Consider the following array:$40636428762456699303157$Note: For quicksort you will use a different set of numbers, because these resulted in pivots being the largest or smallest item too often. For quicksort use these numbers instead:$1372043288663503293640$For problems $1-5,$ create a diagram showing the state of the array above after each pass through the array using the following sorting algorithms. $($In other words, use the method used in lecture to show how each sorting algorithm sorts the numbers above.$)$ Also, for each algorithm, state the average big$-$O running time estimate.For consistency, please use the algorithm as shown in the lecture, not in the text.Selection SortBubble Sort $($No swap flag. In other words, no stopping early when the list is sorted.$)$Insertion SortMerge SortQuicksort. You must use the version given in the lesson and circle the pivot at each step$\mathrm{.}6.$ List each number from the unsorted list above $($the list that starts with $40)$ that will be examined if a linear search is used to search for the number $62.$ Also state the average big$-$O running time estimate for a linear search$\mathrm{.}7.$ Here are the same numbers but sorted:$023031404557626364668799$List each number from the list above that will be examined if a binary search is used to search for the number $99\mathrm{.}8.$ List each number from the list above that will be examined if a binary search is used to search for the number $52.$ Note that $52$ is not in the list. That doesn't change anything. There is still a sequence of numbers that are examined until the algorithm determines that it isn't there$\mathrm{.}9.$ State the average big$-$O running time estimate for binary search.