Dijkstra找最短路径

问题描述

节点0-N，求0到N的最短路径

算法

package com.java;import java.util.ArrayList;import java.util.HashMap;import java.util.HashSet;import java.util.List;import java.util.Map;import java.util.Map.Entry;public class ShortPath {    public static void main(String[] args) {        // TODO Auto-generated method stub        ShortPath solution = new ShortPath();        HashMap<Integer, HashMap<Integer, Integer>> path = new HashMap<Integer, HashMap<Integer,Integer>>();        HashMap<Integer, Integer> path0 = new HashMap<Integer,Integer>();        path0.put(1, 1);        path0.put(2, 5);        HashMap<Integer, Integer> path1 = new HashMap<Integer,Integer>();        path1.put(0, 1);        path1.put(2, 3);        path1.put(4, 5);        path1.put(3, 7);        HashMap<Integer, Integer> path2 = new HashMap<Integer,Integer>();        path2.put(0, 5);        path2.put(1, 3);        path2.put(4, 1);        path2.put(5, 7);        HashMap<Integer, Integer> path3 = new HashMap<Integer,Integer>();        path3.put(1, 7);        path3.put(4, 2);        path3.put(6, 3);        HashMap<Integer, Integer> path4 = new HashMap<Integer,Integer>();        path4.put(1, 5);        path4.put(3, 2);        path4.put(6, 6);        path4.put(7, 9);        path4.put(5, 3);        path4.put(2, 1);        HashMap<Integer, Integer> path5 = new HashMap<Integer,Integer>();        path5.put(2, 7);        path5.put(4, 3);        path5.put(7, 5);        HashMap<Integer, Integer> path6 = new HashMap<Integer,Integer>();        path6.put(3, 3);        path6.put(4, 6);        path6.put(7, 2);        path6.put(8, 7);        HashMap<Integer, Integer> path7 = new HashMap<Integer,Integer>();        path7.put(5, 5);        path7.put(4, 9);        path7.put(6, 2);        path7.put(8, 4);        HashMap<Integer, Integer> path8 = new HashMap<Integer,Integer>();        path8.put(6, 7);        path8.put(7, 4);        path.put(0, path0);        path.put(1, path1);        path.put(2, path2);        path.put(3, path3);        path.put(4, path4);        path.put(5, path5);        path.put(6, path6);        path.put(7, path7);        path.put(8, path8);        System.out.println("0 : " + solution.dijkstra(path,0));        System.out.println("1 : " + solution.dijkstra(path,1));        System.out.println("2 : " + solution.dijkstra(path,2));        System.out.println("3 : " + solution.dijkstra(path,3));        System.out.println("4 : " + solution.dijkstra(path,4));        System.out.println("5 : " + solution.dijkstra(path,5));        System.out.println("6 : " + solution.dijkstra(path,6));        System.out.println("7 : " + solution.dijkstra(path,7));        System.out.println("8 : " + solution.dijkstra(path,8));    }

/* * path存储边信息HashMap<Integer, HashMap<Integer, Integer>> * 第一个是源节点 * 第二个是目标节点 * 第三个是边长 */public int dijkstra (final HashMap<Integer, HashMap<Integer, Integer>> path, int targetNode) {    int node = 0;    int pathMin = 0;    //minPath：已经找到的从0 开始的最短路径    HashMap<Integer, Integer> minPaths = new HashMap<Integer,Integer>();    //finded：已经找到最短路径的点    HashSet<Integer> finded = new HashSet<Integer>();    minPaths.put(0, 0);    boolean tracing = true;    //如果finded中包括了所有节点，则停止遍历    while (tracing) {        tracing = false;         //node节点的path        HashMap<Integer, Integer> nodePath = path.get(node);        int nodeMin = node;        //遍历node节点的path，更新最短距离        for (Entry<Integer, Integer> nodeEveryPath : nodePath.entrySet()) {            int tPath = nodeEveryPath.getValue();            int tNode = nodeEveryPath.getKey();            if (!finded.contains(tNode)) {                tracing = true;                //找到当前权值最小                if (nodeMin == node || nodeMin > tPath) {                    nodeMin = nodeEveryPath.getKey();                }                //更新最短路径                if (minPaths.get(tNode) == null || minPaths.get(tNode) > tPath + pathMin) {                    minPaths.put(tNode, tPath + pathMin);                }            }        }        finded.add(nodeMin);        node = nodeMin;        pathMin = minPaths.get(nodeMin);    }    return minPaths.get(targetNode);}