Fix A* implementation (JuliaGraphs#125)

* Fix A* with additional argument edgetype_to_return

* Concrete key type in A* priority queue

* Add back closed_set and type restriction heuristic::Function

.gitignore

@@ -7,4 +7,4 @@ docs/site/
 benchmark/.results/*
 benchmark/.tune.jld
 *.cov
-Manifest.toml
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docs/Project.toml

@@ -1,5 +1,6 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 
 [compat]
 Documenter = "~0.26.2"

src/shortestpaths/astar.jl

@@ -6,12 +6,11 @@
 function reconstruct_path!(total_path, # a vector to be filled with the shortest path
     came_from, # a vector holding the parent of each node in the A* exploration
     end_idx, # the end vertex
-    g) # the graph
-
-    E = edgetype(g)
+    g,  # the graph
+    edgetype_to_return::Type{E}=edgetype(g)) where {E<:AbstractEdge}
     curr_idx = end_idx
     while came_from[curr_idx] != curr_idx
-        pushfirst!(total_path, E(came_from[curr_idx], curr_idx))
+        pushfirst!(total_path, edgetype_to_return(came_from[curr_idx], curr_idx))
         curr_idx = came_from[curr_idx]
     end
 end
@@ -21,19 +20,17 @@ function a_star_impl!(g, # the graph
     open_set, # an initialized heap containing the active vertices
     closed_set, # an (initialized) color-map to indicate status of vertices
     g_score, # a vector holding g scores for each node
-    f_score, # a vector holding f scores for each node
     came_from, # a vector holding the parent of each node in the A* exploration
     distmx,
-    heuristic)
-
-    E = edgetype(g)
-    total_path = Vector{E}()
+    heuristic,
+    edgetype_to_return::Type{E}) where {E<:AbstractEdge}
+    total_path = Vector{edgetype_to_return}()
 
     @inbounds while !isempty(open_set)
         current = dequeue!(open_set)
 
         if current == goal
-            reconstruct_path!(total_path, came_from, current, g)
+            reconstruct_path!(total_path, came_from, current, g, edgetype_to_return)
             return total_path
         end
 
@@ -56,38 +53,47 @@ function a_star_impl!(g, # the graph
 end
 
 """
-    a_star(g, s, t[, distmx][, heuristic])
+    a_star(g, s, t[, distmx][, heuristic][, edgetype_to_return])
+
+Compute a shortest path using the [A* search algorithm](http://en.wikipedia.org/wiki/A%2A_search_algorithm).
 
-Return a vector of edges comprising the shortest path between vertices `s` and `t`
-using the [A* search algorithm](http://en.wikipedia.org/wiki/A%2A_search_algorithm).
-An optional heuristic function and edge distance matrix may be supplied. If missing,
-the distance matrix is set to [`Graphs.DefaultDistance`](@ref) and the heuristic is set to
-`n -> 0`.
+# Arguments
+- `g::AbstractGraph`: the graph
+- `s::Integer`: the source vertex
+- `t::Integer`: the target vertex
+- `distmx::AbstractMatrix`: an optional (possibly sparse) `n × n` matrix of edge weights. It is set to `weights(g)` by default (which itself falls back on [`Graphs.DefaultDistance`](@ref)).
+- `heuristic::Function`: an optional function mapping each vertex to a lower estimate of the remaining distance from `v` to `t`. It is set to `v -> 0` by default (which corresponds to Dijkstra's algorithm)
+- `edgetype_to_return::Type{E}`: the eltype `E<:AbstractEdge` of the vector of edges returned. It is set to `edgetype(g)` by default. Note that the two-argument constructor `E(u, v)` must be defined, even for weighted edges: if it isn't, consider using `E = Graphs.SimpleEdge`.
 """
 function a_star(g::AbstractGraph{U},  # the g
     s::Integer,                       # the start vertex
     t::Integer,                       # the end vertex
     distmx::AbstractMatrix{T}=weights(g),
-    heuristic::Function=n -> zero(T)) where {T, U}
-
-    E = Edge{eltype(g)}
-
+    heuristic::Function=n -> zero(T),
+    edgetype_to_return::Type{E}=edgetype(g)) where {T, U, E<:AbstractEdge}
     # if we do checkbounds here, we can use @inbounds in a_star_impl!
     checkbounds(distmx, Base.OneTo(nv(g)), Base.OneTo(nv(g)))
 
-    open_set = PriorityQueue{Integer, T}()
+    open_set = PriorityQueue{U, T}()
     enqueue!(open_set, s, 0)
 
     closed_set = zeros(Bool, nv(g))
 
     g_score = fill(Inf, nv(g))
     g_score[s] = 0
 
-    f_score = fill(Inf, nv(g))
-    f_score[s] = heuristic(s)
-
     came_from = fill(-one(s), nv(g))
     came_from[s] = s
 
-    a_star_impl!(g, t, open_set, closed_set, g_score, f_score, came_from, distmx, heuristic)
+    a_star_impl!(
+        g,
+        t,
+        open_set,
+        closed_set,
+        g_score,
+        came_from,
+        distmx,
+        heuristic,
+        edgetype_to_return
+    )
 end

test/shortestpaths/astar.jl

@@ -15,4 +15,11 @@
     g = complete_graph(4)
     w = float([1 1 1 4; 1 1 1 1; 1 1 1 1; 4 1 1 1])
     @test length(a_star(g, 1, 4, w)) == 2
+
+    # test for #120
+    struct MyFavoriteEdgeType <: AbstractEdge{Int}
+        s::Int
+        d::Int
+    end
+    @test eltype(a_star(g, 1, 4, w, n -> 0, MyFavoriteEdgeType)) == MyFavoriteEdgeType
 end