最短路径算法

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到底是贪心还是动态规划?
Dijkstra算法
抽象问题,选择合适的数据结构抽象问题  权重图,本质求两节点最小权重值
从起点开始遍历所有的临接节点,将节点权重维护到最小堆中
每次以最小堆对应的顶点为起点再次遍历临接节点:
0) 默认到最小节点的距离都是MAX INT,用数组存储,index顶点值
1)将节点标记为已遍历,所有临接节点距离与当前数组中距离比较:
2)如果大于当前距离不处理,否则入队并更新数组,未入最小堆进行入堆标记,
结束条件:最小堆对应的节点就是目的节点

A*算法
如果图非常大,那么Dijkstra算法就会十分耗时,A*算法就是对其的改造,是为了快速找出一条接近于最短路线的次优路线。

主要是为了避免开始的远方绕路行为
Dijkstra 判断出堆的点:距离到起点最近的顶点
A*:g(i)+h(i)来判断最先出堆的点,g(i):顶点起始点的距离,h(i):顶点到终点的距离,如果和最小,说明总的距离可能最小。

public class Dijkstra {
    public static void main(String[] args) {

        LinkedList<Edege>[] list = new LinkedList[4];
        LinkedList<Edege> list1 = new LinkedList();
        Edege e1 =new Edege(1,2,3);
        list1.add(e1);
        Edege e2 =new Edege(1,3,10);
        list1.add(e2);

        LinkedList<Edege> list2 = new LinkedList();
        LinkedList<Edege> list3 = new LinkedList();
        Edege e3 =new Edege(2,3,4);
        list2.add(e3);

        list[1] = list1;
        list[2] = list2;
        list[3] = list3;

        Graphic g = new Graphic(3,list);
        System.out.println(getShortedRoad(g,1,3));;

//        PriorityQueue queue = new PriorityQueue(3);
//        Verte a1 = new Verte(1,3);
//        Verte a2 = new Verte(2,2);
//        Verte a3 = new Verte(3,1);
//        queue.add(a1);
//        queue.add(a2);
//        queue.add(a3);
//        a2 = new Verte(2,-1);
//        queue.update(a2);
//        System.out.println();
    }



    public static  int getShortedRoad(Graphic g, int start, int end){
        if(start == end){
            return 0;
        }

        LinkedList<Edege>[] list = g.getList();
        int nodeNum = g.getV();

        // index:图的顶点 value:start到该顶点的最小距离
        int[] roadlength = new int[nodeNum+1];
        for(int i =0; i<nodeNum+1; i++){
            roadlength[i] = Integer.MAX_VALUE;
        }

        boolean[] visited = new boolean[nodeNum+1];
        boolean[] inqueue = new boolean[nodeNum+1];

        PriorityQueue roadDui  = new PriorityQueue(nodeNum+1);
        Verte v = new Verte(1,0);
        roadDui.add(v);
        inqueue[v.getId()] =  true;

        while(!roadDui.isEmpty()){
            Verte  temp = roadDui.poll();
            roadlength[temp.getId()] = temp.getDist();
            if(temp.getId() == end ){
                return temp.getDist();
            }
            if(visited[temp.getId()] == false){
                visited[temp.getId()] = true;
                LinkedList<Edege> edeges = list[temp.getId()];
                if(null != edeges){
                    for(int i=0; i<edeges.size(); i++){
                        Verte v1 = new Verte(edeges.get(i).getTid(), edeges.get(i).getW() + temp.getDist());
                        if(v1.getDist() < roadlength[v1.getId()]){
                            roadlength[v1.getId()] = v1.getDist();
                        }else{
                            v1.setDist(roadlength[v1.getId()]);
                        }
                        if(inqueue[v1.getId()] == true ){
                            roadDui.update(v1);
                        }else{
                            roadDui.add(v1);
                            inqueue[v1.getId()] = true;
                        }
                    }
                }

