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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F032de2f6-d35c-4a3a-a9a2-daefbabd8c32%2F2f7eb37d-a68b-4208-bcee-5b3677cd2667%2F4wzcf7k_processed.png&w=3840&q=75)
Transcribed Image Text: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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