mirror of
https://github.com/krahets/hello-algo.git
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feat: add dart code for chapter_graph (#498)
This commit is contained in:
liuyuxin
124
codes/dart/chapter_graph/graph_adjacency_list.dart
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124
codes/dart/chapter_graph/graph_adjacency_list.dart
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/**
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* File: graph_adjacency_list.dart
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* Created Time: 2023-05-15
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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import '../utils/vertex.dart';
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/* 基于邻接表实现的无向图类 */
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class GraphAdjList {
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// 邻接表，key: 顶点，value：该顶点的所有邻接顶点
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Map<Vertex, List<Vertex>> adjList = {};
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/* 构造方法 */
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GraphAdjList(List<List<Vertex>> edges) {
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for (List<Vertex> edge in edges) {
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addVertex(edge[0]);
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addVertex(edge[1]);
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addEdge(edge[0], edge[1]);
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}
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}
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/* 获取顶点数量 */
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int size() {
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return adjList.length;
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}
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/* 添加边 */
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void addEdge(Vertex vet1, Vertex vet2) {
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if (!adjList.containsKey(vet1) ||
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!adjList.containsKey(vet2) ||
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vet1 == vet2) {
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throw ArgumentError;
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}
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// 添加边 vet1 - vet2
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adjList[vet1]!.add(vet2);
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adjList[vet2]!.add(vet1);
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}
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/* 删除边 */
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void removeEdge(Vertex vet1, Vertex vet2) {
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if (!adjList.containsKey(vet1) ||
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!adjList.containsKey(vet2) ||
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vet1 == vet2) {
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throw ArgumentError;
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}
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// 删除边 vet1 - vet2
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adjList[vet1]!.remove(vet2);
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adjList[vet2]!.remove(vet1);
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}
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/* 添加顶点 */
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void addVertex(Vertex vet) {
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if (adjList.containsKey(vet)) return;
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// 在邻接表中添加一个新链表
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adjList[vet] = [];
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}
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/* 删除顶点 */
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void removeVertex(Vertex vet) {
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if (!adjList.containsKey(vet)) {
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throw ArgumentError;
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}
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// 在邻接表中删除顶点 vet 对应的链表
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adjList.remove(vet);
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// 遍历其他顶点的链表，删除所有包含 vet 的边
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adjList.forEach((key, value) {
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value.remove(vet);
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});
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}
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/* 打印邻接表 */
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void printAdjList() {
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print("邻接表 =");
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adjList.forEach((key, value) {
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List<int> tmp = [];
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for (Vertex vertex in value) {
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tmp.add(vertex.val);
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}
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print("${key.val}: $tmp,");
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});
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}
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}
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/* Driver Code */
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void main() {
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/* 初始化无向图 */
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List<Vertex> v = Vertex.valsToVets([1, 3, 2, 5, 4]);
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List<List<Vertex>> edges = [
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[v[0], v[1]],
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[v[0], v[3]],
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[v[1], v[2]],
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[v[2], v[3]],
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[v[2], v[4]],
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[v[3], v[4]],
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];
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GraphAdjList graph = GraphAdjList(edges);
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print("\n初始化后，图为");
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graph.printAdjList();
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/* 添加边 */
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// 顶点 1, 2 即 v[0], v[2]
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graph.addEdge(v[0], v[2]);
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print("\n添加边 1-2 后，图为");
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graph.printAdjList();
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/* 删除边 */
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// 顶点 1, 3 即 v[0], v[1]
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graph.removeEdge(v[0], v[1]);
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print("\n删除边 1-3 后，图为");
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graph.printAdjList();
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/* 添加顶点 */
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Vertex v5 = Vertex(6);
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graph.addVertex(v5);
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print("\n添加顶点 6 后，图为");
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graph.printAdjList();
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/* 删除顶点 */
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// 顶点 3 即 v[1]
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graph.removeVertex(v[1]);
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print("\n删除顶点 3 后，图为");
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graph.printAdjList();
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}
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134
codes/dart/chapter_graph/graph_adjacency_matrix.dart
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134
codes/dart/chapter_graph/graph_adjacency_matrix.dart
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@@ -0,0 +1,134 @@
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/**
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* File: graph_adjacency_matrix.dart
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* Created Time: 2023-05-15
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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import '../utils/print_util.dart';
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/* 基于邻接矩阵实现的无向图类 */
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class GraphAdjMat {
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List<int> vertices = []; // 顶点元素，元素代表“顶点值”，索引代表“顶点索引”
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List<List<int>> adjMat = []; //邻接矩阵，行列索引对应“顶点索引”
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/* 构造方法 */
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GraphAdjMat(List<int> vertices, List<List<int>> edges) {
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this.vertices = [];
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this.adjMat = [];
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// 添加顶点
