1. Generate an Array A of 10^7 random numbers. Make its copies B and C. Sort A using Merge Sort, B using Heap Sort, and C using Quick Sort.
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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
Now implement Merge Sort, Heap Sort, and Quick Sort in C++ and perform the following
experiment:
1. Generate an Array A of 10^7 random numbers. Make its copies B and C. Sort A using
Merge Sort, B using Heap Sort, and C using Quick Sort.
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- Write a C++ program to take N elements and do the following: a. Insert them into a heap one by one b. Build a heap in linear time. Compare the running time of both algorithms for sorted,reverse-ordered, and random inputs C++ Language Only Please Be thorough in comments for explanation (I tried a class and void functions I got stuck in my code it would be awesome if you utilize that for me) Thank YouPlease answer point 3 and 4 In Data Structures, you studied binary heaps. Binary heaps support the insert and extractMinfunctions in O(lgn), and getMin in O(1). Moreover, you can build a heap of n elements injust 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 followingexperiment:1. Generate an Array A of 10^7 random numbers. Make its copies B and C. Sort A usingMerge 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-tofunction 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 byeach algorithm.4. Present these average counts in a table. These counts give you an indication of how thedi erent algorithms…a) Define the heap data structure, and define any data structures refered to in this definition. b) Why are heaps as used for heapsort most often implemented in array form? Explain your answer. c) How do you find the children of a node in the array in terms of the arithmetic involved? d) How do you find the parent of a node in the array in terms of the arithmetic involved? e) Describe the heapifyUpwards algorithm.
- Assume you have the max-heap 100, 80, 70, 60, 50, 40, 30, 50, 10, 20. What is the final state of the array after one full iteration of heapsort (stop before the recursive call ono sub arrays, Sorts from min to max values, pivot placed at the end) is called? 80, 60, 70, 50, 50, 40, 30, 30, 20, 10, 100 80, 60, 70, 50, 50, 40, 30, 30, 20, 10 100, 80, 70, 60, 50, 50, 40, 30, 30, 20, 10 100, 80, 60, 70, 50, 50, 40, 30, 30, 20, 10 60, 70, 50, 50, 40, 30, 30, 20, 10, 100, 80 Assume you have the following array: 8, 5, 30, 15, 100, 10, 20. What will the array look like after a single pass of the Partition part of the quicksort algorithm (Min to max value, pivot placed at the end)? 5, 8, 15, 20, 30, 10 8, 5, 15, 10, 20, 30, 100 8, 5, 15, 10, 20, 100, 30 8, 5, 15, 10, 100, 30, 20 15, 8, 5, 20, 100, 30 Assume you have the array 7,9,6,10,3,5,8, what are the swaps that occur when we call build-min-heap? 6-5, 9-3 9-3, 7-3 6-5, 7-3, 9-3 9-3, 7-3, 6-5 6-5, 9-3, 7-3 Assume we have the array…In Data Structures, you studied binary heaps. Binary heaps support the insert and extractMinfunctions in O(lgn), and getMin in O(1). Moreover, you can build a heap of n elements injust 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 followingexperiment:1. Generate an Array A of 107 random numbers. Make its copies B and C. Sort A usingMerge Sort, B using Heap Sort, and C using Quick Sort.2. During the sorting process, count the total number of comparisons between array elements made by each algorithm. You may do this by using a global less-than-or-equal-tofunction 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 byeach algorithm.4. Present these average counts in a table. These counts give you an indication of how thedifferent algorithms compare asymptotically (in…Consider the following vector: { 1, 2, 3, 6, 9, 5, 10, 14}(1) Give me the vector version of the binary heap that results when you call Pop() on this heap (vector) (no code needed, just the 7 numbers in order)(2) You would like to sort this specific vector/heap. Which is better to divide and conquer: quick sort using the first element as a pivot or merge sort? Please explain your answer in your own words your decision and the reasons why
- Answer the following briefly. a) Why is a doubly linked list more useful than a singly linked list? b) Explain the steps involved in inserting a new value in a binary heap with the help of a suitable example.Can you please explain this code to me step-by-step? I especially did not get how s.append(x) is iteratively adding the elements back to the stack without any loop. Note: If you can spot any mistake in the function call, please point that out as well. CODE To Delete Middle Element of a Stack: def deleteMid_util(s, sizeOfStack, current): #if current pointer is half of the size of stack then we #are accessing the middle element of stack. if(current==sizeOfStack//2): s.pop() return #storing the top element in a variable and popping it. x = s.pop() current+=1 #calling the function recursively. deleteMid_util(s,sizeOfStack,current) #pushing the elements (except middle element) back #into stack after recursion calls. s.append(x) def deleteMid(s, sizeOfStack): deleteMid_util(s, sizeOfStack, 0) res = deleteMid([1,2,3,4,5], 5) print(res)In C++, Implement a Priority Queue(PQ) using an UNSORTED LIST. Use an array size of 20 elements. Use a circular array: Next index after last index is 0. Add the new node to next available index in the array. When you add an element, add 1 to index (hit max index, go to index 0). Test if array in full before you add. When you remove an element, from the list, move the following elements to the left to fill in the blank, etc ( Like prior program done with LISTS ) Create a class called Node: Have a Name and Priority. Data set - 1 is the highest priority, 10 is lowest priority. Enqueue and dequeue in the following order. Function Name, Priority Enqueue Joe, 3 Enqueue Fred, 1 Enqueue Tuyet, 9 Enqueue Jose, 6 Dequeue Enqueue Jing, 2 Enqueue Xi, 5 Enqueue Moe, 3 Dequeue Enqueue Miko, 7 Enqueue Vlady, 8 Enqueue Frank, 9 Enqueue Anny, 3 Dequeue Enqueue Xi, 2 Enqueue Wali, 2 Enqueue Laschec, 6 Enqueue Xerrax, 8 Dequeue Dequeue Dequeue Dequeue Dequeue Dequeue Dequeue Dequeue Dequeue Dequeue…
- Write three functions in C or C++: one that declares a large arraystatically, one that declares the same large array on the stack, and onethat creates the same large array from the heap. Call each of thesubprograms a large number of times (at least 100,000) and output thetime required by each. Explain the results.7. For a given input array, write a code in c or c++ to construct a Max-Heap using the following algorithms.The code should use inherently the same algorithms which were discussed in the class. (a) Build-Max-Heap(b) Max-Heap-InsertYou are required to demonstrate the running time difference between a linked listand a binary search tree while searching the data. Read the following instructionsand then implement a C++ program that can address the above requirement.1- choose byself a .csv file containing the data named Dataset.csv The dataset file contains a record of 100000 sales records of astore. By using the text file reading method in C++, read the data of the file in alinked list and a binary search tree. (In a single program) After reading the data validate the data reading by implementing a print() method. Take a sales id as an input from the user and search that ID in the linked listand binary search tree. Display the running time difference of both data structures during the searchoperation.