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package class10_17;
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import java.util.HashMap;
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import java.util.HashSet;
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import java.util.Map.Entry;
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// no negative weight
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public class Code01_Dijkstra {
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public static HashMap<Node, Integer> dijkstra1(Node from) {
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HashMap<Node, Integer> distanceMap = new HashMap<>();
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distanceMap.put(from, 0);
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// 打过对号的点
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HashSet<Node> selectedNodes = new HashSet<>();
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Node minNode = getMinDistanceAndUnselectedNode(distanceMap, selectedNodes);
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while (minNode != null) {
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// 原始点 -> minNode(跳转点) 最小距离distance
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int distance = distanceMap.get(minNode);
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for (Edge edge : minNode.edges) {
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Node toNode = edge.to;
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if (!distanceMap.containsKey(toNode)) {
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distanceMap.put(toNode, distance + edge.weight);
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} else { // toNode
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distanceMap.put(edge.to, Math.min(distanceMap.get(toNode), distance + edge.weight));
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}
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}
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selectedNodes.add(minNode);
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minNode = getMinDistanceAndUnselectedNode(distanceMap, selectedNodes);
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}
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return distanceMap;
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}
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public static Node getMinDistanceAndUnselectedNode(HashMap<Node, Integer> distanceMap, HashSet<Node> touchedNodes) {
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Node minNode = null;
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int minDistance = Integer.MAX_VALUE;
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for (Entry<Node, Integer> entry : distanceMap.entrySet()) {
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Node node = entry.getKey();
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int distance = entry.getValue();
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if (!touchedNodes.contains(node) && distance < minDistance) {
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minNode = node;
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minDistance = distance;
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}
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}
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return minNode;
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}
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public static class NodeRecord {
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public Node node;
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public int distance;
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public NodeRecord(Node node, int distance) {
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this.node = node;
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this.distance = distance;
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}
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}
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public static class NodeHeap {
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private Node[] nodes; // 实际的堆结构
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// key 某一个node, value 上面堆中的位置
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private HashMap<Node, Integer> heapIndexMap;
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// key 某一个节点, value 从源节点出发到该节点的目前最小距离
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private HashMap<Node, Integer> distanceMap;
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private int size; // 堆上有多少个点
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public NodeHeap(int size) {
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nodes = new Node[size];
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heapIndexMap = new HashMap<>();
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distanceMap = new HashMap<>();
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size = 0;
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}
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public boolean isEmpty() {
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return size == 0;
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}
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// 有一个点叫node,现在发现了一个从源节点出发到达node的距离为distance
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// 判断要不要更新,如果需要的话,就更新
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public void addOrUpdateOrIgnore(Node node, int distance) {
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if (inHeap(node)) {
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distanceMap.put(node, Math.min(distanceMap.get(node), distance));
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insertHeapify(node, heapIndexMap.get(node));
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}
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if (!isEntered(node)) {
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nodes[size] = node;
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heapIndexMap.put(node, size);
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distanceMap.put(node, distance);
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insertHeapify(node, size++);
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}
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}
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public NodeRecord pop() {
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NodeRecord nodeRecord = new NodeRecord(nodes[0], distanceMap.get(nodes[0]));
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swap(0, size - 1);
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heapIndexMap.put(nodes[size - 1], -1);
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distanceMap.remove(nodes[size - 1]);
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// free C++同学还要把原本堆顶节点析构,对java同学不必
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nodes[size - 1] = null;
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heapify(0, --size);
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return nodeRecord;
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}
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private void insertHeapify(Node node, int index) {
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while (distanceMap.get(nodes[index]) < distanceMap.get(nodes[(index - 1) / 2])) {
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swap(index, (index - 1) / 2);
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index = (index - 1) / 2;
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}
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}
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private void heapify(int index, int size) {
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int left = index * 2 + 1;
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while (left < size) {
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int smallest = left + 1 < size && distanceMap.get(nodes[left + 1]) < distanceMap.get(nodes[left])
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? left + 1
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: left;
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smallest = distanceMap.get(nodes[smallest]) < distanceMap.get(nodes[index]) ? smallest : index;
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if (smallest == index) {
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break;
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}
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swap(smallest, index);
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index = smallest;
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left = index * 2 + 1;
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}
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}
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private boolean isEntered(Node node) {
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return heapIndexMap.containsKey(node);
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}
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private boolean inHeap(Node node) {
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return isEntered(node) && heapIndexMap.get(node) != -1;
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}
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private void swap(int index1, int index2) {
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heapIndexMap.put(nodes[index1], index2);
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heapIndexMap.put(nodes[index2], index1);
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Node tmp = nodes[index1];
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nodes[index1] = nodes[index2];
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nodes[index2] = tmp;
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}
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}
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// 改进后的dijkstra算法
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// 从head出发,所有head能到达的节点,生成到达每个节点的最小路径记录并返回
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public static HashMap<Node, Integer> dijkstra2(Node head, int size) {
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NodeHeap nodeHeap = new NodeHeap(size);
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nodeHeap.addOrUpdateOrIgnore(head, 0);
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HashMap<Node, Integer> result = new HashMap<>();
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while (!nodeHeap.isEmpty()) {
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NodeRecord record = nodeHeap.pop();
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Node cur = record.node;
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int distance = record.distance;
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for (Edge edge : cur.edges) {
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nodeHeap.addOrUpdateOrIgnore(edge.to, edge.weight + distance);
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}
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result.put(cur, distance);
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}
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return result;
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}
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}
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