function next_permutation!(state::Vector{Int}, min::Int, max::Int)
-    while true
-        increment!(state, min, max)
-        has_repeats(state) || break
-    end
-end
-
-function Base.iterate(p::Permutations, state::Vector{Int}=fill(firstindex(p.data), p.length))
-    next_permutation!(state, firstindex(p.data), lastindex(p.data))
-    if first(state) > lastindex(p.data)
-        return nothing
+# The following code basically implements `permutations` in terms of `multiset_permutations` as
+#
+#     permutations(a, t::Integer=length(a)) = Iterators.map(
+#         indices -> [a[i] for i in indices],
+#         multiset_permutations(eachindex(a), t))
+#
+# with the difference that we can also define `eltype(::Permutations)`, which is used in some tests.
+
+function Base.iterate(p::Permutations, state=nothing)
+    if isnothing(state)
+        mp = multiset_permutations(eachindex(p.data), p.length)
+        it = iterate(mp)
+        if isnothing(it) return nothing end
+    else
+        mp, mp_state = state
+        it = iterate(mp, mp_state)
+        if isnothing(it) return nothing end
     end
-    [p.data[i] for i in state], state
+    indices, mp_state = it
+    return [p.data[i] for i in indices], (; mp, mp_state)
 end
 
 function Base.length(p::Permutations)

From 397a684a4bdd93459c1fe179c0fcb12200c6dd36 Mon Sep 17 00:00:00 2001
From: Federico Stra <stra.federico@gmail.com>
Date: Tue, 6 May 2025 15:06:25 +0200
Subject: [PATCH 2/4] fix: use explicit NamedTuple notation tu support Julia
 1.0

---
 src/permutations.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/permutations.jl b/src/permutations.jl
index f008849..855b30f 100644
--- a/src/permutations.jl
+++ b/src/permutations.jl
@@ -33,7 +33,7 @@ function Base.iterate(p::Permutations, state=nothing)
         if isnothing(it) return nothing end
     end
     indices, mp_state = it
-    return [p.data[i] for i in indices], (; mp, mp_state)
+    return [p.data[i] for i in indices], (mp=mp, mp_state=mp_state)
 end
 
 function Base.length(p::Permutations)

From 995a046531e1cea0fd6981810014a349997d595c Mon Sep 17 00:00:00 2001
From: Federico Stra <stra.federico@gmail.com>
Date: Tue, 6 May 2025 15:10:38 +0200
Subject: [PATCH 3/4] fix: don't use `isnothing` to support Julia 1.0

---
 src/permutations.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/permutations.jl b/src/permutations.jl
index 855b30f..a9de3d1 100644
--- a/src/permutations.jl
+++ b/src/permutations.jl
@@ -23,14 +23,14 @@ end
 # with the difference that we can also define `eltype(::Permutations)`, which is used in some tests.
 
 function Base.iterate(p::Permutations, state=nothing)
-    if isnothing(state)
+    if state === nothing
         mp = multiset_permutations(eachindex(p.data), p.length)
         it = iterate(mp)
-        if isnothing(it) return nothing end
+        if it === nothing return nothing end
     else
         mp, mp_state = state
         it = iterate(mp, mp_state)
-        if isnothing(it) return nothing end
+        if it === nothing return nothing end
     end
     indices, mp_state = it
     return [p.data[i] for i in indices], (mp=mp, mp_state=mp_state)

From 3f6ee6198aff32b47a8572614c03fa0b058ebc11 Mon Sep 17 00:00:00 2001
From: Federico Stra <stra.federico@gmail.com>
Date: Wed, 28 May 2025 19:32:22 +0200
Subject: [PATCH 4/4] fix: collect the indices into a `Vector`

Without this fix there are issues with `OffsetArray`: `eachindex`
returns an `OffsetArrays.IdOffsetRange`, which causes troubles when
passed to `multiset_permutations` because
`f = [sum(c == x for c in a)::Int for x in m]`
becomes an `OffsetArray` instead of a Vector`.
---
 src/permutations.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/permutations.jl b/src/permutations.jl
index 093def5..edab08a 100644
--- a/src/permutations.jl
+++ b/src/permutations.jl
@@ -25,7 +25,7 @@ end
 
 function Base.iterate(p::Permutations, state=nothing)
     if state === nothing
-        mp = multiset_permutations(eachindex(p.data), p.length)
+        mp = multiset_permutations(collect(eachindex(p.data)), p.length)
         it = iterate(mp)
         if it === nothing return nothing end
     else