public class ServerGraph

$\{$

$//3$ marks

private class WebServer

$\{$

public string Name;

public List P;

$...$

$\}$

private WebServer$[]$ V;

private bool$[,]$ E;

private int NumServers;

$...$

$//2$ marks

$//$ Create an empty server graph

public ServerGraph$()...$

$//2$ marks

$//$ Return the index of the server with the given name; otherwise return $-1$

private int FindServer$($string name$)...$

$//3$ marks

$//$ Double the capacity of the server graph with the respect to web servers

private void DoubleCapacity$()...$

$//3$ marks

$//$ Add a server with the given name and connect it to the other server

$//$ Return true if successful; otherwise return false

public bool AddServer$($string name, string other$)...$

$//3$ marks

$//$ Add a webpage to the server with the given name

$//$ Return true if successful; other return false

public bool AddWebPage$($WebPage w$,$ string name$)...$

$//4$ marks

$//$ Remove the server with the given name by assigning its connections

$//$ and webpages to the other server

$//$ Return true if successful; otherwise return false

public bool RemoveServer$($string name, string other$)...$

$//3$ marks

$//$ Add a connection from one server to another

$//$ Return true if successful; otherwise return false

$//$ Note that each server is connected to at least one other server

public bool AddConnection$($string from, string to$)...$

$//10$ marks

$//$ Return all servers that would disconnect the server graph into

$//$ two or more disjoint graphs if ever one of them would go down

$//$ Hint: Use a variation of the depth$-$first search

public string$[]$ CriticalServers$()...$

$//6$ marks

$//$ Return the shortest path from one server to another

$//$ Hint: Use a variation of the breadth$-$first search

public int ShortestPath$($string from, string to$)$

$//4$ marks

$//$ Print the name and connections of each server as well as

$//$ the names of the webpages it hosts

public void PrintGraph$()...$

$...$

$\}$