$1.$ Implement the Insertion Sort algorithm.$($Hint: use the function checked$\_$sorted to check if your output isindeed sorted.$)$

$2.$ Implement the Merge Sort algorithm.$($Hint: use the function checked sorted to check if your output isindeed sorted.$)$

$3.$ Implement the Heap Sort algorithm.$($Hint: use the function checked sorted to check if your output isindeed sorted.$)$

$4.$ For each algorithm, try different ranges of numbers to be sorted to test the performance and time complexity.

For example:a$.$ Array$[1\mathrm{.}100]$b$.$ Array$[1\mathrm{.}1000]$c$.$ array$[1\mathrm{.}10000]$d$.$ Array$[1\mathrm{.}100000]$e$.$ Array$[1\mathrm{.}1000000]$f$.$

Write a paragraph discussing your findings on how the different sizes affected the time complexity.

Discuss which algorithm outperformed the other and why.

Graphs are encouraged for visualization and to drawconclusions, but not required.