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!1261 基于SPFA算法实现有向图结构
* 修改注释 * 修改注释 * 修改异常信息 * 修改负环检查的判断条件 当原图为非联通图 以及当前开始节点可触达节点小于总节点数 或者环路路段较短时 所需要循环执行的次数 * Merge branch 'v6-dev' of https://gitee.com/hrnd/hutool into v6-dev * 更新单元测试 * 添加入队SLF优化 * 有向图 基于SPFA 算法实现 * 修改测试用例 * 修改测试用例 * Merge branch 'v6-dev' of https://gitee.com/hrnd/hutool into v6-dev * 实现有向图，提供最短路径方法
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好人难当
Looly
parent
c93d4785d9
commit
8bc2677267
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package org.dromara.hutool.core.map.multi;
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import java.util.*;
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/**
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* 权重有向图
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* 基于 SPFA 算法实现 可以处理负边 可以进行负权环路检查
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*
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* @author NewshiJ
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* @date 2024/8/16 09:01
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*/
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public class DirectedWeightGraph<T> {
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// 全部节点
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private final Set<T> allPoints = new HashSet<>();
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// 邻接边
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private final Map<T, Map<T,Edge<T>>> neighborEdgeMap = new HashMap<>();
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/**
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* 添加边
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* @param fromPoint 开始点
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* @param nextPoint 结束点
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* @param weight 权重
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*/
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public void putEdge(T fromPoint, T nextPoint, long weight) {
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allPoints.add(fromPoint);
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allPoints.add(nextPoint);
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Map<T, Edge<T>> nextPointMap = neighborEdgeMap.computeIfAbsent(fromPoint, k -> new HashMap<>());
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nextPointMap.put(nextPoint, new Edge<>(fromPoint, nextPoint, weight));
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}
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/**
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* 删除边
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* @param fromPoint
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* @param nextPoint
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*/
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public void removeEdge(T fromPoint, T nextPoint) {
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Map<T, Edge<T>> nextPointMap = neighborEdgeMap.computeIfAbsent(fromPoint, k -> new HashMap<>());
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nextPointMap.remove(nextPoint);
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// 重新计算 所有点位
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allPoints.clear();
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neighborEdgeMap.forEach((f,m) -> {
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allPoints.add(f);
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m.forEach((t,e) -> {
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allPoints.add(t);
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});
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});
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}
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/**
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* 删除点
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* @param point
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*/
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public void removePoint(T point){
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allPoints.remove(point);
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neighborEdgeMap.remove(point);
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neighborEdgeMap.forEach((f,m) -> {
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m.remove(point);
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});
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}
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@Override
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public String toString() {
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StringBuilder builder = new StringBuilder();
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neighborEdgeMap.forEach((from,edgeMap) -> {
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edgeMap.forEach((to,edge) -> {
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builder.append(edge);
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builder.append("\r\n");
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});
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});
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return builder.toString();
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}
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/**
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* 计算 从 startPoint 到 所有点 最短路径
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* 基于 SPFA 算法实现
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*
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* @param startPoint 开始节点
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* @throws NegativeRingException 存在负权环路
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* @return 最佳路径集合 如果无可触达顶点 返回空 map
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*/
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public Map<T, Path<T>> bestPathMap(T startPoint) throws NegativeRingException{
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// 全部节点数量
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int pointSize = allPoints.size();
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// 待访问队列
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LinkedList<T> pointQueue = new LinkedList<>();
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// 待访问队列中的节点 加速判断
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HashSet<T> inQueuePoints = new HashSet<>();
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// 最佳路径集合
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HashMap<T, Path<T>> bestPathMap = new HashMap<>();
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Map<T, Edge<T>> map = neighborEdgeMap.get(startPoint);
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// 无可触达路径
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if(map == null || map.isEmpty()){
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return new HashMap<>();
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}
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map.forEach((to,edge) -> {
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Path<T> path = new Path<>(edge);
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bestPathMap.put(to, path);
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pointQueue.add(to);
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inQueuePoints.add(to);
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});
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while (!pointQueue.isEmpty()){
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// 当前节点 开始对 currentPoint 进行扩展
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T currentPoint = pointQueue.removeFirst();
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// 到当前节点的最短路径
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Path<T> currentPath = bestPathMap.get(currentPoint);
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// 标记已出队列
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inQueuePoints.remove(currentPoint);
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Map<T, Edge<T>> edgeMap = neighborEdgeMap.get(currentPoint);
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if(edgeMap == null){
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continue;
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}
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// 扩展当前点的边
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Set<Map.Entry<T, Edge<T>>> entrySet = edgeMap.entrySet();
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for (Map.Entry<T, Edge<T>> entry : entrySet) {
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T nextPoint = entry.getKey();
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Edge<T> edge = entry.getValue();
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// 不存在路径 第一次访问 将当前路径放置到 bestPathMap 中
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Path<T> oldPath = bestPathMap.get(nextPoint);
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if(oldPath == null){
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Path<T> nextPath = currentPath.nextPoint(edge);
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bestPathMap.put(nextPoint,nextPath);
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// 不在队列里就入队
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if(!inQueuePoints.contains(nextPoint)){
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inQueuePoints.add(nextPoint);
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// SLF优化 入队优化
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// 每次出队进行判断扩展出的点与队头元素进行判断，若小于进队头，否则入队尾
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// 尽可能的让 负环路 上的节点 先进入队列头
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if(pointQueue.isEmpty()){
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pointQueue.addLast(nextPoint);
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continue;
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}
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T first = pointQueue.getFirst();
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Path<T> fristPath = bestPathMap.get(first);
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if(nextPath.weight < fristPath.weight){
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pointQueue.addFirst(nextPoint);
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}else {
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pointQueue.add(nextPoint);
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}
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}
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continue;
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}
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long newWeight = currentPath.weight + edge.weight;
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// 新路径更糟糕 没有优化的必要
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if(newWeight >= oldPath.weight){
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continue;
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}
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// 更新最佳路径 如果下一跳没有在队列中 将下一跳放到队列里
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Path<T> nextPath = currentPath.nextPoint(edge);
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bestPathMap.put(nextPoint,nextPath);
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// 不在队列里就入队
