$5.$ Consider the following pseudo$-$code for the BubbleSort algorithm and helper function Swap for answering the questions below. $(10$ pts total$)$

Function Swap$($a$,$ b$)$:

Input: Two elements, a and b$,$ of the same type.

Output: No direct output, but the values of a and b will be swapped upon completion.

c$$a

a$$b

b$$c

Algorithm BubbleSort$($A$)$:

Input: An array A of n comparable elements, indexed from $1$ to n$.$

Output: An ordering of A so that its elements are in non$-$decreasing order.

for i$1$ to n $1,$ do:

for j$1$ to n $$ I, do:

if A$[$j$]>$ A$[$j $+1],$ do:

Swap$($A$[$j$],$ A$[$j$+1])$

return A

$5$a$.$ Identify the lower bound, upper bound, and tight bound $($if possible$)$ time complexity of the Swap function in terms of the input size, n$,$ if applicable. If any of these time complexities differ, explain what kind of input results in each case. $(5$ pts$)$

$\backslash$Omega Swap:

OSwap:

$\backslash$Theta Swap:

$5$b$.$ Identify the lower bound, upper bound, and tight bound $($if possible$)$ time complexity of the BubbleSort function above in terms of the input size, n$,$ if applicable. If any of these time complexities differ, explain what kind of input results in each case. $(5$ pts$)$

$\backslash$Omega BubbleSort:

OBubbleSort:

$\backslash$Theta BubbleSort: