问题
I'm working on a program where I have to find the shortest path between 12 cities, starting in Seattle and ending in Miami. I'm using Dijkstra's Algorithm because the paths are weighted. Here is my code so far, it all works except the answer I get is not the one I need, although it is correct.
This part of the code sets everything up as well as creates the sorting algorithm.
class Graph
{
Dictionary<string, Dictionary<string, int>> vertices = new Dictionary<string, Dictionary<string, int>>();
public void add_vertex(string name, Dictionary<string, int> edges)
{
vertices[name] = edges;
}
public List<string> shortest_path(string start, string finish)
{
var previous = new Dictionary<string, string>();
var distances = new Dictionary<string, int>();
var nodes = new List<string>();
List<string> path = null;
foreach (var vertex in vertices)
{
if (vertex.Key == start)
{
distances[vertex.Key] = 1;
}
else
{
distances[vertex.Key] = int.MaxValue;
}
nodes.Add(vertex.Key);
}
while (nodes.Count != 0)
{
nodes.Sort((x, y) => distances[x] - distances[y]);
var smallest = nodes[0];
nodes.Remove(smallest);
if (smallest == finish)
{
path = new List<string>();
while (previous.ContainsKey(smallest))
{
path.Add(smallest);
smallest = previous[smallest];
}
break;
}
if (distances[smallest] == int.MaxValue)
{
break;
}
foreach (var neighbor in vertices[smallest])
{
var alt = distances[smallest] + neighbor.Value;
if (alt < distances[neighbor.Key])
{
distances[neighbor.Key] = alt;
previous[neighbor.Key] = smallest;
}
}
}
return path;
}
}
Below is where I create the "cities" along with creating the values between them.
class MainClass
{
public static void Main(string[] args)
{
Graph g = new Graph();
g.add_vertex("Seattle", new Dictionary<string, int>() { {"San Francisco", 1306}, {"Denver", 2161}, {"Minneapolis", 2661} });
g.add_vertex("San Francisco", new Dictionary<string, int>() { {"Seattle", 1306}, {"Las Vegas", 919}, {"Los Angeles", 629} });
g.add_vertex("Las Vegas", new Dictionary<string, int>() { {"San Francisco", 919}, {"Los Angeles", 435}, {"Denver", 1225}, {"Dallas", 1983} });
g.add_vertex("Los Angeles", new Dictionary<string, int>() { {"San Francisco", 629}, {"Las Vegas", 435} });
g.add_vertex("Denver", new Dictionary<string, int>() { {"Seattle", 2161}, {"Las Vegas", 1225}, {"Minneapolis", 1483}, {"Dallas", 1258} });
g.add_vertex("Minneapolis", new Dictionary<string, int>() { {"Seattle", 2661}, {"Denver", 1483}, {"Dallas", 1532}, {"Chicago", 661} });
g.add_vertex("Dallas", new Dictionary<string, int>() { {"Las Vegas", 1983}, {"Denver", 1258}, {"Minneapolis", 1532}, {"Washington DC", 2113} });
g.add_vertex("Chicago", new Dictionary<string, int>() { {"Minneapolis", 661}, {"Washington DC", 1145}, {"Boston", 1613} });
g.add_vertex("Washington DC", new Dictionary<string, int>() { {"Dallas", 2113}, {"Chicago", 1145}, {"Boston", 725}, {"New York", 383}, {"Miami", 1709} });
g.add_vertex("Boston", new Dictionary<string, int>() { {"Chicago", 1613}, {"Washington DC", 725}, {"New York", 338} });
g.add_vertex("New York", new Dictionary<string, int>() { {"Washington DC", 383}, {"Boston", 338}, {"Miami", 2145} });
g.add_vertex("Miami", new Dictionary<string, int>() { {"Dallas", 2161}, {"Washington DC", 1709}, {"New York", 2145} });
g.shortest_path("Miami", "Seattle").ForEach(x => Console.Write(x + " > "));
}
}
The part that I need help figuring out is when I run the program, I get: Seattle > Denver > Dallas. That answer is correct for the shortest distance to Miami, but I need the shortest distance to every city, not just Miami. I just don't know what I need to change to display that properly.
