Q$4.$ For the Josephus problem that you programmed as your Assignment $1,$ consider the

following initial conditions:

$($C$2-$PLO$1)(5$ marks$)$

$n=16($i$.$e$.$ the number of people is $16)$

$k=2($i$.$e$.$ every $2^{nd}$ person is killed$)$

Starting point $=1($i$.$e$.I=1)$

Direction $=$ anti$-$clockwise

Show the initial scenario as well as the remaining people $($their numbers$)$ after each

iteration $($round of killing$)$ until only $1$ person remains.

Q$5.$ Bubble Sort is a very simple method that sorts the array elements by repeatedly moving

the largest element to the highest index position of the array segment $($in case of

arranging elements in ascending order$).$

The algorithm for Bubble Sort is given below. Analyze this algorithm to compute its

worst$-$case time complexity represented in Big$-$O notation.

$($C$4-$PLO$2)(5$ marks$)$