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What is Dynamic Programming ?

 




  • What actually dynamic programming is ?

In computer science or mathematics, dynamic programming is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions. Also known as dynamic optimization.

Dynamic programming is similar to divide and conquer only difference is that dynamic programming is used when there is overlapping subproblem property and in divide and conquer there is no overlapping subproblem property.

example, fibonacci series.

When to use dynamic programming ?

Following two attributes suggests that a problem can be solved using dynamic programming :

  1. optimal substructure
  2. overlapping sub-problems.
  • Ways to of using dynamic programming :
  1. Top-Down : Firstly, Start solving the given problem by breaking it down. If you see that the problem has been solved already, then just return the saved answer. If it has not been solved, solve it and save the answer. This is usually easy to think of and very intuitive. This is referred to as Memoization.
  2. Bottom-Up : Analyze the problem and see the order in which the sub-problems are solved and start solving from the trivial subproblem, up towards the given problem. In this process, it is guaranteed that the subproblems are solved before solving the problem. This is referred to as Tabulation.
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