Consider array A of n numbers. We want to design a dynamic programming algorithm to find the maximum sum of consecutive numbers with at least one number. Clearly, if all numbers are positive, the maximum will be the sum of all the numbers. On the other hand, if all of them are negative, the maximum will be the largest negative number. The complexity of your dynamic programming algorithm must be O(n²). However, the running time of the most efficient algorithm is O(n). Design the most efficient algorithm you can and answer the following questions based on it. To get the full points you should design the O(n) algorithm. However, if you cannot do that, still answer the following questions based on your algorithm and you will get partial credit. (a) tion(s) to subproblem(s). Briefly explain how it computes the solution. Do not forget the base case(s) of your recursion. Write the recursion that computes the optimal solution recursively based on the solu-

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
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Consider array A of n numbers. We want to design a dynamic programming algorithm to find the
maximum sum of consecutive numbers with at least one number. Clearly, if all numbers are positive,
the maximum will be the sum of all the numbers. On the other hand, if all of them are negative, the
maximum will be the largest negative number.
The complexity of your dynamic programming algorithm must be O(n2). However, the running time
of the most efficient algorithm is O(n). Design the most efficient algorithm you can and answer the
following questions based on it.
To get the full points you should design the O(n) algorithm. However, if you cannot do that, still
answer the following questions based on your algorithm and you will get partial credit.
Write the recursion that computes the optimal solution recursively based on the solu-
(a)
tion(s) to subproblem(s). Briefly explain how it computes the solution.
Do not forget the base case(s) of your recursion.
Transcribed Image Text:Consider array A of n numbers. We want to design a dynamic programming algorithm to find the maximum sum of consecutive numbers with at least one number. Clearly, if all numbers are positive, the maximum will be the sum of all the numbers. On the other hand, if all of them are negative, the maximum will be the largest negative number. The complexity of your dynamic programming algorithm must be O(n2). However, the running time of the most efficient algorithm is O(n). Design the most efficient algorithm you can and answer the following questions based on it. To get the full points you should design the O(n) algorithm. However, if you cannot do that, still answer the following questions based on your algorithm and you will get partial credit. Write the recursion that computes the optimal solution recursively based on the solu- (a) tion(s) to subproblem(s). Briefly explain how it computes the solution. Do not forget the base case(s) of your recursion.
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