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(Solved): Using the dynamic programming approach, solve the following knapsack problem: The capacity of the k ...
Using the dynamic programming approach, solve the following knapsack problem: The capacity of the knapsack W = 89654 . The number of available items = 10. The weights of the items . The values of the items 41000554168357474870 ). Construct the table and use backtracking to answer the following questions: Was item 1 picked? (write 1 if picked and 0 otherwise) Was item 2 picked? (write 1 if picked and 0 otherwise) Was item 3 picked? (write 1 if picked and 0 otherwise) Was item 4 picked? (write 1 if picked and 0 otherwise) Was item 5 picked? (write 1 if picked and 0 otherwise) Was item 6 picked? (write 1 if picked and 0 otherwise) Was item 7 picked? (write 1 if picked and 0 otherwise) Was item 8 picked? (write 1 if picked and 0 otherwise) Was item 9 picked? (write 1 if picked and 0 otherwise) Was item 10 picked? (write 1 if picked and 0 otherwise) What is the total value of the picked items? What is the total weight of the picked items?
Expert Answer
The knapsack problem involves selecting items with given weights and values to maximize the total value while not exceeding a certain weight capacity. In this specific question, we are given a knapsack capacity and the weights and values of 10 items. The task is to use dynamic programming to find the optimal subset of items to pick, answer whether each item was picked or not, calculate the total value of the picked items, and determine the total weight of the picked items.What is a knapsack problem?The knapsack problem is a classic optimization problem in computer science and mathematics. It gets its name from the scenario of packing a knapsack with items, where each item has a weight and a value associated with it.The problem is defined as follows: Given a knapsack with a maximum weight capacity and a set of items, each with its own weight and value, determine the optimal subset of items to include in the knapsack, such that the total value is maximized without exceeding the weight capacity.The goal is to find a combination of items that maximize the value while keeping the total weight below or equal to the knapsack's capacity. Depending on the specific variation of the problem, there may be additional constraints or requirements.The knapsack problem is often used as a fundamental problem in algorithm design and optimization. It has various applications in real-world scenarios such as resource allocation, project selection, scheduling, and portfolio optimization.