CSharp: Dijkstra Algorithms
/*
# encoding: utf-8
# 版权所有 2026 ©涂聚文有限公司™ ®
# 许可信息查看：言語成了邀功盡責的功臣，還需要行爲每日來值班嗎
# 描述：Dijkstra Algorithms
# Author : geovindu,Geovin Du 涂聚文.
# IDE : vs2026 c# .net 10
# os : windows 10
# database : mysql 9.0 sql server 2019, postgreSQL 17.0 Oracle 21c Neo4j
# Datetime : 2026/07/04 22:16
# User : geovindu
# Product : Visual Studio 2026
# Project : CSharpDesignPattern
# File : City.cs
*/
using System;
using System.Collections.Generic;
using System.Text;
namespace CSharpAlgorithms.Dijkstra
{
// ===================== 数据模型分层 =====================
/// <summary>
/// 城市坐标实体
/// </summary>
public class City
{
public string Name { get; set; }
public float X { get; set; }
public float Y { get; set; }
public City(string name, float x, float y)
{
Name = name;
X = x;
Y = y;
}
}
}
/*
# encoding: utf-8
# 版权所有 2026 ©涂聚文有限公司™ ®
# 许可信息查看：言語成了邀功盡責的功臣，還需要行爲每日來值班嗎
# 描述：Dijkstra Algorithms
# Author : geovindu,Geovin Du 涂聚文.
# IDE : vs2026 c# .net 10
# os : windows 10
# database : mysql 9.0 sql server 2019, postgreSQL 17.0 Oracle 21c Neo4j
# Datetime : 2026/07/04 22:16
# User : geovindu
# Product : Visual Studio 2026
# Project : CSharpDesignPattern
# File : RoadGraph.cs
*/
using System;
using System.Collections.Generic;
using System.Text;
namespace CSharpAlgorithms.Dijkstra
{
/// <summary>
/// 路网邻接图
/// </summary>
public class RoadGraph
{
// 邻接表：起点 -> (终点,权重)
public Dictionary<string, Dictionary<string, double>> Adj { get; }
public RoadGraph()
{
Adj = new Dictionary<string, Dictionary<string, double>>();
}
/// <summary>添加双向道路</summary>
public void AddEdge(string from, string to, double weight)
{
if (!Adj.ContainsKey(from)) Adj[from] = new Dictionary<string, double>();
Adj[from][to] = weight;
if (!Adj.ContainsKey(to)) Adj[to] = new Dictionary<string, double>();
Adj[to][from] = weight;
}
}
}
/*
# encoding: utf-8
# 版权所有 2026 ©涂聚文有限公司™ ®
# 许可信息查看：言語成了邀功盡責的功臣，還需要行爲每日來值班嗎
# 描述：Dijkstra Algorithms
# Author : geovindu,Geovin Du 涂聚文.
# IDE : vs2026 c# .net 10
# os : windows 10
# database : mysql 9.0 sql server 2019, postgreSQL 17.0 Oracle 21c Neo4j
# Datetime : 2026/07/04 22:16
# User : geovindu
# Product : Visual Studio 2026
# Project : CSharpDesignPattern
# File : PathPlanner.cs
*/
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Text;
using static System.Net.Mime.MediaTypeNames;
using System.Drawing.Drawing2D;
using System.IO;
namespace CSharpAlgorithms.Dijkstra
{
/// <summary>
/// 路径规划器：承载约束、计算、绘图
/// </summary>
public class PathPlanner
{
private readonly RoadGraph _graph;
private readonly Dictionary<string, City> _cityMap;
// 约束条件
public List<string> MustPassCities { get; set; } = new();
public HashSet<string> BanCities { get; set; } = new();
public PathPlanner(RoadGraph graph, Dictionary<string, City> cityMap)
{
_graph = graph;
_cityMap = cityMap;
}
/// <summary>
/// Dijkstra 重构：堆只存城市名，抛弃堆内携带完整路径
/// 用前驱表回溯路径，彻底消除元素对比IComparable报错
/// </summary>
public (double totalWeight, List<string> path) Dijkstra(string start, string end)
{
double INF = double.MaxValue;
Dictionary<string, double> dist = new();
Dictionary<string, string> prev = new();
Dictionary<string, bool> visited = new();
// 初始化距离
foreach (var city in _graph.Adj.Keys)
dist[city] = INF;
dist[start] = 0;
// 堆：权重double(可比较)，元素仅string城市名，无复杂对象
PriorityQueue<double, string> pq = new();
