Do you know how i can solve the following python code?

There are n nodes in a network, initially empty. Your task is to implement a class that allows adding edges to the network and checking if the nodes can be colored with two colors such that each edge connects two nodes of different colors.

You can assume that there are at most $50$ nodes and the methods of the class are called at most $100$ times.

Implement a class named Coloring in python file with the following methods:

$*$Constructor that takes the number of nodes as input

$*$add$\_$edge adds an edge between two nodes

$*$check checks if the network can be colored with two colors

class Coloring:

def $\_\_$init$\_\_($self$,$ n$)$:

# TODO

def add$\_$edge$($self$,$ a$,$ b$)$:

# TODO

def check$($self$)$:

# TODO

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

c $=$ Coloring$(4)$

c$.$add$\_$edge$(1,2)$

c$.$add$\_$edge$(2,3)$

c$.$add$\_$edge$(3,4)$

c$.$add$\_$edge$(1,4)$

print$($c$.$check$())$ # True

c$.$add$\_$edge$(2,4)$

print$($c$.$check$())$ # False

c $=$ Coloring$(5)$

print$($c$.$check$())$

print$($c$.$check$())$

c$.$add$\_$edge$(3,4)$

c$.$add$\_$edge$(4,5)$

c$.$add$\_$edge$(4,5)$

print$($c$.$check$())$

c$.$add$\_$edge$(4,5)$

c$.$add$\_$edge$(3,5)$

print$($c$.$check$())$

print$($c$.$check$())$

Expected output:

line $7$: check returns True