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// Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package path
import (
"math"
"testing"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/graph/simple"
)
func TestVerifySpanningTreeTests(t *testing.T) {
t.Parallel()
for _, test := range spanningTreeTests {
var w float64
for _, e := range test.treeEdges {
w += e.W
}
if w != test.want {
t.Fatalf("bad test: %s weight mismatch: %v != %v", test.name, w, test.want)
}
}
}
type spanningGraph interface {
graph.WeightedBuilder
graph.WeightedUndirected
WeightedEdges() graph.WeightedEdges
}
var spanningTreeTests = []struct {
name string
graph func() spanningGraph
edges []simple.WeightedEdge
want float64
treeEdges []simple.WeightedEdge
}{
{
name: "Empty",
graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
want: 0,
},
{
// https://upload.wikimedia.org/wikipedia/commons/f/f7/Prim%27s_algorithm.svg
// Modified to make edge weights unique; A--B is increased to 2.5 otherwise
// to prevent the alternative solution being found.
name: "Prim WP figure 1",
graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
edges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('B'), W: 2.5},
{F: simple.Node('A'), T: simple.Node('D'), W: 1},
{F: simple.Node('B'), T: simple.Node('D'), W: 2},
{F: simple.Node('C'), T: simple.Node('D'), W: 3},
},
want: 6,
treeEdges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('D'), W: 1},
{F: simple.Node('B'), T: simple.Node('D'), W: 2},
{F: simple.Node('C'), T: simple.Node('D'), W: 3},
},
},
{
// https://upload.wikimedia.org/wikipedia/commons/5/5c/MST_kruskal_en.gif
name: "Kruskal WP figure 1",
graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
edges: []simple.WeightedEdge{
{F: simple.Node('a'), T: simple.Node('b'), W: 3},
{F: simple.Node('a'), T: simple.Node('e'), W: 1},
{F: simple.Node('b'), T: simple.Node('c'), W: 5},
{F: simple.Node('b'), T: simple.Node('e'), W: 4},
{F: simple.Node('c'), T: simple.Node('d'), W: 2},
{F: simple.Node('c'), T: simple.Node('e'), W: 6},
{F: simple.Node('d'), T: simple.Node('e'), W: 7},
},
want: 11,
treeEdges: []simple.WeightedEdge{
{F: simple.Node('a'), T: simple.Node('b'), W: 3},
{F: simple.Node('a'), T: simple.Node('e'), W: 1},
{F: simple.Node('b'), T: simple.Node('c'), W: 5},
{F: simple.Node('c'), T: simple.Node('d'), W: 2},
},
},
{
// https://upload.wikimedia.org/wikipedia/commons/8/87/Kruskal_Algorithm_6.svg
name: "Kruskal WP example",
graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
edges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('B'), W: 7},
{F: simple.Node('A'), T: simple.Node('D'), W: 5},
{F: simple.Node('B'), T: simple.Node('C'), W: 8},
{F: simple.Node('B'), T: simple.Node('D'), W: 9},
{F: simple.Node('B'), T: simple.Node('E'), W: 7},
{F: simple.Node('C'), T: simple.Node('E'), W: 5},
{F: simple.Node('D'), T: simple.Node('E'), W: 15},
{F: simple.Node('D'), T: simple.Node('F'), W: 6},
{F: simple.Node('E'), T: simple.Node('F'), W: 8},
{F: simple.Node('E'), T: simple.Node('G'), W: 9},
{F: simple.Node('F'), T: simple.Node('G'), W: 11},
},
want: 39,
treeEdges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('B'), W: 7},
{F: simple.Node('A'), T: simple.Node('D'), W: 5},
{F: simple.Node('B'), T: simple.Node('E'), W: 7},
{F: simple.Node('C'), T: simple.Node('E'), W: 5},
{F: simple.Node('D'), T: simple.Node('F'), W: 6},
{F: simple.Node('E'), T: simple.Node('G'), W: 9},
},
},
{
// https://upload.wikimedia.org/wikipedia/commons/2/2e/Boruvka%27s_algorithm_%28Sollin%27s_algorithm%29_Anim.gif