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for (int val in vertices) {
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addVertex(val);
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}
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// 添加边
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// 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
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for (List<int> e in edges) {
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addEdge(e[0], e[1]);
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}
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}
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/* 获取顶点数量 */
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int size() {
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return vertices.length;
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}
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/* 添加顶点 */
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void addVertex(int val) {
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int n = size();
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// 向顶点列表中添加新顶点的值
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vertices.add(val);
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// 在邻接矩阵中添加一行
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List<int> newRow = List.filled(n, 0, growable: true);
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adjMat.add(newRow);
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// 在邻接矩阵中添加一列
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for (List<int> row in adjMat) {
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row.add(0);
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}
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}
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/* 删除顶点 */
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void removeVertex(int index) {
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if (index >= size()) {
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throw IndexError;
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}
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// 在顶点列表中移除索引 index 的顶点
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vertices.removeAt(index);
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// 在邻接矩阵中删除索引 index 的行
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adjMat.removeAt(index);
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// 在邻接矩阵中删除索引 index 的列
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for (List<int> row in adjMat) {
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row.removeAt(index);
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}
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}
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/* 添加边 */
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// 参数 i, j 对应 vertices 元素索引
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void addEdge(int i, int j) {
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// 索引越界与相等处理
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if (i < 0 || j < 0 || i >= size() || j >= size() || i == j) {
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throw IndexError;
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}
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// 在无向图中，邻接矩阵沿主对角线对称，即满足 (i, j) == (j, i)
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adjMat[i][j] = 1;
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adjMat[j][i] = 1;
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}
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/* 删除边 */
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// 参数 i, j 对应 vertices 元素索引
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void removeEdge(int i, int j) {
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// 索引越界与相等处理
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if (i < 0 || j < 0 || i >= size() || j >= size() || i == j) {
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throw IndexError;
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}
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adjMat[i][j] = 0;
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adjMat[j][i] = 0;
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}
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/* 打印邻接矩阵 */
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void printAdjMat() {
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print("顶点列表 = ");
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print(vertices);
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print("邻接矩阵 = ");
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printMatrix(adjMat);
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}
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}
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/* Driver Code */
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void main() {
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/* 初始化无向图 */
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// 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
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List<int> vertices = [1, 3, 2, 5, 4];
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List<List<int>> edges = [
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[0, 1],
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[0, 3],
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[1, 2],
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[2, 3],
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[2, 4],
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[3, 4],
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];
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GraphAdjMat graph = GraphAdjMat(vertices, edges);
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print("\n初始化后，图为");
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graph.printAdjMat();
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/* 添加边 */
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// 顶点 1, 2 的索引分别为 0, 2
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graph.addEdge(0, 2);
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print("\n添加边 1-2 后，图为");
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graph.printAdjMat();
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/* 删除边 */
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// 顶点 1, 3 的索引分别为 0, 1
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graph.removeEdge(0, 1);
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print("\n删除边 1-3 后，图为");
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graph.printAdjMat();
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/* 添加顶点 */
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graph.addVertex(6);
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print("\n添加顶点 6 后，图为");
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graph.printAdjMat();
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/* 删除顶点 */
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// 顶点 3 的索引为 1
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graph.removeVertex(1);
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print("\n删除顶点 3 后，图为");
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graph.printAdjMat();
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}
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66
codes/dart/chapter_graph/graph_bfs.dart
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66
codes/dart/chapter_graph/graph_bfs.dart
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@@ -0,0 +1,66 @@
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/**
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* File: graph_bfs.dart
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* Created Time: 2023-05-15
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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import 'dart:collection';
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import '../utils/vertex.dart';
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import 'graph_adjacency_list.dart';
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/* 广度优先遍历 BFS */
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List<Vertex> graphBFS(GraphAdjList graph, Vertex startVet) {
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// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点
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// 顶点遍历序列
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List<Vertex> res = [];
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// 哈希表，用于记录已被访问过的顶点
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Set<Vertex> visited = {};
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visited.add(startVet);
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// 队列用于实现 BFS
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Queue<Vertex> que = Queue();
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que.add(startVet);
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// 以顶点 vet 为起点，循环直至访问完所有顶点
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while (que.isNotEmpty) {
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Vertex vet = que.removeFirst(); // 队首顶点出队
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res.add(vet); // 记录访问顶点
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// 遍历该顶点的所有邻接顶点
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for (Vertex adjVet in graph.adjList[vet]!) {
