java 物理路径什么意思 java 路径算法

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mob6454cc623087 2023-07-19 14:20:24

文章标签 java 物理路径什么意思 java python 最短路径子节点 文章分类 Java 后端开发

Dijkstra(迪杰斯特拉)算法是典型的最短路径路由算法，用于计算一个节点到其他所有节点的最短路径。主要特点是以起始点为中心向外层层扩展，直到扩展到终点为止。

Dijkstra一般的表述通常有两种方式，一种用永久和临时标号方式，一种是用OPEN, CLOSE表方式
用OPEN,CLOSE表的方式，其采用的是贪心法的算法策略，大概过程如下：
1.声明两个集合，open和close，open用于存储未遍历的节点，close用来存储已遍历的节点
2.初始阶段，将初始节点放入close，其他所有节点放入open
3.以初始节点为中心向外一层层遍历，获取离指定节点最近的子节点放入close并从新计算路径，直至close包含所有子节点

代码实例如下：
Node对象用于封装节点信息，包括名字和子节点

public class Node { 
    private String name; 
    private Map<Node,Integer> child=new HashMap<Node,Integer>(); 
    public Node(String name){ 
        this.name=name; 
    } 
    public String getName() { 
        return name; 
    } 
    public void setName(String name) { 
        this.name = name; 
    } 
    public Map<Node, Integer> getChild() { 
        return child; 
    } 
    public void setChild(Map<Node, Integer> child) { 
        this.child = child; 
    } 
}
public class Node { 
    private String name; 
    private Map<Node,Integer> child=new HashMap<Node,Integer>(); 
    public Node(String name){ 
        this.name=name; 
    } 
    public String getName() { 
        return name; 
    } 
    public void setName(String name) { 
        this.name = name; 
    } 
    public Map<Node, Integer> getChild() { 
        return child; 
    } 
    public void setChild(Map<Node, Integer> child) { 
        this.child = child; 
    } 
}

MapBuilder用于初始化数据源，返回图的起始节点

public class MapBuilder { 
    public Node build(Set<Node> open, Set<Node> close){ 
        Node nodeA=new Node("A"); 
        Node nodeB=new Node("B"); 
        Node nodeC=new Node("C"); 
        Node nodeD=new Node("D"); 
        Node nodeE=new Node("E"); 
        Node nodeF=new Node("F"); 
        Node nodeG=new Node("G"); 
        Node nodeH=new Node("H"); 
        nodeA.getChild().put(nodeB, 1); 
        nodeA.getChild().put(nodeC, 1); 
        nodeA.getChild().put(nodeD, 4); 
        nodeA.getChild().put(nodeG, 5); 
        nodeA.getChild().put(nodeF, 2); 
        nodeB.getChild().put(nodeA, 1); 
        nodeB.getChild().put(nodeF, 2); 
        nodeB.getChild().put(nodeH, 4); 
        nodeC.getChild().put(nodeA, 1); 
        nodeC.getChild().put(nodeG, 3); 
        nodeD.getChild().put(nodeA, 4); 
        nodeD.getChild().put(nodeE, 1); 
        nodeE.getChild().put(nodeD, 1); 
        nodeE.getChild().put(nodeF, 1); 
        nodeF.getChild().put(nodeE, 1); 
        nodeF.getChild().put(nodeB, 2); 
        nodeF.getChild().put(nodeA, 2); 
        nodeG.getChild().put(nodeC, 3); 
        nodeG.getChild().put(nodeA, 5); 
        nodeG.getChild().put(nodeH, 1); 
        nodeH.getChild().put(nodeB, 4); 
        nodeH.getChild().put(nodeG, 1); 
        open.add(nodeB); 
        open.add(nodeC); 
        open.add(nodeD); 
        open.add(nodeE); 
        open.add(nodeF); 
        open.add(nodeG); 
        open.add(nodeH); 
        close.add(nodeA); 
        return nodeA; 
    } 
}
public class MapBuilder { 
    public Node build(Set<Node> open, Set<Node> close){ 
        Node nodeA=new Node("A"); 
        Node nodeB=new Node("B"); 
        Node nodeC=new Node("C"); 
        Node nodeD=new Node("D"); 
        Node nodeE=new Node("E"); 
        Node nodeF=new Node("F"); 
        Node nodeG=new Node("G"); 
        Node nodeH=new Node("H"); 
        nodeA.getChild().put(nodeB, 1); 
        nodeA.getChild().put(nodeC, 1); 
        nodeA.getChild().put(nodeD, 4); 
        nodeA.getChild().put(nodeG, 5); 
        nodeA.getChild().put(nodeF, 2); 
        nodeB.getChild().put(nodeA, 1); 
        nodeB.getChild().put(nodeF, 2); 
        nodeB.getChild().put(nodeH, 4); 
        nodeC.getChild().put(nodeA, 1); 
        nodeC.getChild().put(nodeG, 3); 
        nodeD.getChild().put(nodeA, 4); 
        nodeD.getChild().put(nodeE, 1); 
        nodeE.getChild().put(nodeD, 1); 
        nodeE.getChild().put(nodeF, 1); 
        nodeF.getChild().put(nodeE, 1); 
        nodeF.getChild().put(nodeB, 2); 
        nodeF.getChild().put(nodeA, 2); 
        nodeG.getChild().put(nodeC, 3); 
        nodeG.getChild().put(nodeA, 5); 
        nodeG.getChild().put(nodeH, 1); 
        nodeH.getChild().put(nodeB, 4); 
        nodeH.getChild().put(nodeG, 1); 
        open.add(nodeB); 
        open.add(nodeC); 
        open.add(nodeD); 
        open.add(nodeE); 
        open.add(nodeF); 
        open.add(nodeG); 
        open.add(nodeH); 
        close.add(nodeA); 
        return nodeA; 
    } 
}

