Add problem definition Dijkstra's shortest path algorithm

Problems/NPComplete/NPC_SHORTESTPATH/SHORTESTPATH_Class.cs

@@ -0,0 +1,76 @@
+using API.Interfaces;
+using API.Problems.NPComplete.NPC_SHORTESTPATH.Solvers;
+using API.Problems.NPComplete.NPC_SHORTESTPATH.Verifiers;
+using API.Problems.NPComplete.NPC_SHORTESTPATH.Visualizations;
+using SPADE;
+
+namespace API.Problems.NPComplete.NPC_SHORTESTPATH;
+
+class SHORTESTPATH: IGraphProblem<DijkstraSolver, DijkstraVerifier, DijkstraDefaultVisualization, UtilCollectionGraph>
+{
+
+    // --- Fields ---
+    public string problemName { get; } = "Shortest Path Problem";
+    public string problemLink { get; } = "https://en.wikipedia.org/wiki/Shortest_path_problem";
+    public string formalDefinition { get; } = "For a weighted graph G= (V,E) with weight function w:E->\\(\\mathbb{R}\\), find the shortest path source s to target t, where path length is the sum of edge weights"; //TODO figure out what it's supposed to be
+    public string problemDefinition { get; } = "Shortest Path Problem is the problem of determining the shortest path from a given source vertex to all other vertices such that the sum of the weights of its inherent edges is minimized.";
+    public string source { get; } = "N/A";
+    public string sourceLink { get; } = "N/A";
+    private static string _defaultInstance = "({1,2,3,4,5},{{2,1,4},{1,3,2},{2,3,1},{3,5,7},{2,4,3},{4,5,9}})";
+    public string defaultInstance { get; } = _defaultInstance;
+    public string instance { get; set; } = string.Empty;
+
+    public string wikiName { get; } = "";
+    private List<string> _nodes = new List<string>();
+    private List<KeyValuePair<string, string>> _edges = new List<KeyValuePair<string, string>>();
+    public DijkstraSolver defaultSolver { get; } = new DijkstraSolver();
+    public DijkstraVerifier defaultVerifier { get; } = new DijkstraVerifier();
+    public DijkstraDefaultVisualization defaultVisualization { get; } = new DijkstraDefaultVisualization();
+    public UtilCollectionGraph graph { get; set; }
+    public string[] contributors { get; } = { "Tiger Sant", "Malaya Witt", "Rajit Nilkar", "Scott Barfuss" };
+
+    // --- Properties ---
+    public List<string> nodes
+    {
+        get
+        {
+            return _nodes;
+        }
+        set
+        {
+            _nodes = value;
+        }
+    }
+    public List<KeyValuePair<string, string>> edges
+    {
+        get
+        {
+            return _edges;
+        }
+        set
+        {
+            _edges = value;
+        }
+    }
+
+    // --- Methods Including Constructors ---
+    public SHORTESTPATH() : this(_defaultInstance)
+    {
+
+    }
+    public SHORTESTPATH(string GInput)
+    {
+        instance = GInput;
+
+        StringParser parser = new("{(N,E) | N is set, E subset N unorderedcross N}");
+        parser.parse(GInput);
+        nodes = parser["N"].ToList().Select(node => node.ToString()).ToList();
+        edges = parser["E"].ToList().Select(edge =>
+        {
+            List<UtilCollection> cast = edge.ToList();
+            return new KeyValuePair<string, string>(cast[0].ToString(), cast[1].ToString());
+        }).ToList();
+
+        graph = new UtilCollectionGraph(parser["N"], parser["E"]);
+    }
+}