pq.Enqueue(0, start);
while (pq.Count > 0)
{
pq.TryDequeue(out double currDist, out string currCity);
// 跳过禁行、已访问
if (BanCities.Contains(currCity) || visited.ContainsKey(currCity))
continue;
if (currCity == end) break;
visited[currCity] = true;
// 遍历邻接节点
foreach (var (neighbor, w) in _graph.Adj[currCity])
{
if (BanCities.Contains(neighbor) || visited.ContainsKey(neighbor))
continue;
double newDist = currDist + w;
if (newDist < dist[neighbor])
{
dist[neighbor] = newDist;
prev[neighbor] = currCity;
pq.Enqueue(newDist, neighbor);
}
}
}
// 回溯完整路径
List<string> fullPath = new List<string>();
string temp = end;
while (!string.IsNullOrEmpty(temp))
{
fullPath.Add(temp);
temp = prev.ContainsKey(temp) ? prev[temp] : null;
}
fullPath.Reverse();
// 校验路径合法性：起点正确、包含所有必经城市、无禁行
bool pathValid = fullPath.Count > 0 && fullPath[0] == start;
if (pathValid)
{
foreach (var reqCity in MustPassCities)
{
if (!fullPath.Contains(reqCity))
{
pathValid = false;
break;
}
}
foreach (var node in fullPath)
{
if (BanCities.Contains(node))
{
pathValid = false;
break;
}
}
}
if (!pathValid)
return (INF, new List<string>());
return (dist[end], fullPath);
}
/// <summary>
/// 绘制路网PNG，带中文城市名称、高亮最优路径
/// </summary>
public void DrawMap(string savePath, List<string> highlightRoute, int width = 2800, int height = 1300)
{
// 超大X偏移，容纳 X=-5 南宁：-5*70 = -350，加400后变为正数
float offsetX = 400f;
float offsetY = 20f;
float scale = 70f;
using Bitmap bmp = new Bitmap(width, height);
using Graphics g = Graphics.FromImage(bmp);
g.Clear(Color.White);
g.SmoothingMode = SmoothingMode.AntiAlias;
using System.Drawing.Font fontCity = new System.Drawing.Font("Microsoft YaHei", 11);
using Pen penRoadNormal = new Pen(Color.Gray, 1);
using Pen penRoadHighlight = new Pen(Color.Red, 4);
using SolidBrush brushCityNode = new SolidBrush(Color.Blue);
using SolidBrush brushText = new SolidBrush(Color.Black);
// 绘制所有普通道路
HashSet<Tuple<string, string>> drawnEdge = new();
foreach (var (from, neighbors) in _graph.Adj)
{
City cFrom = _cityMap[from];
float fx = cFrom.X * scale + offsetX;
float fy = height - (cFrom.Y * scale + offsetY);
foreach (var to in neighbors.Keys)
{
var edgeKey = string.Compare(from, to) < 0
? Tuple.Create(from, to)
: Tuple.Create(to, from);
if (drawnEdge.Contains(edgeKey)) continue;
drawnEdge.Add(edgeKey);
City cTo = _cityMap[to];
float tx = cTo.X * scale + offsetX;
float ty = height - (cTo.Y * scale + offsetY);
g.DrawLine(penRoadNormal, fx, fy, tx, ty);
}
}
// 绘制高亮最优路径
for (int i = 0; i < highlightRoute.Count - 1; i++)
{
string a = highlightRoute[i];
string b = highlightRoute[i + 1];
City ca = _cityMap[a];
City cb = _cityMap[b];
float ax = ca.X * scale + offsetX;
float ay = height - (ca.Y * scale + offsetY);
float bx = cb.X * scale + offsetX;
float by = height - (cb.Y * scale + offsetY);
g.DrawLine(penRoadHighlight, ax, ay, bx, by);
}
// 绘制所有城市圆点+文字（包含负X西部城市）
foreach (var city in _cityMap.Values)
{
float x = city.X * scale + offsetX;
float y = height - (city.Y * scale + offsetY);
float radius = 8;
g.FillEllipse(brushCityNode, x - radius, y - radius, radius * 2, radius * 2);
g.DrawString(city.Name, fontCity, brushText, x + 4, y - radius - 14);
}
bmp.Save(savePath, System.Drawing.Imaging.ImageFormat.Png);
Console.WriteLine($"路网图片已保存：{Path.GetFullPath(savePath)}");