name: "Borůvka WP example",
graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
edges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('B'), W: 13},
{F: simple.Node('A'), T: simple.Node('C'), W: 6},
{F: simple.Node('B'), T: simple.Node('C'), W: 7},
{F: simple.Node('B'), T: simple.Node('D'), W: 1},
{F: simple.Node('C'), T: simple.Node('D'), W: 14},
{F: simple.Node('C'), T: simple.Node('E'), W: 8},
{F: simple.Node('C'), T: simple.Node('H'), W: 20},
{F: simple.Node('D'), T: simple.Node('E'), W: 9},
{F: simple.Node('D'), T: simple.Node('F'), W: 3},
{F: simple.Node('E'), T: simple.Node('F'), W: 2},
{F: simple.Node('E'), T: simple.Node('J'), W: 18},
{F: simple.Node('G'), T: simple.Node('H'), W: 15},
{F: simple.Node('G'), T: simple.Node('I'), W: 5},
{F: simple.Node('G'), T: simple.Node('J'), W: 19},
{F: simple.Node('G'), T: simple.Node('K'), W: 10},
{F: simple.Node('H'), T: simple.Node('J'), W: 17},
{F: simple.Node('I'), T: simple.Node('K'), W: 11},
{F: simple.Node('J'), T: simple.Node('K'), W: 16},
{F: simple.Node('J'), T: simple.Node('L'), W: 4},
{F: simple.Node('K'), T: simple.Node('L'), W: 12},
},
want: 83,
treeEdges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('C'), W: 6},
{F: simple.Node('B'), T: simple.Node('C'), W: 7},
{F: simple.Node('B'), T: simple.Node('D'), W: 1},
{F: simple.Node('D'), T: simple.Node('F'), W: 3},
{F: simple.Node('E'), T: simple.Node('F'), W: 2},
{F: simple.Node('E'), T: simple.Node('J'), W: 18},
{F: simple.Node('G'), T: simple.Node('H'), W: 15},
{F: simple.Node('G'), T: simple.Node('I'), W: 5},
{F: simple.Node('G'), T: simple.Node('K'), W: 10},
{F: simple.Node('J'), T: simple.Node('L'), W: 4},
{F: simple.Node('K'), T: simple.Node('L'), W: 12},
},
},
{
// https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg
// Nodes labelled row major.
name: "Minimum Spanning Tree WP figure 1",
graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
edges: []simple.WeightedEdge{
{F: simple.Node(1), T: simple.Node(2), W: 4},
{F: simple.Node(1), T: simple.Node(3), W: 1},
{F: simple.Node(1), T: simple.Node(4), W: 4},
{F: simple.Node(2), T: simple.Node(3), W: 5},
{F: simple.Node(2), T: simple.Node(5), W: 9},
{F: simple.Node(2), T: simple.Node(6), W: 9},
{F: simple.Node(2), T: simple.Node(8), W: 7},
{F: simple.Node(3), T: simple.Node(4), W: 3},
{F: simple.Node(3), T: simple.Node(8), W: 9},
{F: simple.Node(4), T: simple.Node(8), W: 10},
{F: simple.Node(4), T: simple.Node(10), W: 18},
{F: simple.Node(5), T: simple.Node(6), W: 2},
{F: simple.Node(5), T: simple.Node(7), W: 4},
{F: simple.Node(5), T: simple.Node(9), W: 6},
{F: simple.Node(6), T: simple.Node(7), W: 2},
{F: simple.Node(6), T: simple.Node(8), W: 8},
{F: simple.Node(7), T: simple.Node(8), W: 9},
{F: simple.Node(7), T: simple.Node(9), W: 3},
{F: simple.Node(7), T: simple.Node(10), W: 9},
{F: simple.Node(8), T: simple.Node(10), W: 8},
{F: simple.Node(9), T: simple.Node(10), W: 9},
},
want: 38,
treeEdges: []simple.WeightedEdge{
{F: simple.Node(1), T: simple.Node(2), W: 4},
{F: simple.Node(1), T: simple.Node(3), W: 1},
{F: simple.Node(2), T: simple.Node(8), W: 7},
{F: simple.Node(3), T: simple.Node(4), W: 3},
{F: simple.Node(5), T: simple.Node(6), W: 2},
{F: simple.Node(6), T: simple.Node(7), W: 2},
{F: simple.Node(6), T: simple.Node(8), W: 8},
{F: simple.Node(7), T: simple.Node(9), W: 3},
{F: simple.Node(8), T: simple.Node(10), W: 8},
},
},
{
// https://upload.wikimedia.org/wikipedia/commons/2/2e/Boruvka%27s_algorithm_%28Sollin%27s_algorithm%29_Anim.gif
// but with C--H and E--J cut.
