$(16$ pts$)$ You are given a random array consisting of integers $($including positive, negative, and $0),$ and each element may be repeated.

Note: for all the questions below, please use the iostream library only.

a$)(4$ pts$)$ Write a function bubbleSort to implement Bubble Sort to sort the array in descending order.

Function signature:

void bubbleSort$($int nums$[],$ int $n)$

Example:

$$ Input: nums $=[5,1,9,6,5,1,2],n=7$

$$ Expected realization: nums $=[9,6,5,5,2,1,1]$

b$)(6$ pts$)$ Write a function quickSort to implement Quick Sort to sort the array in descending order.

Function signature:

void quickSort $($int nums$[],$ int $n)$

Example: see above.

c$)(3$ pts$)$ Write a function dedup Licate to remove the repeated integers from your sorted array and return the length of the updated array. Do not use extra memory space.

Function signature:

int deduplicate$($int nums$[],$ int $n)$

Example:

$$ Input: nums $=[9,6,5,5,2,1,1],n=7$

$$ Expected realization: nums $=[9,6,5,2,1]$

$$ Output: $5$

d$)(3$ pts$)$ What are the time and space complexity of each function that you realized above? Explain why.