I want this Lab's C code

There are my false example code at the end of my question

Lab $9$: Course Registration

Description

A newly admitted student must register courses in a way that adheres to prerequisite requirements. A prerequisite is a requirement that one course must be completed before another course can be taken. Each course can have multiple prerequisites, and the prerequisite structure forms a directed acyclic graph. Each course is identified by a unique number from $0$ to N$-1.$ The task is to determine if all courses can be successfully registered by the student.

Specific rules include:

prerequisites$[$i$]=[$a$\_$i$,$ b$\_$i$]$ means that course b$\_$i must be taken before course a$\_$i$.$

An algorithm should be designed to determine if it's possible to complete all courses, returning True if possible and False otherwise.

Input

The input provides the total number of courses N and a list of prerequisite pairs. Each pair $[$a$,$ b$]$ specifies a prerequisite relationship where course b must be completed before course a$.$

The prerequisite pairs are provided as $[[$a$\_0,$ b$\_0],[$a$\_1,$ b$\_1],...,[$a$\_$k$,$ b$\_$k$]].$

a$\_$i and b$\_$i represent courses identified by their numbers. There are no spaces or tabs in the input.

Output

The output should be either True or False, indicating whether all courses can be registered according to the prerequisites.

Constraints

$1<=$ N $<=2000$

$0<=$ prerequisites.length $<=5000$

prerequisites$[$i$].$length $==2$

$0<=$ a$\_$i$,$ b$\_$i $<$ N

This problem essentially involves checking for cycles in a directed graph to determine if a topological ordering of the courses is possible, which allows all courses to be taken in compliance with the prerequisites.

sample input$1$

$2$

$[[1,0]]$

True

Explanation: Course $0->1$ denotes that you must complete course $0$ before taking course $1.$

sample input $2$

$2$

$[[1,0],[0,1]]$

False

Explanation: There is a cycle because course $1$ must be completed before course $0,$ and course $0$ must be completed before course $1.$

sample input$3$

$3$

$[0,0]$

False

Explanation: A course cannot be a prerequisite to itself as it forms an immediate cycle.

#include

#include

#include

using namespace std;

bool canFinish$($int numCourses, vector$>$ &prerequisites$)\{$

$//$ Graph to hold the list of prerequisites for each course

vector$>$ graph$($numCourses$)$;

$//$ Array to track the number of prerequisites $($in$-$degrees$)$ for each course

vector inDegree$($numCourses$,0)$;

$//$ Build the graph and count the in$-$degrees

for $($auto &pre : prerequisites$)\{$

graph$[$pre$[1]].$push$\_$back$($pre$[0])$; $//$ Note the reversal, pre$[1]$ is prerequisite for pre$[0]$

inDegree$[$pre$[0]]++$; $//$ Increment the in$-$degree of the course that needs pre$[1]$

$\}$

$//$ Queue for the courses with no prerequisites

queue zeroInDegree;

for $($int i $=0$; i $<$ numCourses; i$++)\{$

if $($inDegree$[$i$]==0)\{$

zeroInDegree.push$($i$)$; $//$ If no prerequisites, it's ready to be taken

$\}$

$\}$

int visited $=0$; $//$ Counter for the number of courses that can be completed

while $(!$zeroInDegree.empty$())\{$

int course $=$ zeroInDegree.front$()$;

zeroInDegree.pop$()$;

visited$++$; $//$ A course can be taken, mark it visited

$//$ Check the courses that depend on the current course

for $($int next : graph$[$course$])\{$

if $(--$inDegree$[$next$]==0)\{//$ If no more prerequisites for this course

zeroInDegree.push$($next$)$; $//$ It's ready to be taken

$\}$

$\}$

$\}$

$//$ If we were able to visit all courses, then it's possible to finish

return visited $==$ numCourses;

$\}$

int main$()\{$

int N; $//$ Total number of courses

cin $>>$ N;

vector$>$ prerequisites;

int a$,$ b;

char comma; $//$ To handle the comma in the input

$//$ Read pairs of courses in the format $[$a$,$ b$]$

while $($cin $>>$ a $>>$ comma $>>$ b$)\{$

prerequisites.push$\_$back$(\{$a$,$ b$\})$;

$\}$

cout $<<($canFinish$($N$,$ prerequisites$)?$ "True" : "False"$)<<$ endl;

return $0$;

$\}$