Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K?a) T[i, j] = ( T[i − 1, j] or T[i, j − ci])b) T[i, j] = ( T[i − 1, j] and T[i, j − ci ])c) T[i, j] = ( T[i − 1, j] or T[i − 1, j − ci ])d) T[i, j] = ( T[i − 1, j] and T[i − 1, j − cj ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K?a) T[1, K + 1]b) T[n, K]c) T[n, 0]d) T[n, K + 1]

Correct Answer is " C " C. → T[i, j] = (T[i - 1, j] or T[i -1, j - ci]) Explanation : - T[i, j]…

Answered: Given a set of n positive integers, C =…

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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Given a set of n positive integers, C = {c₁,c₂, ..., c_n} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c₁,c₂, ..., c_i} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, c_i ≤ j ≤ K?

a) T[i, j] = ( T[i − 1, j] or T[i, j − c_i])

b) T[i, j] = ( T[i − 1, j] and T[i, j − c_i ])

c) T[i, j] = ( T[i − 1, j] or T[i − 1, j − c_i ])

d) T[i, j] = ( T[i − 1, j] and T[i − 1, j − c_j ])

In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K?

a) T[1, K + 1]

b) T[n, K]

c) T[n, 0]

d) T[n, K + 1]

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