Bonus question. [1Opts] Hierholzer's algorithm for computing an Eulerian circuit Write a program (using Visual C++) to implement the following linear time algorithm due to Hierholzer's for computing and Eulerian circuit described in class. Also, see https://en.wikipedia.org/wiki Eulerian path#Herholzer.27s algorithm Choose any starting vertex v, and follow a trail of edges from that vertex until returning to v. It is not possible to get stuck at any vertex other than v, because the even degree of all vertices ensures that, when the trail enters another vertex w there must be an unused edge leaving w. The tour formed in this way is a closed tour, but may not cover all the vertices and edges of the initial graph. As long as there exists a vertex v that belongs to the current tour but that has adjacent edges not part of the tour, start another trail from v, following unused edges until returning to v, and join the tour formed in this way to the previous tour Give the user the option of inputting the graph G from the keyboard or from a file. The input should consist of the sizc of the graph followed by pairs representing its edge set. For example 4 010 31 3131 2 2 3 represents the multigraph V 0,1,2,3 E-01, 03, 13, 13, 12, 23) Have your program output the adjacency matrix of the multigraph, i.e., A(i,j) is the multiplicity of edge ij, e.g., followed by the Eulerian circuit, e.g., 0 1 23 1 3 0 Suggestion: Implement the multigraph G using its adjacency matrix and implement the Eulerian circuit using a doubly linked list. Also maintain a one-dimensional array U, where UIi] is the number of edges incident with vertex i that are still unused. Bonus question. [1Opts] Hierholzer's algorithm for computing an Eulerian circuit Write a program (using Visual C++) to implement the following linear time algorithm due to Hierholzer's for computing and Eulerian circuit described in class. Also, see https://en.wikipedia.org/wiki Eulerian path#Herholzer.27s algorithm Choose any starting vertex v, and follow a trail of edges from that vertex until returning to v. It is not possible to get stuck at any vertex other than v, because the even degree of all vertices ensures that, when the trail enters another vertex w there must be an unused edge leaving w. The tour formed in this way is a closed tour, but may not cover all the vertices and edges of the initial graph. As long as there exists a vertex v that belongs to the current tour but that has adjacent edges not part of the tour, start another trail from v, following unused edges until returning to v, and join the tour formed in this way to the previous tour Give the user the option of inputting the graph G from the keyboard or from a file. The input should consist of the sizc of the graph followed by pairs representing its edge set. For example 4 010 31 3131 2 2 3 represents the multigraph V 0,1,2,3 E-01, 03, 13, 13, 12, 23) Have your program output the adjacency matrix of the multigraph, i.e., A(i,j) is the multiplicity of edge ij, e.g., followed by the Eulerian circuit, e.g., 0 1 23 1 3 0 Suggestion: Implement the multigraph G using its adjacency matrix and implement the Eulerian circuit using a doubly linked list. Also maintain a one-dimensional array U, where UIi] is the number of edges incident with vertex i that are still unused