0 1 backpack problem (with question list included)

Problem description: A backpack can load w and there are n items. The value of things I is VI and the weight is wi. How many pieces of these N items can be taken into a backpack?

Example: W = 3, n = 3;

Value of things

VI wi
34

4 5

5 6

DP Solution:

First understand this problem from the perspective of recursion, And Then paste a non-recursive template.

Now it is thing number: 0 1 2 3... N-1; we should start with N-1 (in fact, it doesn't matter from which end, don't care about these details). In fact, I don't think this algorithm belongs to DP.

Make (I, j) = max {make (I-1, J-W [I]) + V [I] (take something numbered I), make (I-1, J) (no products numbered I are available )}

0 1 backpack problem (with question list included)