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.
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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.
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