GIVE ANSWER ONLY FOR PART b a. In Data Structures, you studied binary heaps. Binary heaps support the insert and extractMin functions in O(lgn), and getMin in O(1). Moreover, you can build a heap of n elements in just O(n). Refresh your knowledge of heaps from chapter no. 6 of your algorithms text book. Now implement Merge Sort, Heap Sort, and Quick Sort in C++ and perform the following experiment: 1. Generate an Array A of 107 random numbers. Make its copies B and C. Sort A using Merge Sort, B using Heap Sort, and C using Quick Sort. 2. During the sorting process, count the total number of comparisons between array ele- ments made by each algorithm. You may do this by using a global less-than-or-equal-to function to compare numbers, which increments a count variable each time it is called. 3. Repeat this process 5 times to compute the average number of comparisons made by each algorithm. 4. Present these average counts in a table. These counts give you an indication of how the di erent algorithms compare asymptotically (in big-O terms) for a large value of n. b. Now compare the same algorithms in terms of practical time, i.e. the actual running time. Simply, repeat the previous example but use the chrono library to compute the actual times taken by each algorithm, and report the average value of the time for each algorithm.
GIVE ANSWER ONLY FOR PART b
a. In Data Structures, you studied binary heaps. Binary heaps support the insert and extractMin
functions in O(lgn), and getMin in O(1). Moreover, you can build a heap of n elements in
just O(n). Refresh your knowledge of heaps from chapter no. 6 of your algorithms text book.
Now implement Merge Sort, Heap Sort, and Quick Sort in C++ and perform the following
experiment:
1. Generate an Array A of 107 random numbers. Make its copies B and C. Sort A using
Merge Sort, B using Heap Sort, and C using Quick Sort.
2. During the sorting process, count the total number of comparisons between array ele-
ments made by each
function to compare numbers, which increments a count variable each time it is called.
3. Repeat this process 5 times to compute the average number of comparisons made by
each algorithm.
4. Present these average counts in a table. These counts give you an indication of how the
di erent algorithms compare asymptotically (in big-O terms) for a large value of n.
b. Now compare the same algorithms in terms of practical time, i.e. the actual running time.
Simply, repeat the previous example but use the chrono library to compute the actual times
taken by each algorithm, and report the average value of the time for each algorithm.
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