Approaches in Dynamic Programming

Approaches in Dynamic Programming

There are two main approaches to solving DP problems:

• Top-Down Approach (Memoization):

  In this approach, you start with the main problem and recursively break it down into subproblems. When you solve a subproblem, you store its result in a data structure (usually an array or hash table) so that the next time you need to solve the same subproblem, you can retrieve the stored result instead of recalculating it.

  • Pros: Easier to implement, especially for problems where the recursive structure is clear.
  • Cons: Can have higher space complexity due to the recursion stack, and there might be overhead from recursive calls.

  Example: Fibonacci sequence calculation using memoization.

• Bottom-Up Approach (Tabulation):

  In this approach, you solve all possible subproblems first, typically in a tabular format. You start with the smallest subproblems and work your way up to the main problem, filling in a table (usually an array) with the solutions to subproblems.

  • Pros: Generally more space-efficient and avoids the overhead of recursive calls.
  • Cons: Can be less intuitive to implement for some problems compared to the top-down approach.

  Example: Solving the 0/1 Knapsack problem using tabulation.