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：

java 复制代码

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0
		for(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

java 复制代码

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 result
		for(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 notFound
		for(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 notFound
			for(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。