图的结构如下图所示：

Dijkstra对象用于计算起始节点到所有其他节点的最短路径

public class Dijkstra { 
    Set<Node> open=new HashSet<Node>(); 
    Set<Node> close=new HashSet<Node>(); 
    Map<String,Integer> path=new HashMap<String,Integer>();//封装路径距离 
    Map<String,String> pathInfo=new HashMap<String,String>();//封装路径信息 
    public Node init(){ 
        //初始路径,因没有A->E这条路径,所以path(E)设置为Integer.MAX_VALUE 
        path.put("B", 1); 
        pathInfo.put("B", "A->B"); 
        path.put("C", 1); 
        pathInfo.put("C", "A->C"); 
        path.put("D", 4); 
        pathInfo.put("D", "A->D"); 
        path.put("E", Integer.MAX_VALUE); 
        pathInfo.put("E", "A"); 
        path.put("F", 2); 
        pathInfo.put("F", "A->F"); 
        path.put("G", 5); 
        pathInfo.put("G", "A->G"); 
        path.put("H", Integer.MAX_VALUE); 
        pathInfo.put("H", "A"); 
        //将初始节点放入close,其他节点放入open 
        Node start=new MapBuilder().build(open,close); 
        return start; 
    } 
    public void computePath(Node start){ 
        Node nearest=getShortestPath(start);//取距离start节点最近的子节点,放入close 
        if(nearest==null){ 
            return; 
        } 
        close.add(nearest); 
        open.remove(nearest); 
        Map<Node,Integer> childs=nearest.getChild(); 
        for(Node child:childs.keySet()){ 
            if(open.contains(child)){//如果子节点在open中 
                Integer newCompute=path.get(nearest.getName())+childs.get(child); 
                if(path.get(child.getName())>newCompute){//之前设置的距离大于新计算出来的距离 
                    path.put(child.getName(), newCompute); 
                    pathInfo.put(child.getName(), pathInfo.get(nearest.getName())+"->"+child.getName()); 
                } 
            } 
        } 
        computePath(start);//重复执行自己,确保所有子节点被遍历 
        computePath(nearest);//向外一层层递归,直至所有顶点被遍历 
    } 
    public void printPathInfo(){ 
        Set<Map.Entry<String, String>> pathInfos=pathInfo.entrySet(); 
        for(Map.Entry<String, String> pathInfo:pathInfos){ 
            System.out.println(pathInfo.getKey()+":"+pathInfo.getValue()); 
        } 
    } 
    /**
     * 获取与node最近的子节点
     */ 
    private Node getShortestPath(Node node){ 
        Node res=null; 
        int minDis=Integer.MAX_VALUE; 
        Map<Node,Integer> childs=node.getChild(); 
        for(Node child:childs.keySet()){ 
            if(open.contains(child)){ 
                int distance=childs.get(child); 
                if(distance<minDis){ 
                    minDis=distance; 
                    res=child; 
                } 
            } 
        } 
        return res; 
    } 
} 