回答1:
To my understanding, the provided code implements Dijkstra's Algorithm, modified to terminate as soon as some desired destination node is selected into the set of nodes for which the shortest path from the initial node is known. Dijkstra's algorithm solves the so-called Single Source Shortest Path problem. This means that some initial node, in this case Miami, is specified, and the desired result is consituted by the shortest paths to all other nodes. It does not solve the All-Pairs Shortest Path problem, which requires calculation of the respective distance for each pair nodes. This problem can be solved by the Floyd-Warshall Algorithm, however.
In contrast, if you need the shortest path from Miami to all other cities, modifiy the implementation not to break the loop early and remove the second argument.
回答2:
The line
g.shortest_path("Miami", "Seattle").ForEach(x => Console.Write(x + " > "));
is where you both specify the endpoint of "Miami" and write the output to the console.
You need to create a loop around that line that specifies every endpoint you want
foreach(var endpoint in validEndpoints) {
g.shortest_path(endpoint, "Seattle").ForEach(x => Console.Write(x + " > "));
}
This will be slow and there are things you can do such as memoization to speed it up, but should at least produce the output you want.
回答3:
I been posting this code for years. You need a recursive algorithm.
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Data;
namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
//this one uses strings as node names
Dijkstra1.Program.Dijkstra();
//this one uses integers as node names
Dijkstra2.Program.Dijkstra();
}
}
}
namespace Dijkstra1
{
class Program
{
//A connected to B
//B connected to A, C , D
//C connected to B, D
//D connected to B, C , E
//E connected to D.
static List<List<String>> input1 = new List<List<string>>{
new List<String>() {"A","0","1","0","0","0"},
new List<String>() {"B","1","0","1","1","0"},
new List<String>() {"C","0","1","0","1","0"},
new List<String>() {"D","0","1","1","0","1"},
new List<String>() {"E","0","0","0","1","0"}
};
//A | 0 1 2 2 3 |
//B | 1 0 1 1 2 |
//C | 2 1 0 1 2 |
//D | 2 1 1 0 1 |
//E | 3 2 2 1 0 |
static List<List<String>> input2 = new List<List<string>>{
new List<String>() {"A","0","1","2","2","3"},
new List<String>() {"B","1","0","1","1","2"},
new List<String>() {"C","2","1","0","1","2"},
new List<String>() {"D","2","1","1","0","1"},
new List<String>() {"E","3","2","2","1","0"}
};
static public void Dijkstra()
{
CGraph cGraph;
cGraph = new CGraph(input1);
Console.WriteLine("-------------Input 1 -------------");
cGraph.PrintGraph();
cGraph = new CGraph(input2);
Console.WriteLine("-------------Input 2 -------------");
cGraph.PrintGraph();
}
class CGraph
{
List<Node> graph = new List<Node>();
public CGraph(List<List<String>> input)
{
foreach (List<string> inputRow in input)
{
Node newNode = new Node();
newNode.name = inputRow[0];
newNode.distanceDict = new Dictionary<string, Path>();
newNode.visited = false;
newNode.neighbors = new List<Neighbor>();
//for (int index = 1; index < inputRow.Count; index++)
//{
// //skip diagnol values so you don't count a nodes distance to itself.
