用Java实现Dijkstra输出指定起点到终点的最短路径

来源：互联网发布：2015旅游数据编辑：程序博客网时间：2024/05/18 02:28

最近在公司参加了一个比赛，其中涉及的一个问题，可以简化成如是描述：一个二维矩阵，每个点都有权重，需要找出从指定起点到终点的最短路径。

马上就想到了Dijkstra算法，所以又重新温故了一遍，这里给出Java的实现。

而输出最短路径的时候，在网上也进行了查阅，没发现什么标准的方法，于是在下面的实现中，我给出了一种能够想到的比较精简的方式：利用prev[]数组进行递归输出。

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;    }}

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