How to find all solutions to the SUBSET-SUM problem?


Are you facing a problem with dynamic programming? Or are you having trouble with the SUBSET-SUM problem using dynamic programming?

If yes, then we are here to help you out!

The SUBSET-SUM problem is an exemplary issue in math and software engineering. In this problem, you are given a set of numbers and have to find the sum of all subsets of those numbers.

The best way to solve to SUBSET-SUM problem is by using Dynamic Programming,

In this blog, we’ll tell you the aspects of; how to use dynamic programming. What are the best ways to find all solutions to the problem? How can you use the step-by-step approach?

We are further going to explain a couple of tips that will assist you with upgrading your code and further developing execution.

We will also tell you some best ways to find all solutions to the SUBSET-SUM problem using dynamic programming.

Let’s first start with What are Subset Sum Problems actually are

In SUBSET-SUM problems you will be assigned a set of numbers, and have to find the sum of all subsets of those numbers.

Subset problems are solved by Dynamic programming. The reason for solving them with dynamic programming is to break the big problem into small chunks of problems. They are often known as sub-problems.

With  help of dynamic programming, you can find minimum subset sum difference

By using Dynamic programming, the problem becomes easy to solve. As now you are dealing with sub-problems, solve each sub-problem individually and then add them all together.

By adding them you will end up solving a large problem.

How to solve Subset problems in dynamic programming.

There is a wide range of techniques for taking care of the SUBSET-SUM  problems in dynamic programming.

A portion of these methods includes Two- the dimensional table method, the Recursive method, and the branch and bound method.

The two-dimensional table method

This is a straightforward technique for tackling the SUBSET-SUM problem.

  • In this technique, the problem is separated into a series of sub-problems, every one of which can be settled by utilizing the two-dimensional table strategy.
  • You can obtain the solution to the whole problem by adding the initial solution with individual sub-problems
  • In the Two-dimensional table method, you have to divide the problem into tables. By doing so you can easily see the connection between different variables and their optimal solution.
  • This strategy is especially helpful for problems where there are different constraints, like the knapsack problem. By utilizing a two-dimensional table, you can see which things you should include in order to obtain the most ideal outcomes.
  • The two-dimensional table strategy is likewise useful for problems that include different stages, like the Traveling Salesman Problem. By dividing the problem into a table, you can see the ideal way from beginning to end.

So if you want to solve Dynamic Programming problems, then the two-dimensional table method is a perfect option

Recursive Method

The Recursive Method is another basic strategy for tackling the SUBSET-SUM Problem. This strategy includes recursively separating the problem into more small problems.

  • You have to keep dividing the problem until every individual problem can be settled.
  • Again the solution to a parent problem is obtained when you combine all individual sub-problems.
  • A recursive technique is a strategy that calls itself to settle a problem. As discussed earlier Dynamic programming is used for solving complex problems by breaking them into sub-problems.
  • This technique can be utilized to tackle problems by breaking them into more modest subproblems. Similar to Two – the dimensional table method, breaking a complex problem into small chunks will help you in solving it easily.

For instance, consider the problem where you have to find the shortest path from X to Y. For solving this you can break this problem into more subproblems,

like, finding the shortest path from X to point Z, then from  Z to point Y. By tackling these more subproblems, we can track down the shortest path from X to Y.

  • Dynamic programming is mainly used to solve these kinds of complex questions, like tracking down the path from X to Y.
  • Recursive techniques are incredible assets for tackling complex issues. However, they can likewise be hard to understand and debug.
  • If you’re experiencing difficulty in understanding a recursive strategy, drawing an image of the recursion might be helpful.

They are also used to find the minimum subset sum difference for the set of numbers.

Branch And Bound Method

The branch and bound technique is a more modern strategy for tackling the SUBSET-SUM issue. This strategy utilizes a tree-like design to address the potential answers to the problem.

The branch and bound strategy then, at that point, utilize this tree-like structure to find the best possible answer for the problem.

  • The branch and bound technique is an incredible asset for taking care of dynamic programming problems.
  • It is an approach to deliberately identifying all potential answers for a problem, and afterward choosing the best one.
  • The main purpose of this method is to find the best way to represent complex problems. So that they can be tackled by using simple search algorithms.
  • This is generally done by utilizing a graph or tree structure. The algorithm then, at that point, continues by deliberately exploring every single imaginable arrangement, until it sees it as the ideal one.
  • The best part of this technique is that It finds all the ideal arrangements. Moreover, it can frequently find close ideal arrangements rapidly.
  • The principal disadvantage of the technique is that it tends to be very time taking, and is now and again not doable for exceptionally enormous problems.
  • Also, the technique can at times be challenging to comprehend and carry out.
  • Except for these downsides, the branch, and bound technique is an integral asset that can be exceptionally useful for solving dynamic programming problems.
  • It can also print all subsequences of a string dynamic programming.


Breaking big problems into small chunks often solves that problem easily. Similarly, with the help of dynamic programming, you can find all solutions to SUBSET-SUM problems.

By using various techniques like the Two-dimensional table method, Recursive Method, and Branch and Bound Method. You can easily find solutions to the subset-sum problems.


Hi, I'm Raj Hirvate & I am a Tech Blogger from India. I like to post about technology, gadgets, How-to, Errors and product reviews to the readers of my website. Apart from blogging i'm a big Anime fan I Love Watching Naruto, Jujutsu Kaisen, One piece, Death Note and any upcoming animes.

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