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if(!inQueuePoints.contains(nextPoint)){
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inQueuePoints.add(nextPoint);
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// SLF优化 入队优化
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// 每次出队进行判断扩展出的点与队头元素进行判断，若小于进队头，否则入队尾
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// 尽可能的让 负环路 上的节点 先进入队列头
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if(pointQueue.isEmpty()){
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pointQueue.addLast(nextPoint);
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continue;
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}
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T first = pointQueue.getFirst();
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Path<T> fristPath = bestPathMap.get(first);
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if(nextPath.weight < fristPath.weight){
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pointQueue.addFirst(nextPoint);
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}else {
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pointQueue.addLast(nextPoint);
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}
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}
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}
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}
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return bestPathMap;
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}
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/**
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* 边
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* @param <T>
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*/
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public static class Edge<T> {
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// 起始点
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public T fromPoint;
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// 目标点
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public T nextPoint;
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// 权重
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public long weight;
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public Edge(T fromPoint, T nextPoint, long weight) {
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this.fromPoint = fromPoint;
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this.nextPoint = nextPoint;
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this.weight = weight;
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}
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@Override
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public String toString() {
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return fromPoint + "->" + nextPoint + "(" + weight + ")";
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}
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}
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public static class Path<T> {
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// 开始节点
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public T startPoint;
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// 结束节点
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public T endPoint;
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/**
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* 道路 即依次按照顺序经过的边
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*/
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public LinkedList<Edge<T>> way = new LinkedList<>();
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/**
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* 已经经过的点 如果 有一个点已经多次经过了 可以判定已经成环
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* 当源图是一个非联通图时 或者 开始节点处于图路径中下游时 或者 成环路经过的节点数量较少时
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* 使用判断节点经过次数与全部节点数量进行比较会有冗余判断
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* 用成环判断 可以加速这种情况 是针对一些特殊的图结构优化了最差情况
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*/
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public Set<T> passedPoints = new HashSet<>();
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// 总权重
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public long weight;
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public Path(Edge<T> edge){
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startPoint = edge.fromPoint;
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endPoint = edge.nextPoint;
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way.add(edge);
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weight = edge.weight;
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passedPoints.add(edge.fromPoint);
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passedPoints.add(edge.nextPoint);
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}
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public Path(){}
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/**
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* 生成下一跳
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* @param edge
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* @throws NegativeRingException 负环路
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* @return
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*/
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public Path<T> nextPoint(Edge<T> edge) throws NegativeRingException {
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Path<T> nextPath = new Path<>();
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nextPath.startPoint = startPoint;
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nextPath.endPoint = edge.nextPoint;
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nextPath.way.addAll(way);
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nextPath.way.add(edge);
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nextPath.weight = weight + edge.weight;
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nextPath.passedPoints.addAll(passedPoints);
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// 负环检查
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if(nextPath.passedPoints.contains(edge.nextPoint)){
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throw new NegativeRingException("路径:" + nextPath + "存在负环路");
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}
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nextPath.passedPoints.add(edge.nextPoint);
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return nextPath;
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}
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@Override
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public String toString() {
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StringBuilder builder = new StringBuilder();
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builder.append(String.format("[%s->%s(%d)] ", startPoint, endPoint, weight));
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for (Edge<T> edge : way) {
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builder.append(edge);
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builder.append(" ");
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}
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return builder.toString();
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}
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}
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/**
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* 负环异常
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*/
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public static class NegativeRingException extends Exception {
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public NegativeRingException(String msg){
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super(msg);
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}
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}
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}
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@ -0,0 +1,55 @@
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package org.dromara.hutool.core.map;
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import org.dromara.hutool.core.map.multi.DirectedWeightGraph;
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import org.junit.jupiter.api.Test;
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import java.util.List;
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import java.util.Map;
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/**
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* @author newshiJ
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* @date 2024/8/14 17:07
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*/
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public class DirectedWeightGraphTest {
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@Test
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public void test1(){
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DirectedWeightGraph<String> graph = new DirectedWeightGraph<>();
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graph.putEdge("A", "B", 14);
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graph.putEdge("A", "C", 8);
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graph.putEdge("A", "D", 12);
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// graph.putEdge("B", "A", -14);
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graph.putEdge("B", "E", 4);
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graph.putEdge("C", "B", 3);
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graph.putEdge("C", "D", 5);
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graph.putEdge("C", "E", 5);
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graph.putEdge("C", "F", 6);
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graph.putEdge("D", "F", 7);
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// graph.putEdge("E", "B", -14);
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graph.putEdge("E", "G", 4);
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graph.putEdge("G", "B", -9);
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graph.putEdge("F", "G", 2);
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graph.putEdge("X", "Y", 2);
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graph.removePoint("X");
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System.out.println(graph);
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Map<String, DirectedWeightGraph.Path<String>> map = null;
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try {
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map = graph.bestPathMap("A");
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map.forEach((k,v) -> {
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System.out.println(v);
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});
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} catch (DirectedWeightGraph.NegativeRingException e) {
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e.printStackTrace();
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}
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}
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}
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