# A Comprehensive Guide to Know What is Dynamic Programming

Dynamic programming is one of the most significant problem-solving techniques that help break down problems into smaller parts so that the results can be applied again for research purposes. It is a significant aspect of data science technology. According to a Zippia report, the U.S. is currently home to 3,109 data scientists. The percentage is expected to grow by 16% in the decade between 2018 and 2028. So, learning what is dynamic programming can enable aspiring data scientists to enhance their algorithm and optimization techniques to solve problems easily.

Keep reading as we explore the fundamentals of dynamic programming and discover the ways to apply it in practical problem-solving scenarios.

## How Does Dynamic Programming Work?

Dynamic programming is a powerful problem-solving tool that helps break down large, complex problems into smaller subproblems to find the optimal solution more easily and efficiently. It also minimizes redundant calculations. This bottom-up approach to problem-solving works by breaking down a complex problem into smaller subproblems. Then, the solutions to these subproblems are combined to arrive at an optimal solution for the entire problem. This process is repeated until all the possible solutions have been found.

A dynamic programming algorithm starts by analyzing the problem and breaking it up into smaller pieces. It then uses previously solved solutions from these small pieces to build up an overall solution for the entire problem. This makes it possible to arrive at an optimal solution much faster than if you were to solve the whole problem from scratch. Dynamic programming can be used for a variety of applications, from solving complex mathematical equations to software engineering challenges.

## Characteristics of Dynamic Programming

Dynamic programming algorithms have several defining characteristics that make them uniquely effective.

**1. Optimality**

Dynamic programming is based on the principle of optimality, which means that it finds the optimal solution to a given problem.

The programming algorithm can quickly and efficiently arrive at an optimal solution without having to search through all possible solutions.

**2. Efficiency**

Dynamic programming uses previously solved solutions and is much more efficient than other problem-solving methods. This makes it particularly useful for large and complex problems that would otherwise take too long to solve using traditional techniques.

**3. Reusability**

Dynamic programming algorithms can be reused in different scenarios as they provide a general framework for solving a variety of problems.

## Components of Dynamic Programming

Dynamic programming algorithms consist of four parts.

**1. States and State Variables**

A state represents the current status of a problem and can be described by one or more state variables.

**2. Stages**

Stages can be thought of as steps or phases that progress from one solution to the next. This is the order in which each state of a problem should be solved.

**3. Transitional State**

It involves the transition from one particular term to another in a chronological sequence.

**4. Optimal Choice**

It involves looking through all previously solved solutions and choosing the best one that achieves the desired outcome.

**ALSO READ:** The 10 Most Lucrative Coding Languages to Boost Your Career

## Top Dynamic Programming Problems

Dynamic programming algorithms are used to solve a variety of problems. Some of the most common dynamic programming problems include the following.

**1. Longest Common Subsequence Problem**

The Longest Common Subsequence (LCS) problem is finding the longest subsequence present in two sequences in the same order, i.e., finding the longest sequence which can be obtained from the first original sequence by deleting some items and from the second original sequence by deleting other items. The problem differs from the problem of finding the longest common substring. Unlike substrings, subsequences are not required to occupy consecutive positions within the original string.

To illustrate, let’s analyze two sequences X and Y:

X = ABCBDAB

Y = BDCABA

The longest common subsequence (LCS) between these two is 4. The possible LCSs include BDAB, BCAB, and BCBA.

**2. Longest Common Substring Problem**

Seeking the longest common substring between two strings is a formidable objective that differs from finding the Longest Common Subsequence (LCS). It’s crucial to take into account that substrings need to be consecutive characters in order for them to qualify.

For example, when searching ABABC and BABCA, one of the longest matching strings found would be BABC with length 4. Additionally, other less lengthy corresponding substrings such as ABC, A, AB, B , BA , BC or C can also appear.

**3. The Levenshtein distance (Edit distance) Problem**

Measuring the difference between two strings of text? That’s where Levenshtein distance (or Edit Distance) comes in! This method quantifies how dissimilar two strings are by counting the minimum number of operations needed to change one into another. It does this by determining the minimal edit script or a list of single-character edits, such as insertions, deletions, and substitutions that need to be done, with each operation carrying its own unit cost.

For instance, transforming a kitten into sitting requires 3 single-character edits, which come at a specific cost each – making them invaluable for efficient string comparison!

sitten —> sittin (substitution of i for e)

kitten —> sitten (substitution of s for k)

sittin —> sitting (insertion of g at the end)

**4. Shortest Common Supersequence Problem**

In search for the Shortest Common Supersequence (SCS), you are looking for a sequence Z that is composed of two given sequences X and Y, where both X and Y are subsequences of Z. Unlike substrings, which need to occupy consecutive positions within the original string, subsequences can appear in any order – making SCS all the more challenging to find! For example, if we look at this scenario:

X: ABCBDAB

Y: BDCABA

The resultant supersequence length would be 9 with possible solutions like ‘ABCBDCABA’, ‘ABDCABDAB’, or even ‘ABDCBDABA’.

These are just a few of the most popular dynamic programming problems. There are many more that can be solved using dynamic programming algorithms. By understanding how dynamic programming works and its components, you can identify which dynamic programming algorithm is best suited for any given problem.

## Example of Dynamic Programming

To further understand this concept, let’s look at an example. Suppose you need to calculate the Fibonacci sequence up to the 10th term. We would initially break this problem down into its individual components using the dynamic programming technique—calculating each number from 0 to 10.

**Stage 1: Define**

We need to define our state variables: the length of the sequence and the last term in the sequence.

**Stage 2: Determine**

We need to determine the optimal choice to move from one term to the next. In this case, it is adding the two previous terms to get the current term.

**Stage 3: Find the Solution**

Finally, we use these choices to arrive at an optimal solution (the 10th Fibonacci number).

We can use previously solved solutions from the smaller pieces to develop a larger solution for the overall problem. In this case, each Fibonacci number is calculated based on the previous two numbers in the sequence, so we only need to solve for each number once.

This makes it much faster and easier to arrive at an optimal solution without the requirement to repeat any calculations or perform exhaustive searches of all possible solutions.

## Learn More About Dynamic Programming

Dynamic programming is a significant part of data science analytics and enables programmers to break problems down into simpler parts. If you are an aspiring data scientist and want to enhance your skills further, you can enroll in any of the **coding courses**. They will help you prepare for more significant roles using technology to drive business decisions ahead.

*Write to us at content@emeritus.org*