Dijkstra算法——邻接矩阵实现+路径记录

本文是在下面这篇文章的基础上做了一些补充，增加了路径记录的功能。具体Dijkstra的实现过程可以参考下面的这篇文章。
[jarvan：Dijkstra算法详解 通俗易懂](Dijkstra算法详解 通俗易懂 - jarvan的文章 - 知乎
https://zhuanlan.zhihu.com/p/338414118)

创建 GraphAdjMat 类
GraphAdjMat 类用来实现图的邻接矩阵，方便后续的测试，具体代码如下：

package algorithm.graph;import java.util.ArrayList;
import java.util.List;public class GraphAdjMat {private List<Integer> vertices;private List<List<Integer>> adjMat;/*** 构造函数* @param vertices 顶点列表* @param edges 边*/public GraphAdjMat(int[]vertices, int[][]edges) {this.vertices = new ArrayList<>();this.adjMat = new ArrayList<>();for(int v : vertices) {addVertex(v);}for(int[]e : edges) {addEdge(e[0],e[1],e[2]);}//设置顶点自己到自己的权重为0for(int i=0; i<vertices.length; i++) {this.adjMat.get(i).set(i, 0);}}public List<List<Integer>> getAdjMat() {return this.adjMat;}/*** 添加顶点*/public void addVertex(int val) {int n = vertices.size();vertices.add(val);List<Integer> newRow = new ArrayList<>();for(int i=0; i<n; i++) {newRow.add(-1);}adjMat.add(newRow);for(List<Integer> row : adjMat) {row.add(-1);}}/*** 移除顶点*/public void removeVertex(int index) {if(index < 0 || index >= vertices.size()) {throw new IndexOutOfBoundsException();}vertices.remove(index);adjMat.remove(index);for(List<Integer> row : adjMat) {row.remove(index);}}/*** 添加边* @param i 顶点1* @param j 顶点2* @param weight 边权重*/public void addEdge(int i, int j, int weight) {if(i<0||j<0||i>=vertices.size()||j>=vertices.size()||i==j) {throw new IndexOutOfBoundsException();}adjMat.get(i).set(j, weight);adjMat.get(j).set(i, weight);}/*** 移除边*/public void removeEdge(int i, int j) {if(i<0||j<0||i>=vertices.size()||j>=vertices.size()||i==j) {throw new IndexOutOfBoundsException();}adjMat.get(i).set(j, -1);adjMat.get(j).set(i, -1);}public void print() {System.out.println("adj mat:");for(List<Integer> row : adjMat) {for(int v : row) {System.out.printf("%3d", v);}System.out.println();}}}

GraphAdjMat 类中提供了增加顶点、移除顶点、增加边和移除边的操作。
创建 DijkstraAlg 类
该类用于实现 Dijkstra 算法，并打印指定点到所有点的最短距离和路径信息

package algorithm.graph;import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;/*** Dijkstra 算法*/
public class DijkstraAlg {public static void main(String[]args) {char[]vertexNames = {'A','B','C','D'};int[]vertices = {1,2,3,4};int[][]edges = {{0,1,1},{0,3,6},{1,2,4},{1,3,1},{2,3,1}};//构建邻接矩阵GraphAdjMat adjMat = new GraphAdjMat(vertices, edges);adjMat.print();int startVertex = 0;List<ShortestPath> result = dijkstra(adjMat.getAdjMat(),startVertex);System.out.println("dijkstra result: ");for(int i=0; i<vertexNames.length; i++) {System.out.printf("%3s -> %s distence : %d ; ",vertexNames[startVertex], vertexNames[i], result.get(i).distence);List<Integer> path = result.get(i).path;System.out.print("A -> ");for(int j=0; j<path.size(); j++) {if(j < path.size()-1) {					System.out.printf("%s -> ",vertexNames[path.get(j)]);}else {System.out.printf("%s\n", vertexNames[path.get(j)]);}}}}public static List<ShortestPath> dijkstra(List<List<Integer>> graph, int startVertex) {int len = graph.size();List<ShortestPath> result = new ArrayList<>(len);int[]notFound = new int[len];//初始化 resultfor(int i=0; i<len; i++) {ShortestPath shortestPath = new ShortestPath();shortestPath.distence = -1;shortestPath.path = new ArrayList<>();result.add(i, shortestPath);}ShortestPath startVertexPath = new ShortestPath();startVertexPath.distence = 0;startVertexPath.path = new ArrayList<>(0);result.set(startVertex,startVertexPath);//初始化 notFoundfor(int i=0; i<len; i++) {notFound[i] = graph.get(startVertex).get(i);}notFound[startVertex] = -1;//开始 Dijkstra 算法Map<Integer,List<Integer>> recordPathMap = new HashMap<>();for(int i=1; i<len; i++) {int min = Integer.MAX_VALUE;int minIndex = 0;for(int j=0; j<len; j++) {if(notFound[j] > 0 && notFound[j] < min) {min = notFound[j];minIndex = j;}}result.get(minIndex).distence = min;notFound[minIndex] = -1;//刷新 notFoundfor(int j=0; j<len; j++) {//graph.get(minIndex).get(j) > 0 用来确保 minIndex 顶点有边，result[j] == -1 用来确保 j 点没有在结果集中if(graph.get(minIndex).get(j) > 0 && result.get(j).distence == -1) {int newDistence = result.get(minIndex).distence + graph.get(minIndex).get(j);//计算合并距离如果小于直接到j点的距离，或者无法到达j点事将新距离刷新到notFound中if(newDistence < notFound[j] || notFound[j] == -1) {notFound[j] = newDistence;if(!recordPathMap.containsKey(j)) {List<Integer> tempList = new ArrayList<>(1);tempList.add(minIndex);recordPathMap.put(j, tempList);}else {							recordPathMap.get(j).add(minIndex);}}}}}System.out.println(recordPathMap);//推到路径for(int i=0; i<len; i++) {result.get(i).path.addAll(recordPathMap.getOrDefault(i, new ArrayList<>()));result.get(i).path.add(i);}return result;}public static void printArr(int[]arr, String arrName) {System.out.print(arrName);for(int i : arr) {System.out.printf("%3d", i);}System.out.println();}static class ShortestPath {public int distence;public List<Integer> path;}
}

代码在原文代码的基础上通过增加 recordPathMap 来记录最短路径，最终打印最短路径距离和对应路劲信息。