Make Kruskal spanning tree accept weight vector instead of matrix (#486)

* accept spanning tree vector instead of matrix for Kruskal

* replace equality with src and dst

Author: matbesancon

src/spanningtrees/kruskal.jl

@@ -1,31 +1,39 @@
 """
 	kruskal_mst(g, distmx=weights(g); minimize=true)
+	kruskal_mst(g, weight_vector; minimize=true)
 
 Return a vector of edges representing the minimum (by default) spanning tree of a connected, 
 undirected graph `g` with optional distance matrix `distmx` using [Kruskal's algorithm](https://en.wikipedia.org/wiki/Kruskal%27s_algorithm).
 
+Alternative to the distance matrix `distmx`, one can pass a `weight_vector` with weights ordered as `edges(g)`.
+
 ### Optional Arguments
 - `minimize=true`: if set to `false`, calculate the maximum spanning tree.
 """
 function kruskal_mst end
 # see https://github.com/mauro3/SimpleTraits.jl/issues/47#issuecomment-327880153 for syntax
 @traitfn function kruskal_mst(
     g::AG::(!IsDirected), distmx::AbstractMatrix{T}=weights(g); minimize=true
+) where {T<:Number,U,AG<:AbstractGraph{U}}
+    weight_vector = Vector{T}()
+    sizehint!(weight_vector, ne(g))
+    for e in edges(g)
+        push!(weight_vector, distmx[src(e), dst(e)])
+    end
+    return kruskal_mst(g, weight_vector; minimize=minimize)
+end
+
+@traitfn function kruskal_mst(
+    g::AG::(!IsDirected), weight_vector::AbstractVector{T}; minimize=true
 ) where {T<:Number,U,AG<:AbstractGraph{U}}
     connected_vs = IntDisjointSet(nv(g))
 
     mst = Vector{edgetype(g)}()
     nv(g) <= 1 && return mst
     sizehint!(mst, nv(g) - 1)
 
-    weights = Vector{T}()
-    sizehint!(weights, ne(g))
     edge_list = collect(edges(g))
-    for e in edge_list
-        push!(weights, distmx[src(e), dst(e)])
-    end
-
-    for e in edge_list[sortperm(weights; rev=(!minimize))]
+    for e in edge_list[sortperm(weight_vector; rev=(!minimize))]
         if !in_same_set(connected_vs, src(e), dst(e))
             union!(connected_vs, src(e), dst(e))
             push!(mst, e)

test/spanningtrees/kruskal.jl

@@ -8,6 +8,8 @@
         6 10 3 0
     ]
 
+    weight_vector = [distmx[src(e), dst(e)] for e in edges(g4)]
+
     vec_mst = Vector{Edge}([Edge(1, 2), Edge(3, 4), Edge(2, 3)])
     max_vec_mst = Vector{Edge}([Edge(2, 4), Edge(1, 4), Edge(1, 3)])
     for g in test_generic_graphs(g4)
@@ -18,7 +20,15 @@
         # so instead we compare tuples of source and target vertices
         @test sort([(src(e), dst(e)) for e in mst]) == sort([(src(e), dst(e)) for e in vec_mst])
         @test sort([(src(e), dst(e)) for e in max_mst]) == sort([(src(e), dst(e)) for e in max_vec_mst])
+        # test equivalent vector form
+        mst_vec = @inferred(kruskal_mst(g, weight_vector))
+        max_mst_vec = @inferred(kruskal_mst(g, weight_vector, minimize=false))
+        @test src.(mst_vec) == src.(mst)
+        @test dst.(mst_vec) == dst.(mst)
+        @test src.(max_mst_vec) == src.(max_mst)
+        @test dst.(max_mst_vec) == dst.(max_mst)
     end
+
     # second test
     distmx_sec = [
         0 0 0.26 0 0.38 0 0.58 0.16
@@ -32,6 +42,8 @@
     ]
 
     gx = SimpleGraph(distmx_sec)
+    weight_vector_sec = [distmx_sec[src(e), dst(e)] for e in edges(gx)]
+
     vec2 = Vector{Edge}([
         Edge(1, 8), Edge(3, 4), Edge(2, 8), Edge(1, 3), Edge(6, 8), Edge(5, 6), Edge(3, 7)
     ])
@@ -40,9 +52,15 @@
     ])
     for g in test_generic_graphs(gx)
         mst2 = @inferred(kruskal_mst(g, distmx_sec))
+        mst2_vec = @inferred(kruskal_mst(g, weight_vector_sec))
         max_mst2 = @inferred(kruskal_mst(g, distmx_sec, minimize=false))
+        max_mst2_vec = @inferred(kruskal_mst(g, weight_vector_sec, minimize=false))
         @test sort([(src(e), dst(e)) for e in mst2]) == sort([(src(e), dst(e)) for e in vec2])
         @test sort([(src(e), dst(e)) for e in max_mst2]) == sort([(src(e), dst(e)) for e in max_vec2])
+        @test src.(mst2) == src.(mst2_vec)
+        @test dst.(mst2) == dst.(mst2_vec)
+        @test src.(max_mst2) == src.(max_mst2_vec)
+        @test dst.(max_mst2) == dst.(max_mst2_vec)
     end
 
     # non regression test for #362