用Java实现Dijkstra输出指定起点到终点的最短路径

package graph.dijsktra;

import graph.model.Point;

import java.util.*;

/**
* Created by MHX on 2017/9/13.
*/
public class Dijkstra {
private int[][] map; // 地图结构保存
private int[][] edges; // 邻接矩阵
private int[] prev; // 前驱节点标号
private boolean[] s; // S集合中存放到起点已经算出最短路径的点
private int[] dist; // dist[i]表示起点到第i个节点的最短路径
private int pointNum; // 点的个数
private Map<Integer, Point> indexPointMap; // 标号和点的对应关系
private Map<Point, Integer> pointIndexMap; // 点和标号的对应关系
private int v0; // 起点标号
private Point startPoint; // 起点
private Point endPoint; // 终点
private Map<Point, Point> pointPointMap; // 保存点和权重的映射关系
private List<Point> allPoints; // 保存所有点
private int maxX; // x坐标的最大值
private int maxY; // y坐标的最大值

public Dijkstra(int map[][], Point startPoint, Point endPoint) {
this.maxX = map.length;
this.maxY = map[0].length;
this.pointNum = maxX * maxY;
this.map = map;
this.startPoint = startPoint;
this.endPoint = endPoint;
init();
dijkstra();
}

/**
* 打印指定起点到终点的最短路径
*/
public void printShortestPath() {
printDijkstra(pointIndexMap.get(endPoint));
}

/**
* 初始化dijkstra
*/
private void init() {
// 初始化所有变量
edges = new int[pointNum][pointNum];
prev = new int[pointNum];
s = new boolean[pointNum];
dist = new int[pointNum];
indexPointMap = new HashMap<>();
pointIndexMap = new HashMap<>();
pointPointMap = new HashMap<>();
allPoints = new ArrayList<>();

// 将map二维数组中的所有点转换成自己的结构
int count = 0;
for (int x = 0; x < maxX; ++x) {
for (int y = 0; y < maxY; ++y) {
indexPointMap.put(count, new Point(x, y));
pointIndexMap.put(new Point(x, y), count);
count++;
allPoints.add(new Point(x, y));
pointPointMap.put(new Point(x, y), new Point(x, y, map[x][y]));
}
}

// 初始化邻接矩阵
for (int i = 0; i < pointNum; ++i) {
for (int j = 0; j < pointNum; ++j) {
if (i == j) {
edges[i][j] = 0;
} else {
edges[i][j] = 9999;
}
}
}

// 根据map上的权重初始化edges，当然这种算法是没有单独加起点的权重的
for (Point point : allPoints) {
for (Point aroundPoint : getAroundPoints(point)) {
edges[pointIndexMap.get(point)][pointIndexMap.get(aroundPoint)] = aroundPoint.getValue();
}
}

v0 = pointIndexMap.get(startPoint);

for (int i = 0; i < pointNum; ++i) {
dist[i] = edges[v0][i];
if (dist[i] == 9999) {
// 如果从0点（起点）到i点最短路径是9999，即不可达
// 则i节点的前驱节点不存在
prev[i] = -1;
} else {
// 初始化i节点的前驱节点为起点，因为这个时候有最短路径的都是与起点直接相连的点
prev[i] = v0;
}
}

dist[v0] = 0;
s[v0] = true;
}

/**
* dijkstra核心算法
*/
private void dijkstra() {
for (int i = 1; i < pointNum; ++i) { // 此时有pointNum - 1个点在U集合中，需要循环pointNum - 1次
int minDist = 9999;
int u = v0;

for (int j = 1; j < pointNum; ++j) { // 在U集合中，找到到起点最短距离的点
if (!s[j] && dist[j] < minDist) { // 不在S集合，就是在U集合
u = j;
minDist = dist[j];
}
}
s[u] = true; // 将这个点放入S集合

for (int j = 1; j < pointNum; ++j) { // 以当前刚从U集合放入S集合的点u为基础，循环其可以到达的点
if (!s[j] && edges[u][j] < 9999) {
if (dist[u] + edges[u][j] < dist[j]) {
dist[j] = dist[u] + edges[u][j];
prev[j] = u;
}
}
}
}
}

private void printDijkstra(int endPointIndex) {
if (endPointIndex == v0) {
System.out.print(indexPointMap.get(v0) + ",");
return;
}
printDijkstra(prev[endPointIndex]);
System.out.print(indexPointMap.get(endPointIndex) + ",");
}

private List<Point> getAroundPoints(Point point) {
List<Point> aroundPoints = new ArrayList<>();
int x = point.getX();
int y = point.getY();
aroundPoints.add(pointPointMap.get(new Point(x - 1, y)));
aroundPoints.add(pointPointMap.get(new Point(x, y + 1)));
aroundPoints.add(pointPointMap.get(new Point(x + 1, y)));
aroundPoints.add(pointPointMap.get(new Point(x, y - 1)));
aroundPoints.removeAll(Collections.singleton(null)); // 剔除不在地图范围内的null点
return aroundPoints;
}

public static void main(String[] args) {
int map[][] = {
{1, 2, 2, 2, 2, 2, 2},
{1, 0, 2, 2, 0, 2, 2},
{1, 2, 0, 2, 0, 2, 2},
{1, 2, 2, 0, 2, 0, 2},
{1, 2, 2, 2, 2, 2, 2},
{1, 1, 1, 1, 1, 1, 1}
}; // 每个点都代表权重，没有方向限制
Point startPoint = new Point(0, 3); // 起点
Point endPoint = new Point(5, 6); // 终点
Dijkstra dijkstra = new Dijkstra(map, startPoint, endPoint);
dijkstra.printShortestPath();
}
}

package graph.model;

public class Point {
private int x;
private int y;
private int value;

public Point(int x, int y) {
this.x = x;
this.y = y;
}

public Point(int x, int y, int value) {
this.x = x;
this.y = y;
this.value = value;
}

public int getX() {
return x;
}

public void setX(int x) {
this.x = x;
}

public int getY() {
return y;
}

public void setY(int y) {
this.y = y;
}

public int getValue() {
return value;
}

public void setValue(int value) {
this.value = value;
}

@Override
public String toString() {
return "{" +
"x=" + x +
", y=" + y +
'}';
}

@Override
public boolean equals(Object o) {
if (this == o) return true;
if (o == null || getClass() != o.getClass()) return false;

Point point = (Point) o;

if (x != point.x) return false;
return y == point.y;
}

@Override
public int hashCode() {
int result = x;
result = 31 * result + y;
return result;
}
}