Travelling Salesman problem

Advanced.Algorithms.Tests/Advanced.Algorithms.Tests.csproj

@@ -127,6 +127,7 @@
  <Compile Include="DataStructures\Tree\Tree_Tests.cs" />
  <Compile Include="DataStructures\Tree\BinaryTree_Tests.cs" />
  <Compile Include="Geometry\PointRotation_Tests.cs" />
+ <Compile Include="GraphAlgorithms\ShortestPath\TravellingSalesman_Tests.cs" />
  <Compile Include="Miscellaneous\MatrixMultiplication_Tests.cs" />
  <Compile Include="Geometry\ClosestPointPair_Tests.cs" />
  <Compile Include="Geometry\ConvexHull_Tests.cs" />

Advanced.Algorithms.Tests/GraphAlgorithms/ShortestPath/TravellingSalesman_Tests.cs

@@ -0,0 +1,43 @@
+using Advanced.Algorithms.DataStructures.Graph.AdjacencyList;
+using Advanced.Algorithms.GraphAlgorithms;
+using Microsoft.VisualStudio.TestTools.UnitTesting;
+
+namespace Advanced.Algorithms.Tests.GraphAlgorithms.ShortestPath
+{
+ /// <summary>
+ /// Problem details below
+ /// https://en.wikipedia.org/wiki/Travelling_salesman_problem
+ /// </summary>
+ [TestClass]
+ public class TravellingSalesman_Tests
+ {
+ [TestMethod]
+ public void TravellingSalesman_Smoke_Test()
+ {
+ var graph = new WeightedDiGraph<int, int>();
+
+ graph.AddVertex(0);
+ graph.AddVertex(1);
+ graph.AddVertex(2);
+ graph.AddVertex(3);
+
+ graph.AddEdge(0, 1, 1);
+ graph.AddEdge(0, 2, 15);
+ graph.AddEdge(0, 3, 6);
+
+ graph.AddEdge(1, 0, 2);
+ graph.AddEdge(1, 2, 7);
+ graph.AddEdge(1, 3, 3);
+
+ graph.AddEdge(2, 0, 9);
+ graph.AddEdge(2, 1, 6);
+ graph.AddEdge(2, 3, 12);
+
+ graph.AddEdge(3, 0, 10);
+ graph.AddEdge(3, 1, 4);
+ graph.AddEdge(3, 2, 8);
+
+ Assert.AreEqual(21, TravellingSalesman.GetMinWeight(graph));
+ }
+ }
+}

Advanced.Algorithms/GraphAlgorithms/ShortestPath/TravellingSalesman.cs

@@ -0,0 +1,75 @@
+
+using Advanced.Algorithms.DataStructures.Graph.AdjacencyList;
+using System.Collections.Generic;
+using System.Linq;
+
+namespace Advanced.Algorithms.GraphAlgorithms
+{
+ /// <summary>
+ /// Problem details below
+ /// https://en.wikipedia.org/wiki/Travelling_salesman_problem
+ /// Uses dynamic programming and have
+ /// psuedo-polynomial time runtime complexity for this NP hard problem
+ /// </summary>
+ public class TravellingSalesman
+ {
+ public static int GetMinWeight(WeightedDiGraph<int, int> graph)
+ {
+ return GetMinWeight(graph.ReferenceVertex, graph.ReferenceVertex,
+ graph.VerticesCount,
+ new HashSet<WeightedDiGraphVertex<int, int>>(),
+ new Dictionary<string, int>());
+ }
+
+ public static int GetMinWeight(WeightedDiGraphVertex<int, int> currentVertex,
+ WeightedDiGraphVertex<int, int> tgtVertex,
+ int remainingVertexCount,
+ HashSet<WeightedDiGraphVertex<int, int>> visited,
+ Dictionary<string, int> cache)
+ {
+ var cacheKey = $"{currentVertex.Value}-{remainingVertexCount}";
+
+ if (cache.ContainsKey(cacheKey))
+ {
+ return cache[cacheKey];
+ }
+
+ visited.Add(currentVertex);
+
+ var results = new List<int>();
+
+ foreach (var vertex in currentVertex.OutEdges)
+ {
+ //base case
+ if (vertex.Key == tgtVertex
+ && remainingVertexCount == 1)
+ {
+ results.Add(vertex.Value);
+ break;
+ }
+
+ if (!visited.Contains(vertex.Key))
+ {
+ var result = GetMinWeight(vertex.Key, tgtVertex, remainingVertexCount - 1, visited, cache);
+
+ if (result != int.MaxValue)
+ {
+ results.Add(result + vertex.Value);
+ }
+
+ }
+ }
+
+ visited.Remove(currentVertex);
+
+ if (results.Count == 0)
+ {
+ return int.MaxValue;
+ }
+
+ var min = results.Min();
+ cache.Add(cacheKey, min);
+ return min;
+ }
+ }
+}

README.md

@@ -172,6 +172,7 @@ Note: It is observed that among the implementations here in practice, with the e
 - [X] Dijikstra's algorithm ([Implementation](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms/GraphAlgorithms/ShortestPath/Dijikstra.cs) | [Tests](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms.Tests/GraphAlgorithms/ShortestPath/Dijikstras_Tests.cs)) using Fibornacci Heap.
 - [X] Floyd-Warshall algorithm ([Implementation](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms/GraphAlgorithms/ShortestPath/Floyd-Warshall.cs) | [Tests](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms.Tests/GraphAlgorithms/ShortestPath/FloydWarshall_Tests.cs))
 - [X] Johnson's algorithm ([Implementation](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms/GraphAlgorithms/ShortestPath/Johnsons.cs) | [Tests](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms.Tests/GraphAlgorithms/ShortestPath/Johnson_Tests.cs))
+- [X] Travelling Salesman Problem ([Implementation](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms/GraphAlgorithms/ShortestPath/TravellingSalesman.cs) | [Tests](https://github.com/justcoding121/Advanced-Algorithms/tree/develop/Advanced.Algorithms.Tests/GraphAlgorithms/ShortestPath/TravellingSalesman_Tests.cs))
 
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