You will write a C program to process a graph using its adjacency matrix stored in a $.$txt file as

the input $($a sample file is provided$).$ The program should read the graph and provide several

functionalities for interacting with the graph.

Input:

The adjacency matrix $($denoted as A$)$ for the graph will be stored in a $.$txt file, where rows and

columns represent vertices $($numbered $1,2,3,...),$ and the values in the matrix represent the edge

weights. If aij$=0,$ it means that there is no edge between the vertex i and j$.$

Requirements:

$1.$ Command$-$line argument:

o The program should accept the filename of the $.$txt file containing the graph's

adjacency matrix as a command$-$line argument.

o Example usage: $./$a$4$ example$-$graph.txt $($the executable is named a$4).$

$2.$ Menu of Options: Upon running the program, it should present the user with a menu of

options. The user should be able to type the number of an option, and the program should

execute the corresponding functionality.

$$ Display Adjacency List

$$ Perform Breadth$-$First Search $($BFS$)$

$$ Perform Depth$-$First Search $($DFS$)$

$$ Find Shortest Path using Dijkstra's Algorithm

$$ Exit

$3.$ Option Details:

o Option $1$: Display Adjacency List

When this option is selected, the program should print the adjacency list

representation of the graph. Each vertex should list its connected vertices along

with weights of the edges.

o Option $2$: Perform Breadth$-$First Search $($BFS$)$

When this option is selected, the program should perform a Breadth$-$First Search

$($BFS$)$ traversal starting from vertex $1.$ The program should print the vertices in

the order they are visited.

o Option $3$: Perform Depth$-$First Search $($DFS$)$

When this option is selected, the program should perform a Depth$-$First Search

$($DFS$)$ traversal starting from vertex $1.$ The program should print the vertices in

the order they are visited.

o Option $4$: Find Shortest Path $($Dijkstra$\text{'}$s Algorithm$)$

When this option is selected, the program should compute and print the shortest

paths from vertex $1$ to all other vertices using Dijkstra's algorithm.

o Option $5$: Exit

When this option is selected, the program should exit.

example$-$graph $-$

$04500$

$40192$

$51003$

$09000$

$02300$

sample output $-$ Menu: $1.$ Display Adjacency List $2.$ Perform Breadth$-$First Search $($BFS$)3.$ Perform Depth$-$First Search $($DFS$)4.$ Find Shortest Path using Dijkstra's Algorithm $5.$ Exit Enter your choice: $1$ Adjacency List: Vertex $1$: $->2(4)->3(5)$ NULL Vertex $2$: $->1(4)->3(1)->4(9)->5(2)$ NULL Vertex $3$: $->1(5)->2(1)->5(3)$ NULL Vertex $4$: $->2(9)$ NULL Vertex $5$: $->2(2)->3(3)$ NULL Menu: $1.$ Display Adjacency List $2.$ Perform Breadth$-$First Search $($BFS$)3.$ Perform Depth$-$First Search $($DFS$)4.$ Find Shortest Path using Dijkstra's Algorithm $5.$ Exit Enter your choice: $2$ Final BFS Order: $12345$ Menu: $1.$ Display Adjacency List $2.$ Perform Breadth$-$First Search $($BFS$)3.$ Perform Depth$-$First Search $($DFS$)4.$ Find Shortest Path using Dijkstra's Algorithm $5.$ Exit Enter your choice: $312354$ Menu: $1.$ Display Adjacency List $2.$ Perform Breadth$-$First Search $($BFS$)3.$ Perform Depth$-$First Search $($DFS$)4.$ Find Shortest Path using Dijkstra's Algorithm $5.$ Exit Enter your choice: $4$ Shortest distance from vertex $1$ to vertex $1$: $0$ Shortest distance from vertex $1$ to vertex $2$: $4$ Shortest distance from vertex $1$ to vertex $3$: $5$ Shortest distance from vertex $1$ to vertex $4$: $13$ Shortest distance from vertex $1$ to vertex $5$: $6$ Menu: $1.$ Display Adjacency List $2.$ Perform Breadth$-$First Search $($BFS$)3.$ Perform Depth$-$First Search $($DFS$)4.$ Find Shortest Path using Dijkstra's Algorithm $5.$ Exit Enter your choice: $5$ Exiting...