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69 changes: 69 additions & 0 deletions
69
src/commonMain/kotlin/io/github/alexandrepiveteau/graphs/algorithms/TopologicalSort.kt
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,69 @@ | ||
| @file:JvmName("Algorithms") | ||
| @file:JvmMultifileClass | ||
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| package io.github.alexandrepiveteau.graphs.algorithms | ||
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| import io.github.alexandrepiveteau.graphs.DirectedGraph | ||
| import io.github.alexandrepiveteau.graphs.VertexArray | ||
| import io.github.alexandrepiveteau.graphs.asVertexArray | ||
| import io.github.alexandrepiveteau.graphs.internal.collections.IntDequeue | ||
| import kotlin.jvm.JvmMultifileClass | ||
| import kotlin.jvm.JvmName | ||
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| /** | ||
| * Returns a [VertexArray] containing the vertices of the graph, sorted in topological order. If the | ||
| * graph contains a cycle, an [IllegalArgumentException] is thrown. | ||
| * | ||
| * ## Asymptotic complexity | ||
| * - **Time complexity**: O(|N| + |E|), where |N| is the number of vertices in this graph and |E| is | ||
| * the number of edges in this graph. | ||
| * - **Space complexity**: O(|N|), where n is the number of vertices in this graph. | ||
| * | ||
| * @return a [VertexArray] containing the vertices of the graph, sorted in topological order. | ||
| * @receiver the [DirectedGraph] to sort topologically. | ||
| * @throws IllegalArgumentException if the graph contains a cycle. | ||
| */ | ||
| public fun DirectedGraph.topologicalSort(): VertexArray { | ||
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| // 0. Set up a queue of vertices to add to the topological sort, and a boolean array to keep track | ||
| // of the vertices that have already been sorted. | ||
| val queue = IntDequeue() | ||
| val sorted = BooleanArray(size) | ||
| val result = IntDequeue() | ||
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| // 1. Compute the number of incoming edges for each vertex. | ||
| val edges = IntArray(size) | ||
| forEachArc { (_, to) -> edges[get(to)]++ } | ||
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| // 2. Add all the vertices with no incoming edges to the queue. | ||
| for (i in edges.indices) { | ||
| if (edges[i] == 0) { | ||
| queue.addLast(i) | ||
| sorted[i] = true | ||
| } | ||
| } | ||
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| // 3. While there are some vertices to add to the topological sort, add them and remove their | ||
| // outgoing edges. If a vertex has no more outgoing edges and has not been sorted yet, add it to | ||
| // the queue. | ||
| while (queue.size > 0) { | ||
| val vertex = queue.removeFirst() | ||
| result.addLast(vertex) | ||
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| forEachNeighbor(get(vertex)) { | ||
| val to = get(it) | ||
| edges[to]-- | ||
| if (edges[to] == 0 && !sorted[to]) { | ||
| queue.addLast(to) | ||
| sorted[to] = true | ||
| } | ||
| } | ||
| } | ||
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| // 4. If there are still some vertices that have not been sorted, then there is a cycle in the | ||
| // graph. Throw an exception. | ||
| if (result.size != size) throw IllegalArgumentException("The graph contains a cycle.") | ||
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| // 5. Return the result. | ||
| return result.toIntArray().asVertexArray() | ||
| } |
85 changes: 85 additions & 0 deletions
85
src/commonTest/kotlin/io/github/alexandrepiveteau/graphs/algorithms/TopologicalSortTests.kt
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,85 @@ | ||
| package io.github.alexandrepiveteau.graphs.algorithms | ||
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| import io.github.alexandrepiveteau.graphs.Vertex | ||
| import io.github.alexandrepiveteau.graphs.VertexArray | ||
| import io.github.alexandrepiveteau.graphs.arcTo | ||
| import io.github.alexandrepiveteau.graphs.builder.buildDirectedGraph | ||
| import io.github.alexandrepiveteau.graphs.toVertexArray | ||
| import io.github.alexandrepiveteau.graphs.util.Repeats | ||
| import io.github.alexandrepiveteau.graphs.util.assertContentEquals | ||
| import kotlin.test.Test | ||
| import kotlin.test.assertEquals | ||
| import kotlin.test.assertFailsWith | ||
|
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| class TopologicalSortTests { | ||
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| @Test | ||
| fun emptyGraphHasEmptyTopologicalSort() { | ||
| val graph = buildDirectedGraph {} | ||
| val order = graph.topologicalSort() | ||
| assertContentEquals(VertexArray(0), order) | ||
| } | ||
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| @Test | ||
| fun singletonGraphHasSingletonTopologicalSort() { | ||
| val graph = buildDirectedGraph { addVertex() } | ||
| val order = graph.topologicalSort() | ||
| assertContentEquals(VertexArray(1) { Vertex(0) }, order) | ||
| } | ||
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| @Test | ||
| fun loopHasNoTopologicalSort() { | ||
| val graph = buildDirectedGraph { | ||
| val a = addVertex() | ||
| addArc(a arcTo a) | ||
| } | ||
| assertFailsWith<IllegalArgumentException> { graph.topologicalSort() } | ||
| } | ||
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| @Test | ||
| fun bidirectionalGraphHasNoTopologicalSort() { | ||
| val graph = buildDirectedGraph { | ||
| val (a, b) = addVertices() | ||
| addArc(a arcTo b) | ||
| addArc(b arcTo a) | ||
| } | ||
| assertFailsWith<IllegalArgumentException> { graph.topologicalSort() } | ||
| } | ||
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| @Test | ||
| fun disjointGraphHasTopologicalSort() { | ||
| for (count in 0 until Repeats) { | ||
| val graph = buildDirectedGraph { repeat(count) { addVertex() } } | ||
| val order = graph.topologicalSort() | ||
| assertEquals(graph.size, order.size) | ||
| } | ||
| } | ||
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| @Test | ||
| fun lineGraphHasIdenticalTopologicalSort() { | ||
| for (count in 2 until Repeats) { | ||
| val graph = buildDirectedGraph { | ||
| val vertices = VertexArray(count) { addVertex() } | ||
| repeat(count - 1) { addArc(vertices[it] arcTo vertices[it + 1]) } | ||
| } | ||
| val order = graph.topologicalSort() | ||
| assertContentEquals(VertexArray(graph.size) { graph[it] }, order) | ||
| } | ||
| } | ||
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| @Test | ||
| fun geeksForGeeks() { | ||
| val graph = buildDirectedGraph { | ||
| val (v0, v1, v2, v3, v4, v5) = addVertices() | ||
| addArc(v5 arcTo v2) | ||
| addArc(v5 arcTo v0) | ||
| addArc(v4 arcTo v0) | ||
| addArc(v4 arcTo v1) | ||
| addArc(v2 arcTo v3) | ||
| addArc(v3 arcTo v1) | ||
| } | ||
| val order = graph.topologicalSort() | ||
| val expected = arrayOf(graph[4], graph[5], graph[0], graph[2], graph[3], graph[1]) | ||
| assertContentEquals(expected.toVertexArray(), order) | ||
| } | ||
| } |
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