Problem $1$:

An empirical comparative study should be conducted on the following sorting algorithms by counting the number of comparisons:

Bubble Sort

Insertion Sort

Selection Sort

Merge Sort

Heap Sort

Quick Sort

A$.$ Generate the input arrays:

Integer arrays of sizes: $10,100,1,000,10,000,100,000,1,000,000,$ and $10,000,000.($ you may change the range of sizes according to your computer's performance$)$

For each size, generate three types of arrays:

i$.$ Random array.

ii$.$ Sorted array $($ascending order, starting from $0).$

iii. Inversely sorted array $($descending order, from size$-1$ to $0).$

B$.$ Save results in an Excel sheet with the following structure:

Rows represent array sizes.

Columns represent:

i$.$ Theoretical comparisons.

ii$.$ Empirical comparisons for the three array types.

iii. A total of $6$ columns per algorithm.

$(36$ columns in total$).$

C$.$ Visualize the results:

Plot the relationship between empirical and theoretical complexity for each algorithm separately.

Plot the empirical complexity comparison across all algorithms for each case $($random$,$ sorted, and inversely sorted arrays$)$ Using java would be great for the code please create the excel file as well as the visualized graphs $($DONT USE AI$)$