add operations on graph
All checks were successful
continuous-integration/drone/push Build is passing

- fix DirectedCycle
- add DepthFirstOrder
- add SCC
- add TopologicalOrder
This commit is contained in:
Raffaele Mignone 2019-05-19 18:21:36 +02:00
parent ba2e2744ce
commit cfd8054c38
Signed by: norangebit
GPG Key ID: F5255658CB220573
7 changed files with 492 additions and 9 deletions

View File

@ -0,0 +1,71 @@
/*
* MIT License
*
* Copyright (c) 2019 norangebit
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
package it.norangeb.algorithms.graph.operations
import it.norangeb.algorithms.graph.UndirectedGraph
import java.util.ArrayDeque
class DepthFirstOrder(graph: UndirectedGraph) {
private val visited = Array(graph.vertexNumber()) { false }
private val preOrder: MutableCollection<Int> = ArrayDeque()
private val postOrder: MutableCollection<Int> = ArrayDeque()
init {
(0 until graph.vertexNumber())
.forEach {
if (!visited[it])
dfs(graph, it)
}
}
private fun dfs(graph: UndirectedGraph, vertex: Int) {
preOrder.add(vertex)
visited[vertex] = true
graph.adjacentVertex(vertex)
.forEach {
if (!visited[it])
dfs(graph, it)
}
postOrder.add(vertex)
}
fun preOrder(): Iterable<Int> {
return preOrder
}
fun postOrder(): Iterable<Int> {
return postOrder
}
fun reversePostOrder(): Iterable<Int> {
return postOrder.reversed()
}
}

View File

@ -36,7 +36,7 @@ class DirectedCycle(graph: DirectedGraph) {
init {
(0 until graph.vertexNumber())
.forEach {
if (!graphInfo[it].visited)
if (!graphInfo[it].isVisited)
dfs(graph, it)
}
}
@ -44,19 +44,19 @@ class DirectedCycle(graph: DirectedGraph) {
fun hasCycle(): Boolean = cycle != null
private fun dfs(graph: UndirectedGraph, vertex: Int) {
graphInfo[vertex].visited = true
graphInfo[vertex].onStack = true
graphInfo[vertex].isVisited = true
graphInfo[vertex].isOnStack = true
graph.adjacentVertex(vertex)
.forEach {
when {
hasCycle() -> return@forEach
!graphInfo[it].visited -> exploreChild(graph, vertex, it)
graphInfo[it].onStack -> cycle = makeCycle(vertex, it)
!graphInfo[it].isVisited -> exploreChild(graph, vertex, it)
graphInfo[it].isOnStack -> cycle = makeCycle(vertex, it)
}
}
graphInfo[vertex].onStack = false
graphInfo[vertex].isOnStack = false
}
private fun makeCycle(start: Int, end: Int): MutableCollection<Int> {
@ -80,9 +80,9 @@ class DirectedCycle(graph: DirectedGraph) {
dfs(graph, child)
}
data class VertexInfo(
var visited: Boolean = false,
var onStack: Boolean = false,
private data class VertexInfo(
var isVisited: Boolean = false,
var isOnStack: Boolean = false,
var previously: Int = -1
)
}

View File

@ -0,0 +1,65 @@
/*
* MIT License
*
* Copyright (c) 2019 norangebit
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
package it.norangeb.algorithms.graph.operations
import it.norangeb.algorithms.graph.DirectedGraph
import it.norangeb.algorithms.graph.UndirectedGraph
class StronglyConnectedComponents(graph: DirectedGraph) {
private val graphInfo = Array(graph.vertexNumber()) { VertexInfo() }
private var label = 0
init {
DepthFirstOrder(graph.reverse())
.reversePostOrder()
.forEach {
if (!graphInfo[it].isVisited)
dfs(graph, it, label++)
}
}
private fun dfs(graph: UndirectedGraph, vertex: Int, label: Int) {
graphInfo[vertex] = VertexInfo(true, label)
graph.adjacentVertex(vertex)
.forEach {
if (!graphInfo[it].isVisited)
dfs(graph, it, label)
}
}
fun count() = label
fun component(vertex: Int) = graphInfo[vertex].label
fun stronglyConnected(firstVertex: Int, secondVertex: Int) =
component(firstVertex) == component(secondVertex)
private data class VertexInfo(
var isVisited: Boolean = false,
var label: Int = -1
)
}

