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package com.eh.ftd.dsa.ds;
import com.google.common.collect.Lists;
import java.util.ArrayList;
import java.util.List;
/**
* Dijkstra(迪杰斯特拉)算法
* 目标：
* 1. 起点到各节点的最短路径距离
* 2. 打印起点到各节点的最短路径
*
* @author David Li
* @create 2020/07/05 20:19
*/
public class Dijkstra {
/**
* 起点到各节点的最短距离
* dist[1]， 起点到节点1的最短距离
*/
private int[] dist;
/**
* 起点到各节点的最短路径
* path[1], 起点到节点1到的最短路径
*/
private String[] path;
/**
* 图的邻接矩阵表现形式
* 0表示自己指向自己，值为Integer.MAX_VALUE表示无穷远
*/
private int[][] matrix;
/**
* 顶点的表现形式
*/
private List<String> vertexNames;
/**
* 表示顶点是否被访问过， 如果是则表明已经加入到最小生成树中
*/
private boolean[] visited;
public Dijkstra(List<String> vertexNames) {
this.matrix = new int[vertexNames.size()][vertexNames.size()];
this.vertexNames = vertexNames;
this.visited = new boolean[vertexNames.size()];
dist = new int[vertexNames.size()];
// 初始化邻接矩阵
for (int i = 0; i < vertexNames.size(); i++) {
for (int j = 0; j < vertexNames.size(); j++) {
if (i == j) {
matrix[i][j] = 0;
} else {
matrix[i][j] = Integer.MAX_VALUE;
}
}
}
// 初始化路径信息
path = new String[vertexNames.size()];
path[0] = vertexNames.get(0);
// 初始化起点坐标
visited[0] = true;
dist[0] = 0;
}
/**
* 获得顶点对应下标
*
* @param vertexName
* @return
*/
private int getIndexByVertexName(String vertexName) {
for (int i = 0; i < vertexNames.size(); i++) {
if (vertexName.equals(vertexNames.get(i))) {
return i;
}
}
throw new RuntimeException();
}
public void printMinimumPathAndDist() {
for (int i = 0; i < vertexNames.size(); i++) {
System.out.printf("%s(%s) - >\t", path[i], dist[getIndexByVertexName(path[i])]);
}
}
public void dijkstra() {
int leaf = 0;
int count = 1;
while (leaf != -1) {
// 1. 从所有S集合以外的节点中选出最短路径值最小的节点加入到S集合
leaf = -1;
int min = Integer.MAX_VALUE;
for (int i = 1; i < vertexNames.size(); i++) {
if (dist[i] < min && !visited[i]) {
leaf = i;
min = dist[i];
}
}
if (leaf == -1) {
return;
}
// 将leaf加入S
visited[leaf] = true;
path[count++] = vertexNames.get(leaf);
// 2. 调整最短距离
for (int i = 1; i < vertexNames.size(); i++) {
if (matrix[leaf][i] < Integer.MAX_VALUE && !visited[i]) { // 被leaf指向
int newDist = dist[leaf] + matrix[leaf][i];
if (newDist < dist[i]) {
dist[i] = newDist;
}
}
}
}
}
/**
* 有向图
*
* @param v1
* @param v2
* @param weight
*/
public void buildEdge(String v1, String v2, int weight) {
int idx1 = getIndexByVertexName(v1);
int idx2 = getIndexByVertexName(v2);
matrix[idx1][idx2] = weight;
if (idx1 == 0) {
dist[idx2] = weight;
} else if (dist[idx2] == 0) {
dist[idx2] = Integer.MAX_VALUE;
}
}
public static void main(String[] args) {
List cites = Lists.newArrayList("v0", "v1", "v2", "v3", "v4", "v5", "v6");
Dijkstra dijkstra = new Dijkstra(cites);
dijkstra.buildEdge("v0", "v1", 13);
dijkstra.buildEdge("v0", "v2", 8);
dijkstra.buildEdge("v0", "v4", 30);
dijkstra.buildEdge("v0", "v6", 32);
dijkstra.buildEdge("v1", "v5", 9);
dijkstra.buildEdge("v1", "v6", 7);
dijkstra.buildEdge("v2", "v3", 5);
dijkstra.buildEdge("v3", "v4", 6);
dijkstra.buildEdge("v4", "v5", 2);
dijkstra.buildEdge("v5", "v6", 17);
dijkstra.dijkstra();
dijkstra.printMinimumPathAndDist();
}
}
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