Now, we have to iterate over the table and implement the derived formula. Our next task is to make the cost of the items with 0 weight limit or 0 items 0.įor w in 0 to W cost = 0 for i in 0 to n cost = 0 Since we are starting from 0, so the size of the matrix is (n+1)x(W+1).Īlso, our function is going to take values of n, W, weight matrix (wm) and value matrix(vm) as its parameters i.e., KNAPSACK-01(n, W, wm, vm). So, let's start by initializing a 2D matrix i.e., cost =, where n is the total number of items and W is the maximum weight limit. We already discussed that we are going to use tabulation and our table is a 2D one. Now, let's generate the code for the same to implement the algorithm on a larger dataset. So, you can see that we have finally got our optimal value in the cell (4,5) which is 15. So, our main task is to maximize the value i.e., $\sum_$ And the bag has a limitation of maximum weight ($W$). $x_i$ is the number of $i$ kind of items we have picked. There are different kinds of items ($i$) and each item $i$ has a weight ($w_i$) and value ($v_i$) associated with it. This problem is commonly known as the knapsack or the rucksack problem. BSKP has similarities to several other knapsack variations in addition to BKP. So, you need to choose items to put in your bag such that the overall value of items in your bag maximizes. You are also provided with a bag to take some of the items along with you but your bag has a limitation of the maximum weight you can put in it. ![]() ![]() Each item has a different value and weight. Suppose you woke up on some mysterious island and there are different precious items on it.
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