name: "Borůvka WP example cut",
graph: func() spanningGraph { return simple.NewWeightedUndirectedGraph(0, math.Inf(1)) },
edges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('B'), W: 13},
{F: simple.Node('A'), T: simple.Node('C'), W: 6},
{F: simple.Node('B'), T: simple.Node('C'), W: 7},
{F: simple.Node('B'), T: simple.Node('D'), W: 1},
{F: simple.Node('C'), T: simple.Node('D'), W: 14},
{F: simple.Node('C'), T: simple.Node('E'), W: 8},
{F: simple.Node('D'), T: simple.Node('E'), W: 9},
{F: simple.Node('D'), T: simple.Node('F'), W: 3},
{F: simple.Node('E'), T: simple.Node('F'), W: 2},
{F: simple.Node('G'), T: simple.Node('H'), W: 15},
{F: simple.Node('G'), T: simple.Node('I'), W: 5},
{F: simple.Node('G'), T: simple.Node('J'), W: 19},
{F: simple.Node('G'), T: simple.Node('K'), W: 10},
{F: simple.Node('H'), T: simple.Node('J'), W: 17},
{F: simple.Node('I'), T: simple.Node('K'), W: 11},
{F: simple.Node('J'), T: simple.Node('K'), W: 16},
{F: simple.Node('J'), T: simple.Node('L'), W: 4},
{F: simple.Node('K'), T: simple.Node('L'), W: 12},
},
want: 65,
treeEdges: []simple.WeightedEdge{
{F: simple.Node('A'), T: simple.Node('C'), W: 6},
{F: simple.Node('B'), T: simple.Node('C'), W: 7},
{F: simple.Node('B'), T: simple.Node('D'), W: 1},
{F: simple.Node('D'), T: simple.Node('F'), W: 3},
{F: simple.Node('E'), T: simple.Node('F'), W: 2},
{F: simple.Node('G'), T: simple.Node('H'), W: 15},
{F: simple.Node('G'), T: simple.Node('I'), W: 5},
{F: simple.Node('G'), T: simple.Node('K'), W: 10},
{F: simple.Node('J'), T: simple.Node('L'), W: 4},
{F: simple.Node('K'), T: simple.Node('L'), W: 12},
},
},
}
func testMinimumSpanning(mst func(dst WeightedBuilder, g spanningGraph) float64, t *testing.T) {
for _, test := range spanningTreeTests {
g := test.graph()
for _, e := range test.edges {
g.SetWeightedEdge(e)
}
dst := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
w := mst(dst, g)
if w != test.want {
t.Errorf("unexpected minimum spanning tree weight for %q: got: %f want: %f",
test.name, w, test.want)
}
var got float64
for _, e := range graph.WeightedEdgesOf(dst.WeightedEdges()) {
got += e.Weight()
}
if got != test.want {
t.Errorf("unexpected minimum spanning tree edge weight sum for %q: got: %f want: %f",
test.name, got, test.want)
}
gotEdges := graph.EdgesOf(dst.Edges())
if len(gotEdges) != len(test.treeEdges) {
t.Errorf("unexpected number of spanning tree edges for %q: got: %d want: %d",
test.name, len(gotEdges), len(test.treeEdges))
}
for _, e := range test.treeEdges {
w, ok := dst.Weight(e.From().ID(), e.To().ID())
if !ok {
t.Errorf("spanning tree edge not found in graph for %q: %+v",
test.name, e)
}
if w != e.Weight() {
t.Errorf("unexpected spanning tree edge weight for %q: got: %f want: %f",
test.name, w, e.Weight())
}
}
}
}
func TestKruskal(t *testing.T) {
t.Parallel()
testMinimumSpanning(func(dst WeightedBuilder, g spanningGraph) float64 {
return Kruskal(dst, g)
}, t)
}
func TestPrim(t *testing.T) {
t.Parallel()
testMinimumSpanning(func(dst WeightedBuilder, g spanningGraph) float64 {
return Prim(dst, g)
}, t)
}
|