Main用于测试Dijkstra对象
public class Main { 
    public static void main(String[] args) { 
        Dijkstra test=new Dijkstra(); 
        Node start=test.init(); 
        test.computePath(start); 
        test.printPathInfo(); 
    } 
}
public class Dijkstra { 
    Set<Node> open=new HashSet<Node>(); 
    Set<Node> close=new HashSet<Node>(); 
    Map<String,Integer> path=new HashMap<String,Integer>();//封装路径距离 
    Map<String,String> pathInfo=new HashMap<String,String>();//封装路径信息 
    public Node init(){ 
        //初始路径,因没有A->E这条路径,所以path(E)设置为Integer.MAX_VALUE 
        path.put("B", 1); 
        pathInfo.put("B", "A->B"); 
        path.put("C", 1); 
        pathInfo.put("C", "A->C"); 
        path.put("D", 4); 
        pathInfo.put("D", "A->D"); 
        path.put("E", Integer.MAX_VALUE); 
        pathInfo.put("E", "A"); 
        path.put("F", 2); 
        pathInfo.put("F", "A->F"); 
        path.put("G", 5); 
        pathInfo.put("G", "A->G"); 
        path.put("H", Integer.MAX_VALUE); 
        pathInfo.put("H", "A"); 
        //将初始节点放入close,其他节点放入open 
        Node start=new MapBuilder().build(open,close); 
        return start; 
    } 
    public void computePath(Node start){ 
        Node nearest=getShortestPath(start);//取距离start节点最近的子节点,放入close 
        if(nearest==null){ 
            return; 
        } 
        close.add(nearest); 
        open.remove(nearest); 
        Map<Node,Integer> childs=nearest.getChild(); 
        for(Node child:childs.keySet()){ 
            if(open.contains(child)){//如果子节点在open中 
                Integer newCompute=path.get(nearest.getName())+childs.get(child); 
                if(path.get(child.getName())>newCompute){//之前设置的距离大于新计算出来的距离 
                    path.put(child.getName(), newCompute); 
                    pathInfo.put(child.getName(), pathInfo.get(nearest.getName())+"->"+child.getName()); 
                } 
            } 
        } 
        computePath(start);//重复执行自己,确保所有子节点被遍历 
        computePath(nearest);//向外一层层递归,直至所有顶点被遍历 
    } 
    public void printPathInfo(){ 
        Set<Map.Entry<String, String>> pathInfos=pathInfo.entrySet(); 
        for(Map.Entry<String, String> pathInfo:pathInfos){ 
            System.out.println(pathInfo.getKey()+":"+pathInfo.getValue()); 
        } 
    } 
    /**
     * 获取与node最近的子节点
     */ 
    private Node getShortestPath(Node node){ 
        Node res=null; 
        int minDis=Integer.MAX_VALUE; 
        Map<Node,Integer> childs=node.getChild(); 
        for(Node child:childs.keySet()){ 
            if(open.contains(child)){ 
                int distance=childs.get(child); 
                if(distance<minDis){ 
                    minDis=distance; 
                    res=child; 
                } 
            } 
        } 
        return res; 
    } 
} 

