In the computer science world, dynamic programming has been one of the most popular approaches for years. The number of new learners is increasing all these years. As a matter of fact, it is a powerful way of solving complex problems faster. How can you start to learn it yourself? algo.monster will answer these questions.
What is DP?
Dynamic Programming or DP is an algorithmic method for solving a problem. And this involves recursively breaking it down into smaller sub-problems. The ideal solution to each sub-problem determines the optimal solution to the core issue. It is a way to reduce a large problem and solve each sub-problem once, searching for the solution to the larger problem. It always guarantees the best outcomes.
Who developed the concept of the DP algorithm?
Richard Bellman developed the method in the 1950s. In fact, it has been used widely in real life, including in economics and other fields.
Top 5 books about DP for new learners
As a new learner, you may be wondering where to start. Reading books about the concepts and the methods is an ideal option. Masters of dynamic programming wrote many books about DP. Here, we will introduce to you the top 6 on the market for your reference.
Dynamic Programming and Optimized Control, Vol. IV Edition
Dimitri Bertsekas’ Dynamic Programming & Optimal Control prides itself in having special features that make it stand out from the crowd of introductory books on dynamic programming. These topics are presented very clearly in the book:
- Control problems that are deterministic
- Problems with stochastic control
- Pontryagin’s Minimum Principia
It also devotes a whole chapter to sub-optimal controls and related techniques such as:
- Feedback controls for open-loop systems
- Policy with a limited look ahead
- Rollout algorithms
- Model predictive control
The book covers a lot of ground, as you can see. Besides, it is easy to read the book, no matter if you are a graduate student in dynamic programming or a self-learner. This book is useful for mathematicians, control scientists, and anyone who works with systems and control theory. You’ll also be pleased to find that the material is concise and clear.
Algorithm Design Techniques:
(Recursion, Backtracking, Greedy, Divide and Conquer, and Dynamic Programming)
This book from Narasimha Karumanch is an easy-to-read guide that shows you how to apply common algorithms for practical problems coders often face. What’s inside Enumeration possible solutions to the problems. Performance trade-offs between algorithms (time and space complexity) Interview questions about data structures and algorithms. The book explains the concepts in an easy-to-understand way.
Students will be able to use interview questions from actual interviews with different software companies to help them succeed in campus interviews. The book also contains Python-based code samples.
These features make this book unique and outstanding:
- Provide every possible solution to a problem
- Performance trade-offs among algorithms
- Examples of interview questions about algorithms and data structures
- Clear explanations of concepts
- Code examples based on Python
Algorithms Illuminated (Algorithms to NP-Hard Problems)
The fourth book in the series provides a programming language-agnostic introduction to algorithms. Actually, this book includes hints and solutions to all problems. What’s morer, YouTube videos from the author are also included. As a matter of fact, videos and words together make the book easy to understand. The fourth part of the book analyzes algorithmic tools to tackle NP-hard issues, and techniques for fast recognizing NP-hard problems in nature.
Decision Theory
(An Introduction to Dynamic Programming and Sequential Decisions)
Solving optimization-related problems is an interesting topic with various applications. Yet, this allows us to examine multistage decision problems by going backward in time using dynamic programming. Thus, the author explains all the necessary techniques to solve these problems and his fluent style will keep the reader interested in the subject.
Dynamic Programming (Dover Books on Computer Science)
Well, this book was written by the creator of this problem-solving technique. FYI, it’s worth reading. Because this text introduces multistage decision-making processes mathematically. And it uses a functional equation approach to finding optimal policies. Besides, it was written by a prominent developer of such policies and includes a variety of methods, uniqueness, existence theorems, as well as examples of solving the relevant equations. What’s more, it includes existence and uniqueness, the optimal inventory equation and bottleneck problems in multistage production. It also discusses strategies behind multistage games and Markovian decision-making processes.
Dynamic Programming for Coding Interviews (A Bottom-Up approach to problem-solving)
I was interested in computing the 80th term from the Fibonacci series. {I wrote the rampant recursive function, int fib(int n)I wrote the rampant function int fib (int n); return (1==n2==n). 1 : fib(n-1) + fib(n-2); and waited for the result.|1 : fib(1) + fib(2); and waited to see the result.} It takes me so much time to wait. I ended the process and tried to compute the 40th term. It took less than a second. It took me less than a second to check. I was stunned to discover that the above recursive functions were called 204.668,309 times when computing the 40th term. Is it possible to call this function more than 200 million times? Are they scamming the government or performing reporting functions?
DP calculates the 100th Fibonacci term in fractions of a second using a single function call. Thus, it takes linear time and extra memory. However, recursive solutions are not likely to pass all coding competitions. They also don’t impress interviewers for companies like Google and Microsoft. Dynamic programming is the most challenging topic you will meet during interviews and competitions. This book tackles Dynamic Programming head-on. The book begins with simple explanations and then dives deep into complicated DP problems.
Conclusion and suggestions
These books are not just about concepts explaining, practical problems in them help you practice. However, no matter how hard dynamic programming seems, reading books will help you understand it better.
Yet, it requires lots of practice before you become great at it. If you want something more vivid than books, online courses are another choice. Hence, for further information about DP and programming, or coding interviews, Google algo.monster to see what you will get.
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