What is knapsack problem and Implementation

Introduction

 

In this blog, we would discuss What is knapsack problem and its Implementation. If you’re looking for an efficient way to solve the knapsack problem, the greedy algorithm is a good choice. The fractional knapsack greedy algorithm is a variation of the algorithm that allows you to take fractions of items, rather than just whole items. This can be helpful when the items you’re trying to pack are valuable and you want to make sure you get the most value out of them.

 

 

To use the fractional knapsack greedy algorithm, you first need to order the items you’re packing by value. Once you have the items sorted, you can start packing them into the knapsack. The algorithm allows you to take fractions of items, so you can take as much or as little of an item as you want. When you’re finished packing, you’ll have the most valuable items in your knapsack, and you’ll be able to maximize the value you get from them.

 

 

 

Greedy Approach to the knapsack problem 

 

There are several different algorithms that can be used to solve the knapsack problem, but the greedy algorithm is a particularly simple and elegant solution. The idea behind the greedy algorithm is to always choose the item with the highest value-to-weight ratio. This ensures that we maximize the value of the items in our knapsack while still staying within the weight limit.

 

 

One potential issue with the greedy algorithm is that it doesn’t always find the optimal solution. However, it is usually good enough for most practical purposes, and it is much faster than other algorithms that always find the optimal solution.

 

One algorithm that is used to make the most efficient use of resources is the fractional knapsack algorithm. This algorithm is used when there are items with different values and weights. The goal is to choose a combination of items that maximize the value while staying under the weight limit. To do this, the algorithm first sorts the items by value.

 

 

It then starts with the most valuable item and adds it to the knapsack if there is room. If there is not enough room for the entire item, the algorithm adds a fraction of the item until the weight limit is reached. It then moves on to the next most valuable item and repeats the process.

 

 

The fractional knapsack algorithm is a greedy algorithm, meaning it makes the best choice at each step in an attempt to optimize the overall result. In the case of the knapsack problem, the algorithm’s goal is to maximize the value of the items in the knapsack. The algorithm does not always find the optimal solution, but it is usually close. In addition, the algorithm is fast and easy to implement. For these reasons, the fractional knapsack algorithm is a popular choice for resource-constrained problems.

 

 

 

Algorithm

 

Use the steps provided to solve the issue using the strategy described above:

 

 

Determine the value-to-weight ratio for each item.

 

 

Sort every item according to decreasing ratio.

 

 

Set res to 0 and curr cap to the specified value.

 

 

For each item I in the sorted order, perform the following:

 

 

Add the value of the current item into the result if its weight is less than or equal to the remaining capacity; otherwise, add it as much as possible and exit the loop.

 

 

Return res

 

 

 

Implementation of Knapsack Problem

 

class Item:
    def __init__(self, value, weight):
        self.value = value
        self.weight = weight
 
# Main greedy function to solve problem
def fractionalKnapsack(W, arr):
    arr.sort(key=lambda x: (x.value/x.weight), reverse=True)
    finalvalue = 0.0
 
    for item in arr:
        if item.weight <= W:
            W -= item.weight
            finalvalue += item.value
        else:
            finalvalue += item.value * W / item.weight
            break
    return finalvalue
 

if __name__ == "__main__":

    W = 40
    arr = [Item(50, 10), Item(70, 20), Item(100, 30)]
    max_val = fractionalKnapsack(W, arr)
    print ('Maximum value we can obtain = {}'.format(max_val))

Output

 

 

 

Also, read about Naive Bayes.