Create a C$++$ application called "main.cpp$"$ that, given a directed graph without cycles $($DAG$),$ with n vertices and frames, tells whether the graph is a tree and displays its topological order.

loadGraph

Description: Load the edges of the graph and store them in an Adjacency List

Input: Two positive integers

$-$ n $($Number of Vertices$)$

$-$ m $($Number of Arcs$)$

$2*$ m "letters" representing start and end of each arc, two per line $($start and end of each arc$)$

Output: Nothing

Precondition: n and m are positive integers

Postcondition: Nothing

isTree

Description: Tell whether the Directed Graph $($DAG$)$ is a tree or not

Input: The Adjacency List, n $($Vertices$)$ and m $($Arcs$)($pointer$)$

Output: A boolean value telling whether the graph is a tree or not.

Precondition: The graph must be correctly loaded in the adjacency list, n and m must be positive integers.

Postcondition: Nothing

topologicalSort

Description: Sort the nodes of the DAG using Kahn's algorithm

Input: The adjacency list, n $($Vertices$)$ and m $($Arcs$)($pointer$)$

Output: Nothing

Precondition: The graph must be correctly loaded in the adjacency list, n and m must be positive integers.

Postcondition: Nothing

The input to the program is the number of vertices $($n$),$ the number of arcs $($m$)$ as well as each of the arcs.

The output is$,$ first a boolean $($true$|$false$)$ that tells whether the graph is a tree or not, followed by the topological sort of the DAG $($following Kahn's algorithm$)$ writing one node at a time, followed by a space. After the last node, there is also a blank space and a newline at the end

Input example:

$13$

$18$

A D

B D

C A

C B

D G

D H

E A

E D

E F

F J

F K

G I

H I

H J

I L

J L

J M

K J

Output example:

false

C E B A F D K G H I J L M

Important.

This should only be done with libraries.

#include

#include

#include

DO NOT USE ANYTHING WITH DIFFERENT LIBRARIES.