}
}
}
/*
# encoding: utf-8
# 版权所有 2026 ©涂聚文有限公司™ ®
# 许可信息查看：言語成了邀功盡責的功臣，還需要行爲每日來值班嗎
# 描述：Dijkstra Algorithms
# Author : geovindu,Geovin Du 涂聚文.
# IDE : vs2026 c# .net 10
# os : windows 10
# database : mysql 9.0 sql server 2019, postgreSQL 17.0 Oracle 21c Neo4j
# Datetime : 2026/07/04 22:16
# User : geovindu
# Product : Visual Studio 2026
# Project : CSharpDesignPattern
# File : Program.cs
*/
using CSharpAlgorithms.Dijkstra;
namespace CSharpAlgorithms
{
internal class Program
{
static void Main(string[] args)
{
// 1. 城市坐标定义
Dictionary<string, City> cityData = new()
{
{"深圳", new City("深圳", 5, 0)},
{"惠州", new City("惠州", 6, 1)},
{"东莞", new City("东莞", 4, 0)},
{"广州", new City("广州", 3, 0)},
{"佛山", new City("佛山", 2, 0)},
{"肇庆", new City("肇庆", 1, 1)},
{"梧州", new City("梧州", -2, 2)},
{"桂林", new City("桂林", -3, 4)},
{"柳州", new City("柳州", -4, 3)},
{"南宁", new City("南宁", -5, 1)},
{"韶关", new City("韶关", 2, 4)},
{"河源", new City("河源", 7, 3)},
{"赣州", new City("赣州", 8, 6)},
{"吉安", new City("吉安", 9, 9)},
{"南昌", new City("南昌", 10, 8)},
{"萍乡", new City("萍乡", 7, 8)},
{"长沙", new City("长沙", 6, 9)},
{"株洲", new City("株洲", 6, 8)},
{"衡阳", new City("衡阳", 6, 6)},
{"郴州", new City("郴州", 6, 4)},
{"九江", new City("九江", 11, 9)},
{"武汉", new City("武汉", 9, 11)},
{"郑州", new City("郑州", 10, 14)},
{"西安", new City("西安", 7, 15)},
{"福州", new City("福州", 13, 7)},
{"厦门", new City("厦门", 14, 4)},
};
// 2. 构建三类路网
// 里程路网 KM
RoadGraph graphKm = new();
graphKm.AddEdge("深圳", "惠州", 75);
graphKm.AddEdge("深圳", "广州", 140);
graphKm.AddEdge("深圳", "东莞", 65);
graphKm.AddEdge("惠州", "河源", 90);
graphKm.AddEdge("东莞", "广州", 50);
graphKm.AddEdge("广州", "韶关", 190);
graphKm.AddEdge("广州", "佛山", 25);
graphKm.AddEdge("佛山", "肇庆", 70);
graphKm.AddEdge("肇庆", "梧州", 210);
graphKm.AddEdge("梧州", "桂林", 260);
graphKm.AddEdge("桂林", "柳州", 170);
graphKm.AddEdge("柳州", "南宁", 220);
graphKm.AddEdge("韶关", "赣州", 230);
graphKm.AddEdge("河源", "赣州", 180);
graphKm.AddEdge("赣州", "吉安", 240);
graphKm.AddEdge("赣州", "南昌", 390);
graphKm.AddEdge("吉安", "南昌", 215);
graphKm.AddEdge("吉安", "萍乡", 280);
graphKm.AddEdge("萍乡", "长沙", 150);
graphKm.AddEdge("长沙", "武汉", 280);
graphKm.AddEdge("长沙", "株洲", 60);
graphKm.AddEdge("株洲", "衡阳", 130);
graphKm.AddEdge("衡阳", "郴州", 180);
graphKm.AddEdge("郴州", "韶关", 150);
graphKm.AddEdge("南昌", "九江", 130);
graphKm.AddEdge("九江", "武汉", 200);
graphKm.AddEdge("武汉", "郑州", 470);
graphKm.AddEdge("郑州", "西安", 450);
