Implement linearSearch(a,key) and binarySearch(a,key) functions. Part A. In this part we will calculate the average-case running time of each function. 1. Request the user to enter a positive integer, and call it n. (n = 105 ) 2. Generate n random integers between -1000 to 1000 and save them in array a. 3. Sort a (you can use any sorting algorithm you want.) 4. Pick a random number in a and save it in variable called key. 5. Call each function separately to search for the key in the given array. 6. To calculate the average-running time, you need to have a timer to save the total runtime when repeating step 4 and 5 for 100 times. (Note1: Do not forget to divide the runtime by the number of the times you run step 4-5) (Note2: Remember to choose a different random number each time you go back to step 4.) Part B. In this part we will calculate the worst-case running time of each function. 1. Repeat steps 1 to 3 in part A. 2. Now to have the worst-case scenario, set the value of the key to 5000 to make sure it does not exist in the array. 3. Run each function ONLY once to calculate the worst-case running time when n = 105 . 4. Calculate how much time your machine takes to run one single step using your binary search function. (Hint: look at HW4) 5. Now using the previous step, write a code to calculate the worst-case running time for each algorithm when n=107 (You do not use a timer for this step. Just a simple calculation!).