// //node count start at zero
// // index you have to skip the node name
// //so you have to subtract one from the index
// if ((index - 1) != nodeCount)
// {
// string nodeName = input[index - 1][0];
// int distance = int.Parse(inputRow[index]);
// newNode.distanceDict.Add(nodeName, new List<string>() { nodeName });
// }
//}
graph.Add(newNode);
}
//initialize neighbors using predefined dictionary
for (int nodeCount = 0; nodeCount < graph.Count; nodeCount++)
{
for (int neighborCount = 0; neighborCount < graph.Count; neighborCount++)
{
//add one to neighbor count to skip Node name in index one
if (input[nodeCount][neighborCount + 1] != "0")
{
Neighbor newNeightbor = new Neighbor();
newNeightbor.node = graph[neighborCount];
newNeightbor.distance = int.Parse(input[nodeCount][neighborCount + 1]);
graph[nodeCount].neighbors.Add(newNeightbor);
Path path = new Path();
path.nodeNames = new List<string>() { input[neighborCount][0] };
//add one to neighbor count to skip Node name in index one
path.totalDistance = int.Parse(input[nodeCount][neighborCount + 1]);
graph[nodeCount].distanceDict.Add(input[neighborCount][0], path);
}
}
}
foreach (Node node in graph)
{
foreach (Node nodex in graph)
{
node.visited = false;
}
TransverNode(node);
}
}
public class Neighbor
{
public Node node { get; set; }
public int distance { get; set; }
}
public class Path
{
public List<string> nodeNames { get; set; }
public int totalDistance { get; set; }
}
public class Node
{
public string name { get; set; }
public Dictionary<string, Path> distanceDict { get; set; }
public Boolean visited { get; set; }
public List<Neighbor> neighbors { get; set; }
}
static void TransverNode(Node node)
{
if (!node.visited)
{
node.visited = true;
foreach (Neighbor neighbor in node.neighbors)
{
TransverNode(neighbor.node);
string neighborName = neighbor.node.name;
int neighborDistance = neighbor.distance;
//compair neighbors dictionary with current dictionary
//update current dictionary as required
foreach (string key in neighbor.node.distanceDict.Keys)
{
if (key != node.name)
{
int neighborKeyDistance = neighbor.node.distanceDict[key].totalDistance;
if (node.distanceDict.ContainsKey(key))
{
int currentDistance = node.distanceDict[key].totalDistance;
if (neighborKeyDistance + neighborDistance < currentDistance)
{
List<string> nodeList = new List<string>();
nodeList.AddRange(neighbor.node.distanceDict[key].nodeNames);
nodeList.Insert(0, neighbor.node.name);
node.distanceDict[key].nodeNames = nodeList;
node.distanceDict[key].totalDistance = neighborKeyDistance + neighborDistance;
}
}
else
{
List<string> nodeList = new List<string>();
nodeList.AddRange(neighbor.node.distanceDict[key].nodeNames);
nodeList.Insert(0, neighbor.node.name);
Path path = new Path();
path.nodeNames = nodeList;
path.totalDistance = neighbor.distance + neighborKeyDistance;
node.distanceDict.Add(key, path);
}
}
}
}
}
}
public void PrintGraph()
{
foreach (Node node in graph)
{
Console.WriteLine("Node : {0}", node.name);
foreach (string key in node.distanceDict.Keys.OrderBy(x => x))
{
Console.WriteLine(" Distance to node {0} = {1}, Path : {2}", key, node.distanceDict[key].totalDistance, string.Join(",", node.distanceDict[key].nodeNames.ToArray()));
}
}
}
}
}
}
namespace Dijkstra2
{
class Program
{
//0---1---2---3
// |
// 4
// |
// 5---6---7
// \ /
// 8
// |
// 9
static List<List<int>> input1 = new List<List<int>>
{ // 0 1 2 3 4 5 6 7 8 9
new List<int>() {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
new List<int>() {1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0},
new List<int>() {2, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0},
new List<int>() {3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
new List<int>() {4, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0},
new List<int>() {5, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0},
new List<int>() {6, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0},
new List<int>() {7, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
new List<int>() {8, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1},
new List<int>() {9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0},
};
static public void Dijkstra()
{
CGraph cGraph;
cGraph = new CGraph(input1);
Console.WriteLine("-------------Input 1 -------------");
cGraph.PrintGraph();
}
class CGraph
{
List<Node> graph = new List<Node>();
public CGraph(List<List<int>> input)
{
foreach (List<int> inputRow in input)
{
Node newNode = new Node();
newNode.name = inputRow[0];
newNode.distanceDict = new Dictionary<int, Path>();
newNode.visited = false;
newNode.neighbors = new List<Neighbor>();
//for (int index = 1; index < inputRow.Count; index++)
//{
// //skip diagnol values so you don't count a nodes distance to itself.