graphKm.AddEdge("南昌", "福州", 380);
graphKm.AddEdge("福州", "厦门", 230);
// 耗时路网 Hour
RoadGraph graphHour = new();
graphHour.AddEdge("深圳", "惠州", 1.0);
graphHour.AddEdge("深圳", "广州", 1.8);
graphHour.AddEdge("深圳", "东莞", 0.8);
graphHour.AddEdge("惠州", "河源", 1.3);
graphHour.AddEdge("东莞", "广州", 0.7);
graphHour.AddEdge("广州", "韶关", 2.2);
graphHour.AddEdge("广州", "佛山", 0.4);
graphHour.AddEdge("佛山", "肇庆", 0.9);
graphHour.AddEdge("肇庆", "梧州", 2.5);
graphHour.AddEdge("梧州", "桂林", 3.0);
graphHour.AddEdge("桂林", "柳州", 2.0);
graphHour.AddEdge("柳州", "南宁", 2.5);
graphHour.AddEdge("韶关", "赣州", 2.7);
graphHour.AddEdge("河源", "赣州", 2.0);
graphHour.AddEdge("赣州", "吉安", 2.6);
graphHour.AddEdge("赣州", "南昌", 4.2);
graphHour.AddEdge("吉安", "南昌", 2.3);
graphHour.AddEdge("吉安", "萍乡", 3.0);
graphHour.AddEdge("萍乡", "长沙", 1.6);
graphHour.AddEdge("长沙", "武汉", 3.0);
graphHour.AddEdge("长沙", "株洲", 0.8);
graphHour.AddEdge("株洲", "衡阳", 1.4);
graphHour.AddEdge("衡阳", "郴州", 2.0);
graphHour.AddEdge("郴州", "韶关", 1.7);
graphHour.AddEdge("南昌", "九江", 1.4);
graphHour.AddEdge("九江", "武汉", 2.1);
graphHour.AddEdge("武汉", "郑州", 4.8);
graphHour.AddEdge("郑州", "西安", 4.3);
graphHour.AddEdge("南昌", "福州", 4.0);
graphHour.AddEdge("福州", "厦门", 2.4);
// 路费路网 Cost
RoadGraph graphCost = new();
graphCost.AddEdge("深圳", "惠州", 35);
graphCost.AddEdge("深圳", "广州", 65);
graphCost.AddEdge("深圳", "东莞", 30);
graphCost.AddEdge("惠州", "河源", 42);
graphCost.AddEdge("东莞", "广州", 25);
graphCost.AddEdge("广州", "韶关", 85);
graphCost.AddEdge("广州", "佛山", 15);
graphCost.AddEdge("佛山", "肇庆", 35);
graphCost.AddEdge("肇庆", "梧州", 100);
graphCost.AddEdge("梧州", "桂林", 120);
graphCost.AddEdge("桂林", "柳州", 70);
graphCost.AddEdge("柳州", "南宁", 95);
graphCost.AddEdge("韶关", "赣州", 105);
graphCost.AddEdge("河源", "赣州", 80);
graphCost.AddEdge("赣州", "吉安", 110);
graphCost.AddEdge("赣州", "南昌", 180);
graphCost.AddEdge("吉安", "南昌", 95);
graphCost.AddEdge("吉安", "萍乡", 125);
graphCost.AddEdge("萍乡", "长沙", 65);
graphCost.AddEdge("长沙", "武汉", 130);
graphCost.AddEdge("长沙", "株洲", 25);
graphCost.AddEdge("株洲", "衡阳", 55);
graphCost.AddEdge("衡阳", "郴州", 80);
graphCost.AddEdge("郴州", "韶关", 65);
graphCost.AddEdge("南昌", "九江", 55);
graphCost.AddEdge("九江", "武汉", 85);
graphCost.AddEdge("武汉", "郑州", 210);
graphCost.AddEdge("郑州", "西安", 190);
graphCost.AddEdge("南昌", "福州", 170);
graphCost.AddEdge("福州", "厦门", 105);
// 初始化三个规划器
PathPlanner planKm = new PathPlanner(graphKm, cityData);
