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e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
133 lines
3.3 KiB
Dart
133 lines
3.3 KiB
Dart
/**
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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，邻接矩阵关于主对角线对称，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 = $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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