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Problem 1. Suppose you are given an array A[1 n] of integers that can be positive or negative. A contiguous subarray A[i: j] of A is called a positive subarray if sum of its entries is strictly positive, i.e., j ΣA[k] > 0. k=i Design and analyze a dynamic programming algorithm that in O(n²) time finds the smallest number of positive contiguous subarrays of A such that every positive entry of A belongs to exactly one of these subarrays. You can assume that A has at least one positive entry and thus the answer is at least one.

Problem 1. Suppose you are given an array A[1 n] of integers that can be positive or negative. A contiguous subarray A[i: j] of A is called a positive subarray if sum of its entries is strictly positive, i.e., j ΣA[k] > 0. k=i Design and analyze a dynamic programming algorithm that in O(n²) time finds the smallest number of positive contiguous subarrays of A such that every positive entry of A belongs to exactly one of these subarrays. You can assume that A has at least one positive entry and thus the answer is at least one.

Database System Concepts
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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I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n^2).

Problem 1. Suppose you are given an array A[1: n] of integers that can be positive or negative. A contiguous subarray A[i: j] of A is called a positive subarray if sum of its entries is strictly positive, i.e., J ΣA[k] > 0. k=i Design and analyze a dynamic programming algorithm that in O(n²) time finds the smallest number of positive contiguous subarrays of A such that every positive entry of A belongs to exactly one of these subarrays. You can assume that A has at least one positive entry and thus the answer is at least one.
Transcribed Image Text:Problem 1. Suppose you are given an array A[1: n] of integers that can be positive or negative. A contiguous subarray A[i: j] of A is called a positive subarray if sum of its entries is strictly positive, i.e., J ΣA[k] > 0. k=i Design and analyze a dynamic programming algorithm that in O(n²) time finds the smallest number of positive contiguous subarrays of A such that every positive entry of A belongs to exactly one of these subarrays. You can assume that A has at least one positive entry and thus the answer is at least one.
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