// //node count start at zero
// // index you have to skip the node name
// //so you have to subtract one from the index
// if ((index - 1) != nodeCount)
// {
// string nodeName = input[index - 1][0];
// int distance = int.Parse(inputRow[index]);
// newNode.distanceDict.Add(nodeName, new List<string>() { nodeName });
// }
//}
graph.Add(newNode);
}
//initialize neighbors using predefined dictionary
for (int nodeCount = 0; nodeCount < graph.Count; nodeCount++)
{
for (int neighborCount = 0; neighborCount < graph.Count; neighborCount++)
{
//add one to neighbor count to skip Node name in index one
if (input[nodeCount][neighborCount + 1] != 0)
{
Neighbor newNeightbor = new Neighbor();
newNeightbor.node = graph[neighborCount];
newNeightbor.distance = input[nodeCount][neighborCount + 1];
graph[nodeCount].neighbors.Add(newNeightbor);
Path path = new Path();
path.nodeNames = new List<int>() { input[neighborCount][0] };
//add one to neighbor count to skip Node name in index one
path.totalDistance = input[nodeCount][neighborCount + 1];
graph[nodeCount].distanceDict.Add(input[neighborCount][0], path);
}
}
}
foreach (Node node in graph)
{
foreach (Node nodex in graph)
{
node.visited = false;
}
TransverNode(node);
}
}
public class Neighbor
{
public Node node { get; set; }
public int distance { get; set; }
}
public class Path
{
public List<int> nodeNames { get; set; }
public int totalDistance { get; set; }
}
public class Node
{
public int name { get; set; }
public Dictionary<int, Path> distanceDict { get; set; }
public Boolean visited { get; set; }
public List<Neighbor> neighbors { get; set; }
}
static void TransverNode(Node node)
{
if (!node.visited)
{
node.visited = true;
foreach (Neighbor neighbor in node.neighbors)
{
TransverNode(neighbor.node);
int neighborName = neighbor.node.name;
int neighborDistance = neighbor.distance;
//compair neighbors dictionary with current dictionary
//update current dictionary as required
foreach (int key in neighbor.node.distanceDict.Keys)
{
if (key != node.name)
{
int neighborKeyDistance = neighbor.node.distanceDict[key].totalDistance;
if (node.distanceDict.ContainsKey(key))
{
int currentDistance = node.distanceDict[key].totalDistance;
if (neighborKeyDistance + neighborDistance < currentDistance)
{
List<int> nodeList = new List<int>();
nodeList.AddRange(neighbor.node.distanceDict[key].nodeNames);
nodeList.Insert(0, neighbor.node.name);
node.distanceDict[key].nodeNames = nodeList;
node.distanceDict[key].totalDistance = neighborKeyDistance + neighborDistance;
}
}
else
{
List<int> nodeList = new List<int>();
nodeList.AddRange(neighbor.node.distanceDict[key].nodeNames);
nodeList.Insert(0, neighbor.node.name);
Path path = new Path();
path.nodeNames = nodeList;
path.totalDistance = neighbor.distance + neighborKeyDistance;
node.distanceDict.Add(key, path);
}
}
}
}
}
}
public void PrintGraph()
{
foreach (Node node in graph)
{
Console.WriteLine("Node : {0}", node.name);
foreach (int key in node.distanceDict.Keys.OrderBy(x => x))
{
Console.WriteLine(" Distance to node {0} = {1}, Path : {2}", key, node.distanceDict[key].totalDistance, string.Join(",", node.distanceDict[key].nodeNames.ToArray()));
}
}
}
}
}
}
来源：https://stackoverflow.com/questions/29855825/dijkstras-algorithm-issue