Given two strings A$="$wxyz$"$ and B$="$zxw$",$ to find the string editing distance in which three

types of editing $($insertion$,$ deletion and replacement$)$ are allowed.

$(1)$ give the recurrence relation to solve this problem.

$(2)$ illustrate your algorithm by the given example. Note that, not only the distance, but the editing

steps are required to be illustrate,

$(1)$ with the exception that replacement is not allowed.

$(2)$ with the exception that the cost of deletion is $3,$ the cost of insertion is $2,$ while the cost of

replacement is $1.$