array-based sequences - give formal proof that any sequence of append or pop operations on an initially empty dynamic array takes (ntimeif using the strategy described in exercise - - consider variant of exercise - in which an array of capacity is resized to capacity precisely that of the number of elementsany time the number of elements in the array goes strictly below / give formal proof that any sequence of append or pop operations on an initially empty dynamic array takes (ntime - consider variant of exercise - in which an array of capacity nis resized to capacity precisely that of the number of elementsany time the number of elements in the array goes strictly below / show that there exists sequence of operations that requires ( time to execute - in section we described four different ways to compose long string( repeated concatenation( appending to temporary list and then joining( using list comprehension with joinand ( using generator comprehension with join develop an experiment to test the efficiency of all four of these approaches and report your findings - develop an experiment to compare the relative efficiency of the extend method of python' list class versus using repeated calls to append to accomplish the equivalent task - based on the discussion of page develop an experiment to compare the efficiency of python' list comprehension syntax versus the construction of list by means of repeated calls to append - perform experiments to evaluate the efficiency of the remove method of python' list classas we did for insert on page use known values so that all removals occur either at the beginningmiddleor end of the list report your results akin to table - the syntax data remove(valuefor python list data removes only the first occurrence of element value from the list give an implementation of functionwith signature remove all(datavalue)that removes all occurrences of value from the given listsuch that the worst-case running time of the function is (non list with elements not that it is not efficient enough in general to rely on repeated calls to remove - let be an array of size > containing integers from to inclusivewith exactly five repeated describe good algorithm for finding the five integers in that are repeated - given python list of positive integerseach represented with log bitsdescribe an ( )-time method for finding -bit integer not in - argue why any solution to the previous problem must run in (ntime