Question 12: Remember the episode of Tom and Jerry, where Jerry picks…

Remember the episode of Tom and Jerry, where Jerry picks an orange cat and a dog ('Spike') and switches their personalities in the lab. Tom was shocked and could not believe that the orange cat was actually behaving like a dog. Imagine you are a friend of Tom, and you have to explain him that it is possible to switch personalities by mutating their genes. You find the synteny blocks in the chromosomes of the orange cat (henceforth denoted by $\mathit{Cat}$), Tom and Spike as given below.

\begin{aligned} \mathit{Cat} &= {+5}\ {+3}\ {-1}\ {+4}\ {+2} \\ \mathit{Tom} &= {-3}\ {-2}\ {-1}\ {+5}\ {+4} \\ \mathit{Spike} &= {+1}\ {+2}\ {+3}\ {+4}\ {+5} \end{aligned} \tag{1}

Suppose Jerry's machine first runs an algorithm to determine the breakpoint graph and the sequence of transformations and then applies it on the species. Transforming a genome into another using $n$ operations (2-break operations: reversal, translocation, fusion or fission) takes $n$ minutes, as each 2-break operation takes 1 minute to apply. Assume the algorithm only uses the minimum number of transformations needed to convert a species into another. Use the breakpoint graph to determine the total number of minutes Jerry needed to mutate "Cat" into Spike.