boolean is$\_$sorted$($lyst$)$: This is a predicate function that returns True if lyst is sorted, False otherwise. In addition to verifying that lyst is a list, is$\_$sorted$()$ must also verify that every element in the list is an integer. If lyst is not a list, or a non$-$integer element is found in it$,$ is$\_$sorted should raise a TypeError exception. Note: We recommend implementing this function first, so that you can use it to do unit testing as you develop your sorting functions.

$($list$,$ int, int$)$ quicksort$($lyst$)$: This function implements the quicksort algorithm to sort the items in lyst$.$ the function returns a tuple containing the sorted list, followed by the number of comparisons, and finally the number of swaps performed while sorting. lyst must be a Python list containing comparable data $($i$.$e$.$ things that the $>,<,$ etc. operators can be used on to determine an ordering between two items$).$ If lyst is not a list, quicksort$()$ must raise a TypeError Exception.

$($list$,$ int, int$)$ mergesort$($lyst$)$: This function implements the mergesort algorithm to sort the items in lyst$.$ the function returns a tuple containing the sorted list, followed by the number of comparisons, and finally the number of swaps performed while sorting. lyst must be a Python list containing comparable data $($i$.$e$.$ things that the $>,<,$ etc. operators can be used on to determine an ordering between two items$).$ If lyst is not a list, mergesort$()$ must raise a TypeError Exception.

$($list$,$ int, int$)$ selection$\_$sort$($lyst$)$: This function implements the selection sort algorithm to sort the items in lyst$.$ the function returns a tuple containing the sorted list, followed by the number of comparisons, and finally the number of swaps performed while sorting. lyst must be a Python list containing comparable data $($i$.$e$.$ things that the $>,<,$ etc. operators can be used on to determine an ordering between two items$).$ If lyst is not a list, selection$\_$sort$()$ must raise a TypeError Exception.

$($list$,$ int, int$)$ insertion$\_$sort$($lyst$)$: This function implements the insertion sort algorithm to sort the items in lyst$.$ the function returns a tuple containing the sorted list, followed by the number of comparisons, and finally the number of swaps performed while sorting. lyst must be a Python list containing comparable data $($i$.$e$.$ things that the $>,<,$ etc. operators can be used on to determine an ordering between two items$).$ If lyst is not a list, insertion$\_$sort$()$ must raise a TypeError Exception.