            }
        }
        return -1;
    }

    // 下面这个类是为了dijkstra实现用的
    private static  class Verte {
        public int id; // 顶点编号ID
        public int dist; // 从起始顶点到这个顶点的距离
        public Verte(int id, int dist) {
            this.id = id;
            this.dist = dist;
        }

        public int getId() {
            return id;
        }

        public void setId(int id) {
            this.id = id;
        }

        public int getDist() {
            return dist;
        }

        public void setDist(int dist) {
            this.dist = dist;
        }
    }

    // 因为Java提供的优先级队列,没有暴露更新数据的接口,所以我们需要重新实现一个
    private static  class PriorityQueue { // 根据vertex.dist构建小顶堆
        private Verte[] nodes;
        private int count;
        public PriorityQueue(int v) {
            this.nodes = new Verte[v+1];
            this.count = v;
        }
        public Verte poll() {
            Verte v = nodes[1];
            nodes[1] = null;
            int i =1;
            while(2*i<count && (nodes[2*i] != null || nodes[2*1+1] != null)){
                if(nodes[2*i] != null && nodes[2*i+1] != null){
                    // 左右节点均不为空
                    if(nodes[2*i].getDist() < nodes[2*i+1].getDist() ){
                        nodes[i] = nodes[2*i];
                        nodes[2*i] = null;
                        i = 2*1;
                    }else{
                        // 右节点不为空
                        nodes[i] = nodes[2*i+1];
                        nodes[2*i+1] = null;
                         i = 2*1+1;
                    }
                }else if(nodes[2*i] != null){
                    // 左节点不为空
                    nodes[i] = nodes[2*i];
                    nodes[2*i] = null;
                    i = 2*1;
                }else{
                    // 右节点不为空
                    nodes[i] = nodes[2*i+1];
                    nodes[2*i+1] = null;
                    i = 2*1+1;
                }
            }
            return v;
        }

        public void add(Verte vertex) {
            int index  = 1;
            for(int i=1; i<=count; i++){
                if(nodes[i]==null){
                    nodes[i]=vertex;
                    index = i;
                    break;
                }
            }
            int i =index;
            while( i != 1 && nodes[i].getDist() < nodes[i/2].getDist()){
                Verte temp = nodes[i/2];
                nodes[i/2] = nodes[i];
                nodes[i] = temp;
                i = i/2;
            }
        }

        // 更新结点的值,并且从下往上堆化,重新符合堆的定义。时间复杂度O(logn)。
        public void update(Verte vertex) {
            int index = 0;
            for(int i = 1; i<=count; i++){
                if(null != nodes[i] && nodes[i].getId() == vertex.getId()){
                    nodes[i] = vertex;
                    index = i ;
                    break;
                }
            }
            if(index == 0 ){
                return;
            }
            int left = index*2;
            int right = index*2+1;

            while(left<=count && (nodes[left] != null || nodes[right] != null)){
                if(nodes[left] != null && nodes[index].getDist() > nodes[left].getDist()  ){
                    Verte temp = nodes[left];
                    nodes[left] = nodes[index];
                    nodes[index] = temp;
                    index = left;
                }else if(nodes[right] != null && nodes[index].getDist() > nodes[right].getDist()  ){
                    Verte temp = nodes[right];
                    nodes[right] = nodes[index];
                    nodes[index] = temp;
                    index = right;
                }else{
                    break;
                }
                left = index*2;
                right = index*2+1;
            }

            int parent  = index/2;
            while(parent != 0 && nodes[parent].getDist() > nodes[index].getDist()){
                Verte temp = nodes[parent];
                nodes[parent] = nodes[index];
                nodes[index] = temp;
                index = parent;
                parent  = index/2;
            }
        }
        public boolean isEmpty() {
            return nodes[1] == null;
        }

    }


    static class Graphic{
        int v;
        LinkedList<Edege>[] list ;
        public Graphic(int v, LinkedList<Edege>[] list){
            this.v = v;
            this.list = list;
        }

        public int getV() {
            return v;
        }

        public void setV(int v) {
            this.v = v;
        }

        public LinkedList<Edege>[] getList() {
            return list;
        }

        public void setList(LinkedList<Edege>[] list) {
            this.list = list;
        }
    }

    static class Edege{
        public int sid;
        public int tid;
        public int w;

        public Edege(int sid, int tid, int w){
            this.sid = sid;
            this.tid = tid;
            this.w = w;
        }

        public int getSid() {
            return sid;
        }

        public void setSid(int sid) {
            this.sid = sid;
        }

        public int getTid() {
            return tid;
        }

        public void setTid(int tid) {
            this.tid = tid;
        }

        public int getW() {
            return w;
        }

        public void setW(int w) {
            this.w = w;
        }
    }
}

 

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