Problem 4: Divide and conquer. (i) Let A be an array containing n different integers. Elements in A are sorted in increasing order. Given an integer x describe an algorithm which in time O(log n) finds an index i of x in A, that is, A[i] = x, where the length n of A is unknown (you may assume that the implementation of an array is such that for A[i], where i > n, a special character ∞ is returned). (ii) Let A be an array containing n different integers. Elements in A are not necessary sorted. Given an integer x describe an algorithm which in time O(n log n) tests whether there exist two elements u and v in A such that their sum is equal to x, that is, u + v = x. The length n of A is known.

Problem 4: Divide and conquer. (i) Let A be an array containing n different integers. Elements in A are sorted in increasing order. Given an integer x describe an algorithm which in time O(log n) finds an index i of x in A, that is, A[i] = x, where the length n of A is unknown (you may assume that the implementation of an array is such that for A[i], where i > n, a special character ∞ is returned). (ii) Let A be an array containing n different integers. Elements in A are not necessary sorted. Given an integer x describe an algorithm which in time O(n log n) tests whether there exist two elements u and v in A such that their sum is equal to x, that is, u + v = x. The length n of A is known.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter16: Searching, Sorting And Vector Type

Section: Chapter Questions

Problem 16SA

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