# What is 0-1 knapsack problem explain with an example?

## What is 0-1 knapsack problem explain with an example?

In this item cannot be broken which means thief should take the item as a whole or should leave it. That’s why it is called 0/1 knapsack Problem. Each item is taken or not taken. Cannot take a fractional amount of an item taken or take an item more than once.

Can we solve Knapsack using linear programming?

1 Answer. Knapsack can be written as an integer linear programming program. Unlike normal linear programming, this problem requires that variables in the solution are integers. Linear programming is known to be solvable in polynomial time, while integer linear programming is NP-complete.

Which method solves the 0-1 knapsack problem?

Method 1: Recursion by Brute-Force algorithm OR Exhaustive Search. Approach: A simple solution is to consider all subsets of items and calculate the total weight and value of all subsets.

### What is the solution to the knapsack problem?

The most obvious solution to this problem is brute force recursive. This solution is brute-force because it evaluates the total weight and value of all possible subsets, then selects the subset with the highest value that is still under the weight limit.

Why is it called 0 1 knapsack?

In 0-1 Knapsack, items cannot be broken which means the thief should take the item as a whole or should leave it. This is reason behind calling it as 0-1 Knapsack. 0-1 Knapsack cannot be solved by Greedy approach. Greedy approach does not ensure an optimal solution.

What is multiple knapsack problem?

Abstract. The multiple knapsack problem is a generalization of the standard knapsack problem (KP) from a single knapsack to m knapsacks with (possibly) different capacities.

## What’s the difference between dynamic programming and linear programming?

The first one is linear programming (LP) algorithm which is particularly suitable for solving linear optimization problems, and the second one is dynamic programming (DP) which can guarantee the global optimality of a solution for a general nonlinear optimization problem with non-convex constraints.

Where knapsack problem is used?

Knapsack problems appear in real-world decision-making processes in a wide variety of fields, such as finding the least wasteful way to cut raw materials, selection of investments and portfolios, selection of assets for asset-backed securitization, and generating keys for the Merkle–Hellman and other knapsack …

Can 01 knapsack problem be solved using greedy algo?

0-1 Knapsack cannot be solved by Greedy approach. Greedy approach does not ensure an optimal solution.

### Is knapsack problem NP hard?

The decision version of the 0-1 knapsack problem is an NP-Complete problem. Therefore, the knapsack problem can be reduced to the Subset-Sum problem in polynomial time. Further, the complexity of this problem depends on the size of the input values , .

Which approach is the best in knapsack problem?

Greedy and Genetic algorithms can be used to solve the 0-1 Knapsack problem within a reasonable time complexity. The worst-case time complexity (Big-O) of both algorithms is O(N). Nevertheless, these algorithms cannot find the exact solution to the problem; they are helpful in finding a local optimal result only. 03/12/2020