$[10$ points$]$ Suppose prisoners numbered $1,2,3,...,$ n are standing in a circle in

the clockwise order. Starting from the first prisoner, every kth prisoner in the

clockwise direction is killed in every step. We would like to compute the jth person

to be killed.

$($i$)$ Design a natural algorithm JOSEPHUSPROBLEM$-$ARRAY$($n$,$ k$,$ j$)$ using an array

to solve the problem.

$($ii$)$ Design a natural algorithm JOSEPHUSPROBLEM$-$CSLL$($n$,$ k$,$ j$)$ using circularly

singly linked list to solve the problem