狄克斯特拉 Dijkstra 算法 C#实现

今天在看《算法图解》，看了加权最小路径算法，决定用代码实现一下。

首先是画有向图，在网上找了一下，有不错的开源软件graphviz,该源代码托管在GitLab上。该软件是一个图形可视化软件。
画了一个有向图如下：

画图用的代码：

digraph dijkstra{
start->A[label="6"]
start->B[label="2"]
A->end[label="1"]
B->A[label="3"]
B->end[label="5"]
}

我建了一个控制台应用程序：

class Program{public static List<Node> NodeList { get; set; }public static Dictionary<string,int> CostDictionary { get; set; }public static Dictionary<string, string> ParentDictionary { get; set; }public static List<string> CheckedNodeName { get; set; }public Program(){NodeList= new List<Node>{new Node{NodeName = "start",RelatedNode = new Dictionary<string, int>(){{"A", 6},{"B", 2}}},new Node{NodeName = "A",RelatedNode = new Dictionary<string, int>(){{"end", 1}}},new Node{NodeName = "B",RelatedNode = new Dictionary<string, int>(){{"A", 3},{"end", 5}}},new Node{NodeName = "end",RelatedNode = new Dictionary<string, int>()}};CostDictionary = new Dictionary<string,int>(){{"A",6},{"B",2},{"end",int.MaxValue}};ParentDictionary = new Dictionary<string, string>(){{"A","start"},{"B","start"},{"end",""}};CheckedNodeName=new List<string>();}static void Main(string[] args){var progra=new Program();Console.WriteLine($"{"parent",10}|{"node",10}|{"cost",10}");foreach ( var item in NodeList.SelectMany(node=>node.RelatedNode,(node,relatenode)=>new {node.NodeName,relatenode})){Console.WriteLine($"{item.NodeName,10}|{item.relatenode.Key,10}|{item.relatenode.Value,10}");}while (CheckedNodeName.Count!=CostDictionary.Count){//找到Cost最小的节点var currentNode = FindMinCostNode(CostDictionary);//取出relatednode，if (currentNode != null){//循环如果subNode的Cost小于CostDictionary的Costforeach (var subNode in currentNode.RelatedNode){if (subNode.Value < CostDictionary[subNode.Key]){//替换CostDictionary[subNode.Key] = subNode.Value+ CostDictionary[currentNode.NodeName];ParentDictionary[subNode.Key] = currentNode.NodeName;}}CheckedNodeName.Add(currentNode.NodeName);}}Console.WriteLine("最短路径:"+ GetTheMinCostPath());Console.WriteLine("最短路径开销:"+CostDictionary["end"]);Console.ReadKey();}public static string GetTheMinCostPath(){bool isStart=false;string startKey="end";string path= "end=>";while (!isStart){path += ParentDictionary[startKey]+"=>";startKey = ParentDictionary[startKey];if (!ParentDictionary.ContainsKey(ParentDictionary[startKey])){path += ParentDictionary[startKey];isStart = true;}}return path;}public static Node FindMinCostNode(Dictionary<string,int> costDictionary){var costItems= costDictionary.Where(c => !CheckedNodeName.Contains(c.Key)).ToList();if (costItems.Any()){var minCostItem = costItems.OrderBy(c => c.Value).First().Key;return NodeList.FirstOrDefault(n => n.NodeName == minCostItem);}return null;}}public class Node{public string NodeName { get; set; }public Dictionary<string, int> RelatedNode { get; set; }}public class CostItem{public string ParentName { get; set; }public string NodeName { get; set; }public int Cost { get; set; }}