Use the following ideas to develop a nonrecursive, linear-time algorithm for the maximum-subarray problem. Start at the left end of the array, and progress toward the right, keeping track of the maximum subarray seen so far. Knowing a maximum subarray of A[1.. j], extend the answer to find a maximum subarray ending at in- dex j+1 by using the following observation: a maximum subarray of A[1.. j + 1] is either a maximum subarray of A[1.. j] or a subarray A[i.. j +1], for some 1 ≤ i ≤ j + 1. Determine a maximum subarray of the form A[i.. j + 1] in constant time based on knowing a maximum subarray ending at index i.

Use the following ideas to develop a nonrecursive, linear-time algorithm for the maximum-subarray problem. Start at the left end of the array, and progress toward the right, keeping track of the maximum subarray seen so far. Knowing a maximum subarray of A[1.. j], extend the answer to find a maximum subarray ending at in- dex j+1 by using the following observation: a maximum subarray of A[1.. j + 1] is either a maximum subarray of A[1.. j] or a subarray A[i.. j +1], for some 1 ≤ i ≤ j + 1. Determine a maximum subarray of the form A[i.. j + 1] in constant time based on knowing a maximum subarray ending at index i.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

4.1-5
Use the following ideas to develop a nonrecursive, linear-time algorithm for the
maximum-subarray problem. Start at the left end of the array, and progress toward
the right, keeping track of the maximum subarray seen so far. Knowing a maximum
subarray of A[1.. j], extend the answer to find a maximum subarray ending at in-
dex j +1 by using the following observation: a maximum subarray of A[1 .. j + 1]
is either a maximum subarray of A[1…. j] or a subarray A[i …. j + 1], for some
1 ≤ i ≤ j + 1. Determine a maximum subarray of the form A[i.. j + 1] in
constant time based on knowing a maximum subarray ending at index j.

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