View File

@ -0,0 +1,41 @@
/*
* MIT License
*
* Copyright (c) 2019 norangebit
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
package it.norangeb.algorithms.graph.operations
import it.norangeb.algorithms.graph.DirectedGraph
class TopologicalOrder(graph: DirectedGraph) {
var order: Iterable<Int>? = null
init {
val cycle = DirectedCycle(graph)
if (!cycle.hasCycle())
order = DepthFirstOrder(graph).reversePostOrder()
}
fun isDag() = order != null
}

View File

@ -0,0 +1,64 @@
/*
* MIT License
*
* Copyright (c) 2019 norangebit
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
package it.norangeb.algorithms.graph.operations
import it.norangeb.algorithms.graph.DiGraph
import org.amshove.kluent.`should equal`
import org.spekframework.spek2.Spek
import org.spekframework.spek2.style.gherkin.Feature
object DepthFirstOrderTest : Spek({
Feature("order of graph traverse") {
Scenario("traverse linear graph") {
val graph by memoized { DiGraph() }
Given("graph 0 -> 1, 1 -> 2, 2 -> 3, 3 -> 4") {
graph.addEdge(0, 1)
graph.addEdge(1, 2)
graph.addEdge(2, 3)
graph.addEdge(3, 4)
}
lateinit var result: DepthFirstOrder
When("execute a depth first order traver") {
result = DepthFirstOrder(graph)
}
Then("preOrder should equal listOf(0, 1, 2, 3, 4)") {
result.preOrder().toList() `should equal` listOf(0, 1, 2, 3, 4)
}
Then("postOrder should equal listOf(4, 3, 2, 1, 0)") {
result.postOrder().toList() `should equal` listOf(4, 3, 2, 1, 0)
}
Then("reversePostOrder should equal listOf(0, 1, 2, 3, 4)") {
result.reversePostOrder() `should equal` listOf(0, 1, 2, 3, 4)
}
}
}
})

