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Algorithms | Dynamic Programming | Question 7
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]
Answer
Please comment below if you find anything wrong in the above post
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