Main用于测试Dijkstra对象
public class Main { 
    public static void main(String[] args) { 
        Dijkstra test=new Dijkstra(); 
        Node start=test.init(); 
        test.computePath(start); 
        test.printPathInfo(); 
    } 
}

打印输出如下：
D:A->D
E:A->F->E
F:A->F
G:A->C->G
B:A->B
C:A->C
H:A->B->H

矩阵实现：

public class Dijkstra {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[][] weight = {
                {0,3,9999999,7,9999999},
                {3,0,4,2,9999999},
                {9999999,4,0,5,6},
                {7,2,5,0,4},
                {9999999,9999999,6,4,0}
        };
        
        int[] path = Dijsktra(weight,0);
        for(int i = 0;i < path.length;i++)
            System.out.print(path[i] + "  ");
    }
    

    public static int[] Dijsktra(int[][] weight,int start){
        //接受一个有向图的权重矩阵，和一个起点编号start（从0编号，顶点存在数组中）
        //返回一个int[] 数组，表示从start到它的最短路径长度
        int n = weight.length;        //顶点个数
        int[] shortPath = new int[n];    //存放从start到其他各点的最短路径
        int[] visited = new int[n];        //标记当前该顶点的最短路径是否已经求出,1表示已求出
        
        //初始化，第一个顶点求出
        shortPath[start] = 0;
        visited[start] = 1;
        
        for(int count = 1;count <= n - 1;count++)        //要加入n-1个顶点
        {
            int k = -1;    //选出一个距离初始顶点start最近的未标记顶点
            int dmin = 1000;
            for(int i = 0;i < n;i++)
            {
                if(visited[i] == 0 && weight[start][i] < dmin)
                {
                    dmin = weight[start][i];
                    k = i;
                }    
            }
            
            //将新选出的顶点标记为已求出最短路径，且到start的最短路径就是dmin
            shortPath[k] = dmin;
            visited[k] = 1;
            
            //以k为中间点想，修正从start到未访问各点的距离
            for(int i = 0;i < n;i++)
            {
                if(visited[i] == 0 && weight[start][k] + weight[k][i] < weight[start][i])
                     weight[start][i] = weight[start][k] + weight[k][i];
            }    
    
        }
        
        return shortPath;
    }
}
public class Dijkstra {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[][] weight = {
                {0,3,9999999,7,9999999},
                {3,0,4,2,9999999},
                {9999999,4,0,5,6},
                {7,2,5,0,4},
                {9999999,9999999,6,4,0}
        };
        
        int[] path = Dijsktra(weight,0);
        for(int i = 0;i < path.length;i++)
            System.out.print(path[i] + "  ");
    }
    

    public static int[] Dijsktra(int[][] weight,int start){
        //接受一个有向图的权重矩阵，和一个起点编号start（从0编号，顶点存在数组中）
        //返回一个int[] 数组，表示从start到它的最短路径长度
        int n = weight.length;        //顶点个数
        int[] shortPath = new int[n];    //存放从start到其他各点的最短路径
        int[] visited = new int[n];        //标记当前该顶点的最短路径是否已经求出,1表示已求出
        
        //初始化，第一个顶点求出
        shortPath[start] = 0;
        visited[start] = 1;
        
        for(int count = 1;count <= n - 1;count++)        //要加入n-1个顶点
        {
            int k = -1;    //选出一个距离初始顶点start最近的未标记顶点
            int dmin = 1000;
            for(int i = 0;i < n;i++)
            {
                if(visited[i] == 0 && weight[start][i] < dmin)
                {
                    dmin = weight[start][i];
                    k = i;
                }    
            }
            
            //将新选出的顶点标记为已求出最短路径，且到start的最短路径就是dmin
            shortPath[k] = dmin;
            visited[k] = 1;
            
            //以k为中间点想，修正从start到未访问各点的距离
            for(int i = 0;i < n;i++)
            {
                if(visited[i] == 0 && weight[start][k] + weight[k][i] < weight[start][i])
                     weight[start][i] = weight[start][k] + weight[k][i];
            }    
    
        }
        
        return shortPath;
    }
}

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