PathPlanner planHour = new PathPlanner(graphHour, cityData);
PathPlanner planCost = new PathPlanner(graphCost, cityData);
// 打印城市列表
var cityList = cityData.Keys.ToList();
Console.WriteLine("===== C# .NET10 高速路径规划系统 =====");
Console.WriteLine($"可用城市：{string.Join("、", cityList)}");
Console.WriteLine("----------------------------------------");
// 交互输入
Console.Write("输入起点城市：");
string start = Console.ReadLine()?.Trim() ?? "";
Console.Write("输入终点城市：");
string end = Console.ReadLine()?.Trim() ?? "";
Console.Write("必须途经城市（多城顿号分隔，无直接回车）：");
string mustInput = Console.ReadLine()?.Trim() ?? "";
Console.Write("禁止绕行城市（多城顿号分隔，无直接回车）：");
string banInput = Console.ReadLine()?.Trim() ?? "";
// 解析约束
List<string> ParseCityStr(string s)
{
if (string.IsNullOrEmpty(s)) return new();
return s.Split("、", StringSplitOptions.RemoveEmptyEntries).Select(x => x.Trim()).ToList();
}
var mustCities = ParseCityStr(mustInput);
var banCities = ParseCityStr(banInput);
// 绑定约束到三个规划器
void SetConstraint(PathPlanner p)
{
p.MustPassCities = new List<string>(mustCities);
p.BanCities = new HashSet<string>(banCities);
}
SetConstraint(planKm);
SetConstraint(planHour);
SetConstraint(planCost);
// 计算路线
var (kmTotal, kmPath) = planKm.Dijkstra(start, end);
var (hourTotal, hourPath) = planHour.Dijkstra(start, end);
var (costTotal, costPath) = planCost.Dijkstra(start, end);
// 拼接路径文本
string JoinPath(List<string> path) => path.Count == 0 ? "无路线" : string.Join(" → ", path);
// 输出结果
Console.WriteLine("\n==================================================");
Console.WriteLine($"【{start} → {end} 规划结果】");
Console.WriteLine("==================================================");
Console.WriteLine(kmPath.Count > 0
? $"📏 最短里程：{kmTotal:F0} km | 路线：{JoinPath(kmPath)}"
: "📏 最短里程：无可行路线（约束过滤）");
Console.WriteLine(hourPath.Count > 0
? $"⏰ 最短耗时：{hourTotal:F1} h | 路线：{JoinPath(hourPath)}"
: "⏰ 最短耗时：无可行路线（约束过滤）");
Console.WriteLine(costPath.Count > 0
? $"💰 最低路费：{costTotal:F0} 元 | 路线：{JoinPath(costPath)}"
: "💰 最低路费：无可行路线（约束过滤）");
Console.WriteLine("==================================================");
// 绘制PNG图（里程最优路线）
if (kmPath.Count > 0)
{
planKm.DrawMap("route_map.png", kmPath);
}
}
}
}
输出：
哲学管理(学)人生, 文学艺术生活, 自动(计算机学)物理(学)工作, 生物(学)化学逆境, 历史(学)测绘(学)时间, 经济(学)数学金钱(理财), 心理(学)医学情绪, 诗词美容情感, 美学建筑(学)家园, 解构建构(分析)整合学习, 智商情商(IQ、EQ)运筹(学)生存.---Geovin Du(涂聚文）
浙公网安备 33010602011771号