## What is the 0-1 knapsack problem?

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.

## 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 knapsack problem explain it with an example?**

The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

### Who discovered knapsack problem?

George Dantzig proposed a greedy approximation algorithm to unbounded knapsack problem which can also be used to solve the 0-1 QKP. The algorithm consists of two phrases: identify an initial solution and improve it. since for the worst case every possible combination of items will be identified.

### What is the difference between knapsack and 0-1 knapsack?

Given weights and values of n items, we need to put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In the 0-1 Knapsack problem, we are not allowed to break items. We either take the whole item or don’t take it.

**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 , .

## What is the goal of knapsack problem?

What is the objective of the knapsack problem? Explanation: The objective is to fill the knapsack of some given volume with different materials such that the value of selected items is maximized.

## How do humans solve problems?

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution.

**What is DP in C++?**

Dynamic programming is a powerful technique for solving problems that might otherwise appear to be extremely difficult to solve in polynomial time. Dynamic programming works by solving subproblems and using the results of those subproblems to more quickly calculate the solution to a larger problem.

### How can I get better at DP?

7 Steps to solve a Dynamic Programming problem

- How to recognize a DP problem.
- Identify problem variables.
- Clearly express the recurrence relation.
- Identify the base cases.
- Decide if you want to implement it iteratively or recursively.
- Add memoization.
- Determine time complexity.

### What is the condition for 0 1 knapsack problem for killing a node?

If at node Z the values of xi , 1 £ i £ k have already been determined, then an upper bound for Z can be obtained by relaxing the requirement xi = 0 or 1 to 0 £ xi £ 1 for k+1 £ i £ n and use the greedy method to solve the relaxed problem.