Tutorial Playlist

Data Structure Tutorial

Overview

Arrays in Data Structures: A Guide With Examples

Lesson - 1

All You Need to Know About Two-Dimensional Arrays

Lesson - 2

All You Need to Know About a Linked List in a Data Structure

Lesson - 3

The Complete Guide to Implement a Singly Linked List

Lesson - 4

The Ultimate Guide to Implement a Doubly Linked List

Lesson - 5

The Fundamentals for Understanding Circular Linked List

Lesson - 6

The Ultimate Guide To Understand The Differences Between Stack And Queue

Lesson - 7

Implementing Stacks in Data Structures

Lesson - 8

Your One-Stop Solution for Stack Implementation Using Array

Lesson - 9

Your One-Stop Solution for Queue Implementation Using Array

Lesson - 10

Your One-Stop Solution to Learn Depth-First Search(DFS) Algorithm From Scratch

Lesson - 11

Your One-Stop Solution for Stack Implementation Using Linked-List

Lesson - 12

The Definitive Guide to Understand Stack vs Heap Memory Allocation

Lesson - 13

All You Need to Know About Linear Search Algorithm

Lesson - 14

All You Need to Know About Breadth-First Search Algorithm

Lesson - 15

A One-Stop Solution for Using Binary Search Trees in Data Structure

Lesson - 16

The Best Tutorial to Understand Trees in Data Structure

Lesson - 17

A Complete Guide to Implement Binary Tree in Data Structure

Lesson - 18

A Holistic Look at Using AVL Trees in Data Structures

Lesson - 19

All You Need to Know About Tree Traversal in Data Structure

Lesson - 20

The Best Guide You’ll Ever Need to Understand B-Tree in Data Structure

Lesson - 21

The Best Guide You'll Ever Need to Understand Spanning Tree in Data Structure

Lesson - 22

The Best and Easiest Way to Understand an Algorithm

Lesson - 23

Your One-Stop Solution to Understand Shell Sort Algorithm

Lesson - 24

Your One-Stop Solution to Quick Sort Algorithm

Lesson - 25

The Most Useful Guide to Learn Selection Sort Algorithm

Lesson - 26

Everything You Need to Know About Radix Sort Algorithm

Lesson - 27

Everything You Need to Know About the Counting Sort Algorithm

Lesson - 28

Everything You Need to Know About the Merge Sort Algorithm

Lesson - 29

Insertion Sort Algorithm: One-Stop Solution That Will Help You Understand Insertion Sort

Lesson - 30

Everything You Need to Know About the Bubble Sort Algorithm

Lesson - 31

The Best Guide You’ll Ever Need to Understand Bucket Sort Algorithm

Lesson - 32

Your One-Stop Solution to Understand Recursive Algorithm in Programming

Lesson - 33

The Definitive Guide to Understanding Greedy Algorithm

Lesson - 34

Your One-Stop Solution to Understand Backtracking Algorithm

Lesson - 35

The Fundamentals of the Bellman-Ford Algorithm

Lesson - 36

Your One-Stop Solution for Graphs in Data Structures

Lesson - 37

The Best Guide to Understand and Implement Solutions for Tower of Hanoi Puzzle

Lesson - 38

A Simplified and Complete Guide to Learn Space and Time Complexity

Lesson - 39

All You Need to Know About the Knapsack Problem : Your Complete Guide

Lesson - 40

The Fibonacci Series: Mathematical and Programming Interpretation

Lesson - 41

The Holistic Look at Longest Common Subsequence Problem

Lesson - 42

The Best Article to Understand What Is Dynamic Programming

Lesson - 43

A Guide to Implement Longest Increasing Subsequence Using Dynamic Programming

Lesson - 44

A Holistic Guide to Learn Stop Solution Using Dynamic Programming

Lesson - 45

One Stop Solution to All the Dynamic Programming Problems

Lesson - 46

Understanding the Fundamentals of Binomial Distribution

Lesson - 47
A Holistic Guide to Learn Stop Solution Using Dynamic Programming

Most of the time, dynamic programming is just a faster way to do things with recursion. You use dynamic programming to optimize any recursive solution that makes use of the same inputs repeatedly. Subproblem results will be stored, so they do not have to be recomputed in the future as needed. This straightforward optimization decreases the time complexity from exponential to polynomial levels.

By the end of this tutorial, you will better understand the recursion and dynamic programming approach to the subset sum problem with all the necessary details and practical implementations.

Post Graduate Program: Full Stack Web Development

in Collaboration with Caltech CTMEEnroll Now
Post Graduate Program: Full Stack Web Development

What Is the Problem Statement for the Subset Sum Problem?

You will be given a set of non-negative integers and a value of variable sum, and you must determine if there is a subset of the given set with a sum equal to a given sum.

Now, look at the recursive solution to solve the subset sum problem.

What Is the Recursion Based Solution to the Subset Sum Problem?

Subset_sum-recursion-solution-img1

For the recursion based approach, you will look at two scenarios:

  1. Start with the last element and work your way up to the goal sum by subtracting the value of the 'last' element from the total number of elements.
  2. 'Final' element will be removed, and the required sum will equal the target sum, with the number of elements equal to the total elements minus 1.

And this is how you solve the subset sum problem using recursion. Now, implement this solution through a simple C++ code.

How Do You Implement the Recursion-Based Solution of the Subset Sum Problem?

You will be provided with a set with elements {10, 7, 8, 9, 1, 5}. You are to find a subset whose sum must be equal to 16, which is set {7, 9}.

