Figure $3$: Graph

Given the graph in Figure above, perform the following tasks:

a$.$ Write a C$++$ program that implements a graph using an adjacency list.

b$.$ Create a method to add edges between nodes.

c$.$ Represent the nodes and edges of the graph as shown in the Figure.

d$.$ Implement a method to check whether the graph has a Euler circuit. A Euler circuit in a graph is a path that starts and ends at the same vertex and travels through every edge in the graph exactly once.

e$.$ If the graph has a Euler circuit, find and display one such circuit.

f$.$ Implement a method to perform a Breadth$-$First Search $($BFS$)$ traversal starting from node $0.$

g$.$ Display the nodes in the order they are visited during the BFS traversal.

h$.$ Implement a method to perform a Depth First Search $($DFS$)$ traversal starting from node $0.$

i$.$ Display the nodes in the order they are visited during the DFS traversal.