So I need a python code which will traverse a graph and will return the time

complexity. We will pick a random attack path from root to leaf. Let's say the attack

path will be $P1=V1,V2,V3,V4,V5.$ Now the program will calculate the risk of P $1$ and

store it$,$ also it will count the vulnerabilities lying in P$1$ and will store it$.$ The program

will set P$1$ as the optimal path, "Popt" and the risk as optimal as well which is "Ropt$=$

R$1."$ Then, the program will take another attack path which is P $2,$ and it will select

the next leaf node from the first path. Means, if P $1$ is $P1=V1,V2,V3,V4,V5$ is this

one, then P $2$ will be$,P2=V1,V2,V3,V4,V6($means the next leaf node of V $5).$ Now, it

will calculate the risk of P$2,$ store the risk, calculate the number of vulnerabilities in

$P2$ and store it as well. Now, it will compare the risks of $P1$ and $P2.$ If $R(P2)$ is greater

than R$($P$1),$ it will update the current optimal: Popt $-P2$ and Ropt $R(P2).$ Else,

take another new path to check with the current optimal but this time, don't take

any nodes from the leaf anymore, move $1$ level up$,$ and take path like: V$1,$ V$2,$V$3,$V$7.$

So in this way, the program should continue, and keep checking the whole tree. And

at the end of traversing, the program should be able to return the time complexity,

the attack path with highest risk and the set of associated vulnerabilities in that

path.