Question

A thief tries to rob a store. There are $n$ items in the store. Let the $k^{\text {th }}$ item has a value, $v_k$ and weight, $w_k$. The thief has a bag (or a knapsack) that can hold a maximum weight, $W$.

Answer 1

The subject of this question is Mathematics and the grade level is High School. This question is related to the concept of the knapsack problem.

Step-by-step explanation:

The subject of this question is Mathematics and the grade level is High School.

This question is related to the concept of the knapsack problem.

In the knapsack problem, the thief is trying to maximize the total value of the items they can steal while staying within the weight limit of their bag. The thief needs to decide which items to take and which ones to leave behind.

To solve the knapsack problem, one approach is to use dynamic programming. We can create a table where the rows represent the items and the columns represent the weight capacity of the bag. We then fill in the table by considering each item and calculating the maximum value that can be obtained with the given weight capacity.