Dynamic Programming

Dynamic Programming vs. D&C, Recursion, and Memoization 

Dynamic programming is becoming increasingly popular as a key technique for solving problems in computer science. This programming is becoming more popular among young people, whether they are looking for work or simply to improve their skills. Some people aren’t familiar with the basics of dynamic programming. This article is for beginners who want to learn about dynamic programming. Hopefully, also. monster will help you with your dynamic programming study.

Who invented the DP technique?

Richard Bellman, an American pioneer in dynamic programming, created it in the 1950s. We know from his autobiography that he used the name “dynamic” to refer to the time-varying aspects of the problems. He thought it was a great name.

The name DP is a bit misleading. Programming in DP does not refer to the actual act of creating computer codes. It refers to the decision or optimization it makes. This is something that many people don’t realize.

Dynamic programming (What is it and what does it do?)

When you search on Google, the Wikipedia definition will be available. Here’s my explanation if you have difficulty understanding its meaning. DP stands for dynamic programming. It is an algorithmic technique. It is an algorithmic technique that solves certain types of complex problems. DP divides the main problem into smaller pieces called sub-problems. It has two distinct characteristics: optimal substructures and sub-problems that overlap. Besides, it is considered one of the most effective strategies to solve optimization-related problems.

Two features of dynamic programming

DP is composed of two main characters: overlapping sub-problems and optimal substructures.

  • Sub-problems that overlap: The problem can be broken down into smaller, similar sub-problems. These sub-problems can overlap. These sub-problems will need to be computed multiple times.
  • The optimal substructures are the ones that provide the best solution to all sub-problems.

Two approaches to DP

These are the two methods for the DP technique.

  • Starting from the top: top-down using memoization

The natural way to solve problems is by using the top-down approach. The top-down method involves breaking down complex problems into smaller parts. We then solve the larger target by finding recursive solutions to smaller sub-problems. We use memoization to store previously calculated results for future reference. The cached result can be used for future use if the sub-problems are the same. This allows us to save time and avoid repeating the calculation.

  • Beginning from the bottom: tabulation in the bottom-up approach

The Bottom-up approach is to move upwards from the bottom. This is the opposite of top-down. This approach starts with the smallest sub-problem. The smaller sub-problems are dealt with first, and then the larger ones until the entire problem is resolved.

How can you tell if you can solve a problem using DP?

Unluckily, DP cannot solve all problems. What problems can DP solve? It is important to ensure that these issues have overlapping sub-problems as well as optimal substructures. It’s a complex problem that can be broken down into sub-problems. There is recursion, repeated computation. DP allows you to save your solved problems and reuse them the next time the problem arises. This is where you will reap the benefits of DP.

Do we use DP to solve problems in life?

DP’s primary function is to stop you from doing repetitive work. DP saves the solution to sub-problems so that you don’t have the same problem again. This speeds up the algorithm and increases your performance.

Dynamic programming is a way to determine the shortest distance between two points in real life. Google Maps actually does the same thing through dynamic programming.

Dynamic programming can solve a classic problem

Problem with the Knapsack: A bag is too heavy to carry on a long trip. Your bag is limited in size. You need to maximize the number of items you bring. How do you choose which items to bring? It is important to be efficient and not lose out on the most important.

Besides, scientists also use DP in other areas such as Genetics and Financial Optimizations.

Memoization and DP

Both dynamic programming and memorization only calculate sub-problems once.

You can see memoization as a top-down optimization of dynamic programming algorithms that relies on recursion, is a method to memorize.

The method of memoization allows you to save sub-problems in caches, so you can only calculate it once. You can always use the existing solution if you see the sub-problem repeats. DP is a problem-solving strategy that uses memoization to its maximum effect. 

Recursion and dynamic programming algorithm

Recursion is a result of a top-down approach. It calls itself again. Some people view dynamic programming as recursion and memoization. It saves time because DP saves results for future reference.

Sometimes, recursion solves the same sub-problems again. DP increases efficiency by avoiding recalculation.

Dynamic programming, recursion or divide and conquer?

Recursion and dynamic programming both divide a problem into smaller sub-problems. Recursion and DP are both forms of divide-and-conquer. Both can only solve sub-problems once.

  • Divide and conquer breaks down a major problem into smaller problems. It then conquers each sub-problem by solving them recursively. Then, you solve the goal issue by combining all the sub solutions.
  • DP solves the problem by dividing it into smaller problems in an efficient way. You can then solve the problem using the stored results from the sub-problems.

The major difference between DP and D&C:

  • The divide and conquer algorithm is different in that the sub-problems do not overlap. This means that each sub-problem is an independent, individual problem. It solves each sub-problem only once, just like DP. Similar to DP, each sub-problem is the same. However, all previous results are saved so you can only solve each sub-problem once.

Conclusion

Some belief that divide and conquer plus memoization equals top-down dynamic programming. Also, DP is just recursion minus repetition. To some extent, I believe they’re right. What’s your idea?

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