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Optimal Sorting Algorithms Analysis in Different Input Scenarios

Explore the efficiency of various sorting algorithms in different input scenarios - sorted order, reversed order, nearly correct order. Understand how Bubble, Insertion, Selection, and Heap sort perform based on input type.

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Optimal Sorting Algorithms Analysis in Different Input Scenarios

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  1. Midterm Review CS112 Fall 2003

  2. Problem 1 You are a manager. You must implement some functionality. A number of your subordinates bring to you a number of proposed implementation methods. The corresponding performance characteristics are given below. • Order these in order of your preference, best choice first (assume your applications require very large n): • A(n) = (n3 lg n / 2n) = O(1) o(1) 1 • B(n) = n3 / lg n = (n3/lg n) 5 • C(n) = 1000 n lg n = (n lg n) 3 • D(n) = 5 n2 = (n2) 4 • E(n) = 100 n = (n) 2 • One of the engineers advocates an algorithm for which he can only show that it is(lg n). What can you say about it as compared to the above?Definitely worse than A. All others can be either. • Another engineer advocates another algorithm for which he can only show that it isO(n2). What can you say about it as compared to those in ‎a)? [do not confuse O and ]Definitely, better than B.All others can be either.

  3. 3 7 1 8 1 3 2 L Problem 2 Assume that linked lists are implemented using the following declaration class ListNode { public: int data; ListNode * next; }; Consider the following function: void grow(ListNode * L) { p = L; while(p != NULL) { while((p->next!=NULL)&&(p->data <= 2*p->next->data)) p->next = p->next->next; p = p->next; } } Let L be a pointer on the following linked list: p

  4. Problem 3 How fast each of the following sorting algorithms work on the input of n elements given in • the correct sorted order (e.g. 1,2,3,4,5,6,7,8) • Bubble: (n) n-1 • Insertion: (n) n-1 • Selection: (n2) n(n-1)/2 • Heap: (n lg n) < 3n lg n • in the reversed sorted order (e.g. 8,7,6,5,4,3,2,1) • Bubble: (n2) n(n-1)/2 • Insertion: (n2) n(n-1)/2 • Selection: (n2) • Heap: (n lg n)

  5. Problem 3 How fast each of the following sorting algorithms work on the input of n elements given in • in almost correct order: the largest element is in the first position, (e.g. 8,1,2,3,4,5,6,7) • Bubble: (n) 2n-3 • Insertion: (n) 2n-3 • Selection: (n2) n(n-1)/2 • Heap: (n lg n) < 3n lg n • as above, except the smallest element is in the last position, (e.g. 2,3,4,5,6,7,8,1) • Bubble: (n2) n(n-1)/2 • Insertion: (n) 2n-3 • Selection: (n2) n(n-1)/2 • Heap: (n lg n) < 3n lg n

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