# Google Treasure Hunt 3: a Depth-First Search Solution

July 26, 2008

This is another Google Treasure Hunt I solved. I know that with this one, you really doesn’t need to use any kind of programming skills. But I guess that there would be no fun if you just use only your mind to solve it! Try to teach your computer to make it for you… The problem I got was the following:

“Below is a diagram of a computer network. The nodes are hosts on the network, and the lines between them are links. A packet is sent out from host P with a destination of 4.229.231.150. Which nodes does the packet pass through on its way to the destination? (include start and final node in your answer)”

The diagram for the given computer network can be designated by the routing table below:

A                 26.40.28.17                    75.174.216.140 => 126.186.188.58  26.40.28.17 => 17.100.195.84           4.229.231.0/24 => 75.174.216.140                      13.157.234.26

B                 13.157.234.26                76.246.145.72 => 53.12.68.161         126.186.188.58 => 75.174.216.140   53.12.68.0/24 => 26.40.28.17                     17.100.195.84

C                  53.12.68.161                  75.174.216.140 => 219.88.219.35     229.23.61.42 => 13.157.234.26         17.100.195.0/24 => 103.19.57.145                     126.186.188.58

D                 103.19.57.145                86.60.122.237 => 86.60.122.237       117.146.177.141 => 53.12.68.161     229.23.61.0/24 => 219.88.219.35                     212.222.1.12

E                  4.229.231.150                4.229.231.150 => 103.19.57.145       54.35.7.207 => 54.35.7.207                                   126.186.188.0/24 => 199.223.210.72              229.23.61.42

F                  54.35.7.207                    4.229.231.150 => 229.23.61.42         13.157.234.26 => 199.223.210.72     26.40.28.0/24 => 4.229.231.150                     86.60.122.237

G                 86.60.122.237                229.23.61.42 => 54.35.7.207             13.157.234.26 => 103.19.57.145       103.19.57.0/24 => 212.222.1.12                     219.88.219.35

H                 212.222.1.12                  126.186.188.58 => 219.88.219.35     75.174.216.140 => 86.60.122.237     103.19.57.0/24 => 103.19.57.145                     229.23.61.42

I                   229.23.61.42                  4.229.231.150 => 4.229.231.150       117.146.177.141 => 54.35.7.207       126.186.188.0/24 => 199.223.210.72                    212.222.1.12

J                  199.223.210.72              53.12.68.161 => 229.23.61.42           4.229.231.150 => 54.35.7.207           219.88.219.0/24 => 219.88.219.35                     4.229.231.150

K                  219.88.219.35                4.229.231.150 => 199.223.210.72     17.100.195.84 => 212.222.1.12         126.186.188.0/24 => 86.60.122.237                     103.19.57.145

L                  117.146.177.141            4.229.231.150 => 219.88.219.35       117.146.177.141 => 126.186.188.58 26.40.28.0/24 => 76.246.145.72                     75.174.216.140

M                75.174.216.140              199.223.210.72 => 13.157.234.26     4.229.231.150 => 117.146.177.141   126.186.188.0/24 => 17.100.195.84                     26.40.28.17

N                 17.100.195.84                4.229.231.150 => 26.40.28.17           219.88.219.35 => 13.157.234.26       17.100.195.0/24 => 75.174.216.140                     76.246.145.72

O                 76.246.145.72                4.229.231.150 => 17.100.195.84       86.60.122.237 => 126.186.188.58     13.157.234.0/24 => 53.12.68.161                     117.146.177.141

P                  126.186.188.58              13.157.234.26 => 53.12.68.161         4.229.231.150 => 76.246.145.72       103.19.57.0/24 => 26.40.28.17                     117.146.177.141

As you may suppose, the first symbol is the character identifying the network node, followed by its IP number. Next, you have a sequence of 3 routing rules, where the related node can see if one of these rules can fit with the incoming packet. The last IP number gives us the “default route”, just in the case the network node couldn’t find any matching rule. In this case, the packet will be forwarded through the outgoing network card to the given host in the last column.

I proposed a solution with C++, which uses depth-first search as the method to look for a valid path going from a given point to another in the problem network model. My main idea is to put my depth-first search function walking node by node (labeled as A, B, C, etc.), iterating over each one of the routing table rules, and searching for one of these rules that can route my packet through the network. The function below is self-explainable:

bool RoutingTable::routeTo( string node, string* resp )

{

bool do_it_again = true;

RoutingEntry rentry = findRouteEntry( node );

if ( rentry.doneThis() )

return false;

resp->append( rentry.getId() );

if ( rentry.getAddress().compare(getFinalDestination()) == 0 ) {

return false;

}

vector<RoutingRule> routing_rules = rentry.getRules();

vector<RoutingRule>::iterator i;

rentry.markThis(true);

// go through each of the routing rules

for ( i = routing_rules.begin(); ( i != routing_rules.end() ) &&

do_it_again; i++ )

{

if ( (*i).canRoute(getFinalDestination()) ) {

do_it_again = routeTo( (*i).getRedirection(), resp );

} // if

} // for

rentry.markThis(false);

// no rules; asks the default gateway…

if ( do_it_again )

{

do_it_again = routeTo( rentry.getDefaultRoute().getRedirection(),

&nb

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