DP Introduction
Dynamic Programming (DP) is a method for solving complex problems by breaking them down into simpler subproblems, solving each subproblem only once, and storing the results. It is used when a problem has overlapping subproblems and optimal substructure.
Key concepts:
- Overlapping Subproblems – The same subproblem appears multiple times.
- Optimal Substructure – The optimal solution to a problem can be constructed from optimal solutions of its subproblems.
DP can be implemented in two ways:
- Top-Down (Memoization) – Recursive with caching.
- Bottom-Up (Tabulation) – Iterative, building from base cases.
Example: Fibonacci numbers – we'll see both approaches in the next chapters.
Two Minute Drill
- DP solves problems by storing results of subproblems.
- Overlapping subproblems and optimal substructure are required.
- Two approaches: top-down (memoization) and bottom-up (tabulation).
- DP is used for optimization problems (min/max, count, yes/no).
Need more clarification?
Drop us an email at career@quipoinfotech.com