Knapsack restore solution complexity
In order to solve integer knapsack problem, we used iterative memorization algorithm (via n*w
sized matrix where n
is the number of items, and w
is the knapsack's max weight capacity). We were asked to restore the solution (the items inserted to the knapsack) using the matrix. We're not sure about the restore algorithm run time complexity. The restore pseudo code is as follows (where w(j)
is the weight of item j
and v(j)
is the value of item j
):
**RestoreItems(M)**
I is an empty set.
j=n, T = W.
while j>0 and T>0
if M[j,T] = M[j-1,T]
j=j-1
if M[j,T] = M[j-1,T-w(j)] +v(j) and w(j) <= T
I = I + j
j = j-1
T = T - w(j)
return I
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