Lab 5 done.

//

// Created by Ari Trachtenberg on 11/1/24.

//

// Chapter 13

/**

 * A graph is a collection of vertices, together with edges connecting

 * some of the vertices.

 *

 * Implement a Graph class with the following properties:

 * -  There is only one public default constructor that produces an

 *    empty graph with no vertices (or edges).

 * -  operator+= is used to add a vertex with a given ID to the graph.

 *       if a vertex already has the given ID, a logic_error exception

 *       should be thrown.

 * -  hasEdge(int ID1, int ID2) returns true iff an edge between vertices

 *       with ids ID1 and ID2 exists.

 * -  addEdge(int ID1, int ID2) adds an edge between vertices with

 *       ids ID1 and ID2, respectively.

 *       if one of the IDs does not exist, or the edge already exists,

 *       an invalid_argument exception should be thrown.

 * -  operator[](int ii) returns the ii-th vertex in the graph (0-indexed)

 * -  numVertices() returns the number of vertices in the graph

 * -  numEdges() returns the number of edges in the graph

 *

 * @example

 * Graph G;

 * G+=3;

 * G+=5;

 * G+=3;            // throws logic_error

 * G.hasEdge(3,5);  // returns false

 * G.addEdge(5,3);  // adds an edge connecting vertex 5 and 3.

 * G.hasEdge(3,5);  // returns true (edge between 5 to 3 == between 3 and 5).

 * G[0];            // returns 3

 * G.numVertices(); // returns 2 - vertex ID 3 and ID 5

 * G.numEdges();    // returns 1 - between vertex ID 3 and ID 5

 */

class Graph;

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