Data Structures and Algorithm Analysis - Computer Science at ...

Sec. 3.14 Projects 893.24 Prove that if an algorithm is Θ(f(n)) in the average case, then it is O(f(n))in the best case.3.14 Projects3.1 Imagine that you are trying to store 32 Boolean values, and must accessthem frequently. Compare the time required to access Boolean values storedalternatively as a single bit field, a character, a short integer, or a long integer.There are two things to be careful of when writing your program. First, besure that your program does enough variable accesses to make meaningfulmeasurements. A single access takes much less time than a single unit ofmeasurement (typically milliseconds) for all four methods. Second, be surethat your program spends as much time as possible doing variable accessesrather than other things such as calling timing functions or incrementing forloop counters.3.2 Implement sequential search and binary search algorithms on your computer.Run timings for each algorithm on arrays of size n = 10 i for i ranging from1 to as large a value as your computer’s memory and compiler will allow. Forboth algorithms, store the values 0 through n − 1 in order in the array, anduse a variety of random search values in the range 0 to n − 1 on each sizen. Graph the resulting times. When is sequential search faster than binarysearch for a sorted array?3.3 Implement a program that runs and gives timings for the two Fibonacci sequencefunctions provided in Exercise 2.11. Graph the resulting runningtimes for as many values of n as your computer can handle.