summation for the running time of your algorithm on piecesand then derive closed-form solution for the summation can the average case cost for an algorithm be worse than the worst case costcan it be better than the best case costexplain why or why not prove that if an algorithm is th( ( )in the average casethen it is ohm( ( )in the worst case prove that if an algorithm is th( ( )in the average casethen it is ( ( )in the best case projects imagine that you are trying to store boolean valuesand must access them frequently compare the time required to access boolean values stored alternatively as single bit fielda charactera short integeror long integer there are two things to be careful of when writing your program firstbe sure that your program does enough variable accesses to make meaningful measurements single access is much smaller than the measurement rate for all four methods secondbe sure that your program spends as much time as possible doing variable accesses rather than other things such as calling timing functions or incrementing for loop counters implement sequential search and binary search algorithms on your computer run timings for each algorithm on arrays of size for ranging from to as large value as your computer' memory and compiler will allow for both algorithmsstore the values through in order in the arrayand use variety of random search values in the range to on each size graph the resulting times when is sequential search faster than binary search for sorted array implement program that runs and gives timings for the two fibonacci sequence functions provided in exercise graph the resulting running times for as many values of as your computer can handle