View File

@ -0,0 +1,141 @@
/*
* MIT License
*
* Copyright (c) 2019 norangebit
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
package it.norangeb.algorithms.graph.operations
import it.norangeb.algorithms.graph.DiGraph
import org.amshove.kluent.`should be equal to`
import org.spekframework.spek2.Spek
import org.spekframework.spek2.style.gherkin.Feature
object StronglyConnectedComponentsTest : Spek({
Feature("compute strongly connected components") {
Scenario("compute strongly connected components on a graph") {
val graph by memoized { DiGraph() }
Given("a graph with five scc") {
graph.addEdge(0, 1)
graph.addEdge(0, 5)
graph.addEdge(2, 0)
graph.addEdge(2, 3)
graph.addEdge(3, 2)
graph.addEdge(3, 5)
graph.addEdge(4, 2)
graph.addEdge(4, 3)
graph.addEdge(5, 4)
graph.addEdge(6, 0)
graph.addEdge(6, 4)
graph.addEdge(6, 8)
graph.addEdge(6, 9)
graph.addEdge(7, 6)
graph.addEdge(7, 9)
graph.addEdge(8, 6)
graph.addEdge(9, 10)
graph.addEdge(9, 11)
graph.addEdge(10, 12)
graph.addEdge(11, 4)
graph.addEdge(11, 12)
graph.addEdge(12, 9)
}
lateinit var result: StronglyConnectedComponents
When("compute the scc") {
result = StronglyConnectedComponents(graph)
}
Then("components should be 5") {
result.count() `should be equal to` 5
}
Then("connected on 0, 1 should be false") {
result.stronglyConnected(0, 1) `should be equal to` false
}
Then("connected on 3, 4 should be true") {
result.stronglyConnected(3, 4) `should be equal to` true
}
Then("connected on 4, 3 should be true") {
result.stronglyConnected(4, 3) `should be equal to` true
}
Then("connected on 9, 12 should be true") {
result.stronglyConnected(9, 12) `should be equal to` true
}
Then("connected on 9, 8 should be false") {
result.stronglyConnected(9, 8) `should be equal to` false
}
Then("connected on 1, 1 should be true") {
result.stronglyConnected(1, 1) `should be equal to` true
}
Then("connected on 7, 6 should be false") {
result.stronglyConnected(7, 6) `should be equal to` false
}
}
Scenario("compute scc on dag") {
val dag by memoized { DiGraph() }
Given("a dag") {
dag.addEdge(0, 1)
dag.addEdge(0, 3)
dag.addEdge(3, 1)
dag.addEdge(2, 0)
dag.addEdge(2, 1)
dag.addEdge(2, 3)
}
lateinit var result: StronglyConnectedComponents
When("compute the scc") {
result = StronglyConnectedComponents(dag)
}
Then("count should be equal to number of vertexes") {
result.count() `should be equal to` dag.vertexNumber()
}
Then("every vertex is sc only with it self") {
(0 until dag.vertexNumber())
.forEach { from ->
(0 until dag.vertexNumber())
.forEach { to ->
when (from) {
to ->
result
.stronglyConnected(from, to) `should be equal to` true
else -> result
.stronglyConnected(from, to) `should be equal to` false
}
}
}
}
}
}
})

View File

@ -0,0 +1,101 @@
/*
* MIT License
*
* Copyright (c) 2019 norangebit
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
package it.norangeb.algorithms.graph.operations
import it.norangeb.algorithms.graph.DiGraph
import org.amshove.kluent.`should be equal to`
import org.amshove.kluent.`should equal`
import org.spekframework.spek2.Spek
import org.spekframework.spek2.style.gherkin.Feature
object TopologicalOrderTest : Spek({
Feature("topological order") {
Scenario("topological order on DAG") {
val dag by memoized { DiGraph() }
Given("a dag") {
dag.addEdge(0, 1)
dag.addEdge(0, 2)
dag.addEdge(0, 5)
dag.addEdge(1, 4)
dag.addEdge(3, 2)
dag.addEdge(3, 4)
dag.addEdge(3, 5)
dag.addEdge(3, 6)
dag.addEdge(5, 2)
dag.addEdge(6, 0)
dag.addEdge(6, 4)
}
lateinit var result: TopologicalOrder
When("calculate the topological order") {
result = TopologicalOrder(dag)
}
Then("isDag should be true") {
result.isDag() `should be equal to` true
}
Then("topological order should equal listOf(3, 6, 0, 5, 2, 1, 4") {
result.order `should equal` listOf(3, 6, 0, 5, 2, 1, 4)
}
}
Scenario("topological order into cyclic graph") {
val cyclicGraph by memoized { DiGraph() }
Given("a cyclic graph") {
cyclicGraph.addEdge(0, 1)
cyclicGraph.addEdge(0, 2)
cyclicGraph.addEdge(0, 5)
cyclicGraph.addEdge(1, 4)
cyclicGraph.addEdge(3, 2)
cyclicGraph.addEdge(3, 4)
cyclicGraph.addEdge(3, 5)
cyclicGraph.addEdge(3, 6)
cyclicGraph.addEdge(4, 6)
cyclicGraph.addEdge(5, 2)
cyclicGraph.addEdge(6, 0)
cyclicGraph.addEdge(6, 4)
}
lateinit var result: TopologicalOrder
When("compute the topological order") {
result = TopologicalOrder(cyclicGraph)
}
Then("isDag should be false") {
result.isDag() `should be equal to` false
}
Then("order should be null") {
result.order `should equal` null
}
}
}
})