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The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1 <= i <= n, 0 <= j <= W, is TRUE if and only if there is a subset of {a1 ,a2 ,...,ai} whose elements sum to j. Which of the following is valid for 2 <= i <= n and ai <= j <= W?
  • a)
    X[i, j] = X[i - 1, j] ∨ X[i, j -ai]
  • b)
    X[i, j] = X[i - 1, j] ∨ X[i - 1, j - ai]
  • c)
    X[i, j] = X[i - 1, j] ∧ X[i, j - ai]
  • d)
    X[i, j] = X[i - 1, j] ∧ X[i -1, j - ai]
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The subset-sum problem is defined as follows. Given a set of n positiv...
X[I, j] (2 <= i <= n and ai <= j <= W), is true if any of the following is true 1) Sum of weights excluding ai is equal to j, i.e., if X[i-1, j] is true. 2) Sum of weights including ai is equal to j, i.e., if X[i-1, j-ai] is true so that we get (j – ai) + ai as j
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The subset-sum problem is defined as follows. Given a set of n positiv...
The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1, a2, a3, ..., an} and a target integer, t, the problem is to determine whether there exists a subset of S whose sum is equal to t.

Formally, the subset-sum problem can be stated as finding a subset S' ⊆ S such that ∑S' = t, where ∑S' denotes the sum of all elements in S'.

For example, consider the set S = {2, 4, 6, 8} and the target integer t = 10. In this case, there exists a subset S' = {2, 8} whose sum is equal to 10, so the subset-sum problem has a solution.

The subset-sum problem is known to be NP-complete, meaning that it is computationally difficult to find an optimal solution in polynomial time. Various algorithms and heuristics have been developed to solve the subset-sum problem, including dynamic programming, backtracking, and branch and bound techniques.
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The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1 <= i <= n, 0 <= j <= W, is TRUE if and only if there is a subset of {a1 ,a2 ,...,ai} whose elements sum to j. Which of the following is valid for 2 <= i <= n and ai <= j <= W?a)X[i, j] = X[i - 1, j] ∨ X[i, j -ai]b)X[i, j] = X[i - 1, j] ∨ X[i - 1, j - ai]c)X[i, j] = X[i - 1, j] ∧ X[i, j - ai]d)X[i, j] = X[i - 1, j] ∧ X[i -1, j - ai]Correct answer is option 'B'. Can you explain this answer?
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The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1 <= i <= n, 0 <= j <= W, is TRUE if and only if there is a subset of {a1 ,a2 ,...,ai} whose elements sum to j. Which of the following is valid for 2 <= i <= n and ai <= j <= W?a)X[i, j] = X[i - 1, j] ∨ X[i, j -ai]b)X[i, j] = X[i - 1, j] ∨ X[i - 1, j - ai]c)X[i, j] = X[i - 1, j] ∧ X[i, j - ai]d)X[i, j] = X[i - 1, j] ∧ X[i -1, j - ai]Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1 <= i <= n, 0 <= j <= W, is TRUE if and only if there is a subset of {a1 ,a2 ,...,ai} whose elements sum to j. Which of the following is valid for 2 <= i <= n and ai <= j <= W?a)X[i, j] = X[i - 1, j] ∨ X[i, j -ai]b)X[i, j] = X[i - 1, j] ∨ X[i - 1, j - ai]c)X[i, j] = X[i - 1, j] ∧ X[i, j - ai]d)X[i, j] = X[i - 1, j] ∧ X[i -1, j - ai]Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1 <= i <= n, 0 <= j <= W, is TRUE if and only if there is a subset of {a1 ,a2 ,...,ai} whose elements sum to j. Which of the following is valid for 2 <= i <= n and ai <= j <= W?a)X[i, j] = X[i - 1, j] ∨ X[i, j -ai]b)X[i, j] = X[i - 1, j] ∨ X[i - 1, j - ai]c)X[i, j] = X[i - 1, j] ∧ X[i, j - ai]d)X[i, j] = X[i - 1, j] ∧ X[i -1, j - ai]Correct answer is option 'B'. Can you explain this answer?.
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