Imagine you are asked to take gems out of a bad full of valuable gems, what would be your goal? Obviously to ensure that the most precious gems lie with you.

This happens in the system as well. Can you guess how the system stores data conveniently to maximize the application and output efficiency? Or how you can manage the data especially when it lies in the **longest common subsequence**.

In such cases, we consider this as a knapsack problem. Let’s understand why this problem is named knapsack.

Knapsack here stands for a bag or simply a sack in which you will have to collect meaningful data.

These data or items are available with different weights and profits. All you need to do is figure out a way in which you can improve your profit. You will have to convert these items into your profit while placing them in your bag.

It is quite simple to understand this problem however, the solution to this problem will require accurate approaches.

If you are also searching for an optimized approach to resolve this issue whenever you face it, this article will save the day for you.

So, let’s have a look at the details of this problem along with its types.

And of course, the useful approaches that will help you find resolution of this problem easily.

**Contents**hide

**What is the knapsack problem?**

The knapsack problem is similar to the problem mentioned in the above section.

The knapsack problem is encountered when you have to fill a bag of limited weightage with items of different weights.

You have to fill these items in such a form that the sum of weights of individual items is lesser or equal to the weight of the container/sack itself.

Make sure you pick out elements in a way that their profit is maximized.

However, there are different scenarios in which you will get this issue. There are different types of Knapsack problems. How about we discuss the types of knapsack problems in detail?

**Types of the knapsack problem**

There are two types of knapsack problems faced by users quite often. Namely, the two kinds of knapsack problems are the **0 1 knapsack problem **and the fractional knapsack problem.

It’s not enough to know just the names of these problems as you will have to understand how it works. Hence, we should take a deeper look at these types to establish a better understanding.

Starting with the first type of this problem, the **0 1 knapsack problem** is somewhat conditional. According to this problem, either the knapsack will be filled up to the top (100% ) or simply stay empty.

You can not fill a portion or fraction of the knapsack in this situation by picking up the divided items.

All the items will have to be taken as a whole or null. You can not take a part or specific percentage of the item and maximize your profits.

However, you can resolve this type of problem by simply applying the dynamic programming rules. Make sure you follow a definite approach for the same.

The second type of knapsack problem is the **fractional knapsack problem.** This type of problem is faced by users when they are allowed to divide the items.

This problem allows you to divide the items into different parts and fractions to fill up your knapsack. You can maximize your profit by dividing the items in the required format.

Once you do so, you will have to follow a certain approach to fill your bag as well.

Usually, this type of knapsack problem is resolved through a greedy approach.

But is that it? You can apply these particular approaches to resolve these problems. There are different approaches through which you can resolve knapsack problems in programming.

**How to resolve the knapsack problem?**

You know there are several paths you can take to reach a certain goal. Similarly, you can adopt different approaches to solve the knapsack problem.

Following are the ways in which you can resolve the knapsack problem:

**Approach 1: By using a brute force algorithm and Exhaustive search**

Under this approach, you can easily consider the subsets of the data items and estimate their value. You can calculate the weight and value of the items. This will help you to use these values appropriately to maximize your profit.

Once calculated, you can pick out the subset that has maximum weight yet the weight lies within the range. By range, we mean that the sum of weights of items is lesser than that required by the bag.

**Approach 2: By using dynamic programming**

This approach is similar to the exhaustive search method. However, the only difference between the two is how you select the maximum value of weight.

In this method, the items are searched individually for the largest weight and then multiplied by their value.

The major basis of the difference between these two methods is in dynamic programming, optimized space complexity is used.

**Approach 3: By using the Memoization technique**

Complexity level of this method is comparatively high. You can consider this method as an extension of the brute force algorithm.

In this method, the overall working is kept similar but the efficiency is improved. Using this method you can resolve time complexity issues by not processing redundant cases.

This method is executed by saving the data in a 2-D array that will store the maximum value. You can provide this value in the form of (n,w) and pass it as a constant throughout the code. Whenever the data or exact coordinates are found within the array, the value will be returned.

You will not have to calculate or monitor every single value and exponentially calculate the same. This will affect your efficiency and the complexity to make it simpler for you.

**Bonus Topic**

**What Are Arrays?**

An Array is a collection of related data elements stored in contiguous memory locations. It is the most basic data structure in which each data element may be retrieved simply by its index number alone.

In programming, most of the time, we need to store a huge amount of data of the same type. We need to establish multiple variables to store such a large amount of data. It would be quite difficult to remember all variable names when developing the programs. Instead, create an array and store all of the items in it.

For example, if we want to keep a student’s marks in ten subjects, we don’t need to establish distinct variables for each topic. Instead, we may build an array that stores the data items in contiguous memory regions.

Array **marks[10**] denote the marks scored by a student in 10 different subjects, where each subject’s marks are located at a specific location in the array, i.e., **marks[0]** denote the marks scored in the first subject, **marks[1]** denotes the marks scored in the second subject, **marks[2]** denotes the marks scored in the third subject and so on.

**Conclusion**

So we can conclude, that you can resolve the **0 1 knapsack problem **and the fractional knapsack problem with the accurate type of approach.

With the help of these approaches we hope that you can now handle any minor or even the **longest common subsequence** coming your way.

**Also Read – Just what is meant by “Binary Cross Entropy?**