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if (visited.contains(adjVet)) {
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continue; // 跳过已被访问过的顶点
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}
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que.add(adjVet); // 只入队未访问的顶点
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visited.add(adjVet); // 标记该顶点已被访问
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}
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}
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// 返回顶点遍历序列
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return res;
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}
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/* Dirver Code */
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void main() {
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/* 初始化无向图 */
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List<Vertex> v = Vertex.valsToVets([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
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List<List<Vertex>> edges = [
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[v[0], v[1]],
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[v[0], v[3]],
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[v[1], v[2]],
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[v[1], v[4]],
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[v[2], v[5]],
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[v[3], v[4]],
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[v[3], v[6]],
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[v[4], v[5]],
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[v[4], v[7]],
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[v[5], v[8]],
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[v[6], v[7]],
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[v[7], v[8]],
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];
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GraphAdjList graph = GraphAdjList(edges);
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print("\n初始化后，图为");
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graph.printAdjList();
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/* 广度优先遍历 BFS */
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List<Vertex> res = graphBFS(graph, v[0]);
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print("\n广度优先遍历（BFS）顶点序列为");
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print(Vertex.vetsToVals(res));
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}
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59
codes/dart/chapter_graph/graph_dfs.dart
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59
codes/dart/chapter_graph/graph_dfs.dart
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@@ -0,0 +1,59 @@
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/**
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* File: graph_dfs.dart
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* Created Time: 2023-05-15
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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import '../utils/vertex.dart';
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import 'graph_adjacency_list.dart';
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/* 深度优先遍历 DFS 辅助函数 */
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void dfs(
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GraphAdjList graph,
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Set<Vertex> visited,
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List<Vertex> res,
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Vertex vet,
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) {
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res.add(vet); // 记录访问顶点
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visited.add(vet); // 标记该顶点已被访问
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// 遍历该顶点的所有邻接顶点
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for (Vertex adjVet in graph.adjList[vet]!) {
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if (visited.contains(adjVet)) {
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continue; // 跳过已被访问过的顶点
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}
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// 递归访问邻接顶点
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dfs(graph, visited, res, adjVet);
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}
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}
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/* 深度优先遍历 DFS */
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List<Vertex> graphDFS(GraphAdjList graph, Vertex startVet) {
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// 顶点遍历序列
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List<Vertex> res = [];
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// 哈希表，用于记录已被访问过的顶点
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Set<Vertex> visited = {};
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dfs(graph, visited, res, startVet);
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return res;
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}
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/* Driver Code */
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void main() {
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/* 初始化无向图 */
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List<Vertex> v = Vertex.valsToVets([0, 1, 2, 3, 4, 5, 6]);
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List<List<Vertex>> edges = [
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[v[0], v[1]],
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[v[0], v[3]],
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[v[1], v[2]],
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[v[2], v[5]],
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[v[4], v[5]],
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[v[5], v[6]],
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];
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GraphAdjList graph = GraphAdjList(edges);
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print("\n初始化后，图为");
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graph.printAdjList();
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/* 深度优先遍历 DFS */
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List<Vertex> res = graphDFS(graph, v[0]);
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print("\n深度优先遍历（DFS）顶点序列为");
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print(Vertex.vetsToVals(res));
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}
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@@ -16,6 +16,14 @@ class Trunk {
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Trunk(this.prev, this.str);
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}
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void printMatrix(List<List<int>> matrix) {
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print("[");
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for (List<int> row in matrix) {
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print(" $row,");
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}
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print("]");
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}
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void printLinkedList(ListNode? head) {
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List<String> list = [];
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29
codes/dart/utils/vertex.dart
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29
codes/dart/utils/vertex.dart
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@@ -0,0 +1,29 @@
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/**
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* File: Vertex.dart
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* Created Time: 2023-05-15
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* 顶点类 */
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class Vertex {
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int val;
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Vertex(this.val);
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/* 输入值列表 vals ，返回顶点列表 vets */
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static List<Vertex> valsToVets(List<int> vals) {
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List<Vertex> vets = [];
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for (int i in vals) {
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vets.add(Vertex(i));
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}
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return vets;
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}
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/* 输入顶点列表 vets ，返回值列表 vals */
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static List<int> vetsToVals(List<Vertex> vets) {
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List<int> vals = [];
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for (Vertex vet in vets) {
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vals.add(vet.val);
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}
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return vals;
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}
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}
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