A Beginner’s Guide to Dynamic Programming

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Dynamic programming is a computer programming technique used to solve a wide variety of optimization problems. It breaks down a problem into smaller subproblems.

A common misconception about the programming technique is that it is somehow difficult to understand, but in reality, it is quite simple once you get the hang of it. This article will attempt to explain what it is, its features, approaches, benefits, and other aspects.

What is Dynamic Programming?

The concept was first described in the 1950s by Richard Bellman. Although it is a solution to a specific type of problem (optimization problem), it can solve different types of problems too.

Dynamic programming refers to the kind of computer programming in which the program can change during runtime. A major feature of dynamic programming languages is recursion. The entire operation can be performed using recursive functions.

In particular, it is concerned with optimization problems whose solution involves finding and producing an optimal or near-optimal solution to a given optimization problem instance.

It is the practice of delaying some of the computations required to solve a given problem until we already have some of the results of these computations or we can factor out parts of these computations from the rest of the code.

Features

Dynamic programming is very powerful. It allows writing programs that evaluate truth based on input instead of simply printing out a result. Some of its important features are:

  1. It is a process of breaking a complex problem into subproblems. We continue doing so until the subproblems can be solved in isolation.
  2. It solves problems faster and more accurately than any other method.
  3. The programming technique uses a memorized function, which retains its input and output values. It stores the results of subproblems. The process of storing the results of subproblems is known as memoization.
  4. It can be easily adapted to different codebases and doesn’t require compilation.

Approaches

Dynamic programming has many ways to solve a problem. Bottom-up and top-down are its 2 approaches. By studying these approaches, you’ll be able to utilize them in your area of expertise.

1. Top-down

The top-down approach is one of the two fundamental approaches to dynamic programming. Following this approach, we split the DP problem at hand into subproblems by using recursive calls. This is done to solve these subproblems until they become so tiny that they cannot be split into smaller ones.

2. Bottom-up

The bottom-up approach makes it possible to develop the solution step-by-step from the leaves to the root node. On each iteration, some nodes are removed from the problem and not processed further.

Benefits

  • Dynamic programming is the technique of adding functions to a computer language in order to make it more powerful or efficient. The addition of these functions allows the computer to understand and execute more complex functions.
  • It is an approach to computer programming that is more dynamic, or able to change while executing, than static programming. Using the programming technique allows a software program to evolve constantly by adding new capabilities as required without necessarily changing every piece of the code.
  • It is especially important for software systems that are evolving in a dynamically shared space, like a web server or cloud database. Dynamic systems typically use higher-level abstractions and abstract networking procedures from application logic.
  • Dynamic languages are particularly good at producing efficiently runnable applications. This is so because they let you add features at will without having to recompile the entire application whenever we add a new function added or instantiate a new class.

Where to Use It?

Dynamic programming in Excel has been around for years. However, many people have recently begun to use this powerful tool for a wide range of purposes, including data analysis and various creative tasks. The most general use for the programming technique is to create formulae that can run automatically upon meeting certain conditions.

Many businesses use the programming technique in their promotions to automatically send out email offers or text messages when certain conditions are met. Dynamic programming looks simple on the surface but can have very surprising effects. You can use it to sort, filter, and transform data in a huge variety of ways.

Some Real-world Examples of Dynamic Programming

  • Google Maps

It is the quick and most accurate in-car navigator. Google Maps leverages the programming technique to discover the shortest path between the source and the series of destinations out of the several available paths.

  • Networking

The concept also finds use in networking to pass data from a communicator to various receivers in a pre-order manner.

Dynamic Programming Languages

  • C# (through Reflection)
  • Groovy
  • JavaScript
  • Julia
  • Lua
  • Perl
  • PHP
  • Python
  • R
  • Raku
  • Ruby
  • Smalltalk
  • VBScript

Conclusion

Dynamic programming is a very useful technique for solving many of the problems associated with programming. Oftentimes the easiest way to solve optimization problems is by learning the programming technique, and in some cases, a step-by-step process for doing so may be useful. Happy coding!

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