DiJkstra（狄克斯特拉）算法

是从一个顶点到其余各顶点的最短路径算法，解决的是有权图中最短路径问题。

迪杰斯特拉算法主要特点是从起始点开始，采用贪心算法的策略，每次遍历到始点距离最近且未访问过的顶点的邻接节点，直到扩展到终点为止。

要求：图中不能有累加和为负数的环

思路：

  代码： 

package Algorithms.Graph;

import java.util.HashMap;
import java.util.HashSet;
import java.util.Map.Entry;

public class Dijkstra {
    //获取从head出发到所有点的最小距离
    public static HashMap<Node, Integer> dijkstra1(Node head) {
        //所有的距离指的是从唯一的源头（head）到当前点的最小距离
        // key：从head出发到达key
        // value：从head出发到达key的最小距离
        //如果在表中没有T的记录，含义是从head出发到T这个点的距离为正无穷
        HashMap<Node, Integer> distanceMap = new HashMap<>();
        distanceMap.put(head, 0);//把从head到head的最小距离0加入distanceMap中
        //selectedNodes用于存放已经求过距离的节点，以后再不不碰
        HashSet<Node> selectedNodes = new HashSet<>();

        //得到一个距离最小的点A
        Node minNode = getMinDistanceAndUnselectedNode(distanceMap, selectedNodes);
        while (minNode != null) {
            int distance = distanceMap.get(minNode); //计算最小距离
            for (Edge edge : minNode.edges) { //循环点A的所有边
                Node toNode = edge.to; //边所对应的点X
                if (!distanceMap.containsKey(toNode)) { //如果点X不在distanceMap中
                    distanceMap.put(toNode, distance + edge.weight); //在distanceMap中记录从head到X点的距离
                } else {
                    //如果X在distanceMap中，更新最小距离
                    distanceMap.put(toNode, Math.min(distanceMap.get(toNode), distance + edge.weight));
                }
            }
            selectedNodes.add(minNode); //把点A添加到已经求过距离的节点
            //再次得到distanceMap中距离最小的节点B，然后重复以上操作，
            minNode = getMinDistanceAndUnselectedNode(distanceMap, selectedNodes);
            // 最后所有的点都会进入selectedNode,minNode就会为null，退出循环，返回distanceMap
        }
        return distanceMap;
    }

    //在distanceMap选择最小距离的节点，但不能是已经选过的点selectedNode
    public static Node getMinDistanceAndUnselectedNode(HashMap<Node, Integer> distanceMap,
                                                       HashSet<Node> selectedNode) {
        Node minNode = null;
        int minDistance = Integer.MAX_VALUE; //到每点距离默认为系统最大值
        for (Entry<Node, Integer> entry : distanceMap.entrySet()) { //遍历distanceMap
            Node node = entry.getKey(); //取当前节点
            int distance = entry.getValue(); //取当前节点所对应的距离
            //如果这个Node不在已经求过节点的集合中且这个距离比当前最小距离小
            if (!selectedNode.contains(node) && distance < minDistance) {
                minNode = node; //更新最小距离的节点
                minDistance = distance;  //更新最小距离
            }
        }
        return minNode;
    }   
} 

package Algorithms.Graph;

import java.util.HashMap;

public class Dijkstra {    

    public static class NodeRecord {
        public Node node;
        public int distance;

        public NodeRecord(Node node, int distance) {
            this.node = node;
            this.distance = distance;
        }
    }

    public static class NodeHeap {
        private Node[] nodes;
        private HashMap<Node, Integer> heapIndexMap;
        private HashMap<Node, Integer> distanceMap;
        private int size;

        public NodeHeap(int size) {
            nodes = new Node[size];
            heapIndexMap = new HashMap<>();
            distanceMap = new HashMap<>();
            this.size = 0;
        }

        public boolean isEmpty() {
            return size == 0;
        }

        public void addOrUpdateOrIgnore(Node node, int distance) {
            if (inHeap(node)) {
                distanceMap.put(node, Math.min(distanceMap.get(node), distance));
                insertHeapify(node, heapIndexMap.get(node));
            }
            if (!isEntered(node)) {
                nodes[size] = node;
                heapIndexMap.put(node, size);
                distanceMap.put(node, distance);
                insertHeapify(node, size++);
            }
        }

        public NodeRecord pop() {
            NodeRecord nodeRecord = new NodeRecord(nodes[0], distanceMap.get(nodes[0]));
            swap(0, size - 1);
            heapIndexMap.put(nodes[size - 1], -1);
            distanceMap.remove(nodes[size - 1]);
            nodes[size - 1] = null;
            heapify(0, --size);
            return nodeRecord;
        }

        private void insertHeapify(Node node, int index) {
            while (distanceMap.get(nodes[index]) < distanceMap.get(nodes[(index - 1) / 2])) {
                swap(index, (index - 1) / 2);
                index = (index - 1) / 2;
            }
        }

        private void heapify(int index, int size) {
            int left = index * 2 + 1;
            while (left < size) {
                int smallest = left + 1 < size && distanceMap.get(nodes[left + 1]) < distanceMap.get(nodes[left])
                        ? left + 1 : left;
                smallest = distanceMap.get(nodes[smallest]) < distanceMap.get(nodes[index]) ? smallest : index;
                if (smallest == index) {
                    break;
                }
                swap(smallest, index);
                index = smallest;
                left = index * 2 + 1;
            }
        }

        private boolean isEntered(Node node) {
            return heapIndexMap.containsKey(node);
        }

        private boolean inHeap(Node node) {
            return isEntered(node) && heapIndexMap.get(node) != -1;
        }

        private void swap(int index1, int index2) {
            heapIndexMap.put(nodes[index1], index2);
            heapIndexMap.put(nodes[index2], index1);
            Node tmp = nodes[index1];
            nodes[index1] = nodes[index2];
            nodes[index2] = tmp;
        }
    }

    public static HashMap<Node, Integer> dijkstra2(Node head, int size) {
        NodeHeap nodeHeap = new NodeHeap(size);
        nodeHeap.addOrUpdateOrIgnore(head, 0);
        HashMap<Node, Integer> result = new HashMap<>();
        while (!nodeHeap.isEmpty()) {
            NodeRecord record = nodeHeap.pop();
            Node cur = record.node;
            int distance = record.distance;
            for (Edge edge : cur.edges) {
                nodeHeap.addOrUpdateOrIgnore(edge.to, edge.weight + distance);
            }
            result.put(cur, distance);
        }
        return result;
    }
}

优化