Task $5.$Then we should integrate all the above functions to derive the following algorithm:

while there remain one or more breakpoints:

$$locate a potential strip $[$a$,$b$]$ whose reversal would remove the maximum number of breakpoints

$$if that reversal would remove $1$ or more breakpoints:

$$perform the reversal

$$else:

$$there must not be any decreasing subsequences

$$find the first increasing strip beyond the one starting with $0$

$$reverse that strip

$$

def sort$\_$by$\_$reversal$($data$)$: $"""$Convert original data back to the identity, and return the number of reversal steps that were used.""" reversals $=0$ # total number of reversal steps # implement your codes, better to print out each updated sequence every time the reversal step is executed

return reversals, final$\_$ordered$\_$sequence