Code:

// A c++ program to illustrate recursion based solution

#include <bits/stdc++.h>

using namespace std;

//It will return true if subset of set[] 

//has sum equal to given sum; false otherwise

bool is_subset_sum(int set[], int n, int sum)

{

// Base Cases

if (sum == 0)

return true;

if (n == 0)

return false;

// If last element is greater than sum,

// then we will ignore it

if (set[n - 1] > sum)

return is_subset_sum(set, n - 1, sum);

/* otherwise,we will check if the sum can be obtained by any

of the following:

(a) including the last element

(b) excluding the last element */

return is_subset_sum(set, n - 1, sum)

|| is_subset_sum(set, n - 1, sum - set[n - 1]);

}

// Driver code

int main()

{

int set[] = { 10, 7, 8, 9, 1, 5 };

int sum = 16;

int n = sizeof(set) / sizeof(set[0]);

if (is_subset_sum(set, n, sum) == true)

cout <<"Found a subset with given sum";

else

cout <<"No subset with given sum was found";

return 0;

}

Subset_sum-recursion-implementation-img1

You have now explored the recursive approach to the subset sum problem with a code. Now, look at the dynamic programming-based solution to this problem.

New Course: Full Stack Development for Beginners

Learn Git Command, Angular, NodeJS, Maven & MoreEnroll Now
New Course: Full Stack Development for Beginners

What Is the Dynamic Programming Based Solution to the Subset Sum Problem?

Subset_sum-dp-solution-img1

You use dynamic programming to solve the problem in pseudo-polynomial time,

  • Make a boolean-type 2D array of size (arr.size() + 1) * (target + 1).
  • If there is a subset of elements from A[0....i] with sum value = 'j,' the state DP[i][j] is true.
  • To avoid duplicating previous cases' answers, you will have to ensure that the current element has a value greater than the "current sum value."
  • So, check if any prior states have already encountered the sum='j' OR have previously experienced the value 'j – A[i], which will help you achieve your purpose if it is bigger than the current total value.

And this is how you solve this problem using dynamic programming. Now implement this solution through a simple C++ code.

Full Stack Web Developer Course

To become an expert in MEAN StackView Course
Full Stack Web Developer Course

How Do You Implement the Dynamic Programming Based Solution of the Subset Sum Problem?

You will be given a set with elements as {10, 7, 8, 4, 1, 6}. You have to find a subset whose sum must be equal to 16, which is set {10, 6}.

Code: 

// A C++ program to demonstrate Dynamic Programming 

//approach to solve this problem

#include <bits/stdc++.h>

using namespace std;

//It will return true if subset of set[] 

//has sum equal to given sum; false otherwise

bool is_subset_sum(int set[], int n, int target_sum)

{

//If set[0..j-1] has a subset with 

//target_sum equal to i then the 

//value of sub_set[i][j] will be true.

bool sub_set[n + 1][target_sum + 1];

// If target_sum is 0, then answer is true

for (int i = 0; i <= n; i++)

sub_set[i][0] = true;

// If target_sum is not 0 and set is empty,

// then answer is false

for (int i = 1; i <= target_sum; i++)

sub_set[0][i] = false;

// we will now fill the subset table in bottom up manner

for (int i = 1; i <= n; i++) {

for (int j = 1; j <= target_sum; j++) {

if (j < set[i - 1])

sub_set[i][j] = sub_set[i - 1][j];

if (j >= set[i - 1])

sub_set[i][j] = sub_set[i-1][j]

|| sub_set[i - 1][j - set[i - 1]];

}

}

/* // we can uncomment this code to print table

for (int i = 0; i <= n; i++)

{

for (int j = 0; j <= target_sum; j++)

printf ("%4d", sub_set[i][j]);

cout <<"\n";

}*/

return sub_set[n][target_sum];

}

int main()

{

int set[] = { 10, 7, 8, 4, 1, 6 };

int target_sum = 16;

int n = sizeof(set) / sizeof(set[0]);

if (is_subset_sum(set, n, target_sum) == true)

cout <<"Found a subset with given sum = "<<target_sum;

else

cout <<"No subset found with given sum = "<<target_sum;

return 0;

}

Subset_sum-dp-implementation-img1

With this, you have come to an end of this tutorial. You will now look at what could be your next steps to conquer dynamic programming problems.

Advance your career as a MEAN stack developer with the Full Stack Web Developer - MEAN Stack Master's Program. Enroll now!

Next Steps

Your next stop in mastering dynamic programming problems should be matrix chain multiplication. Given a list of matrices, you must find the most efficient way to multiply a set of matrices together. The issue isn't whether or not to multiply, but rather which multiplications to perform first.

If you're searching for a more in-depth understanding of software development that can help you carve out a successful career in the field, look no further. If that's the case, consider Simplilearn's Postgraduate Program in Full Stack Web Development, which is offered in collaboration with Caltech CTME, the world's largest technology education institution. This Post-Graduate Program will teach you how to master both front-end and back-end Java technologies, beginning with the fundamentals and progressing to the more advanced aspects of Full Stack Web Development. In this web development course, you'll study Angular, Spring Boot, Hibernate, JSPs, and MVC, which will help you get started as a full-stack developer. 

If you have any questions or require clarification on this "Subset Sum Problem" tutorial, please leave them in the comments section below. Our expert team will review them and respond as soon as possible.

About the Author

Vaibhav KhandelwalVaibhav Khandelwal

Vaibhav Khandelwal is a proactive tech geek who's always on the edge of learning new technologies. He is well versed in competitive programming and possess sound knowledge of web development. He likes to read fictional and sci-fi novels and likes to play strategy games like chess.

View More
  • Disclaimer
  • PMP, PMI, PMBOK, CAPM, PgMP, PfMP, ACP, PBA, RMP, SP, and OPM3 are registered marks of the Project Management Institute, Inc.