What is dynamic programming and how does it work?

What is dynamic programming and how does it work?

Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable when the subproblems overlap, allowing for the reuse of previously computed results.

Can you give me an example of a problem that can be solved using dynamic programming?

Sure! A classic example is the Fibonacci sequence. Instead of calculating each Fibonacci number recursively, which can be inefficient, dynamic programming allows us to store previously calculated values to avoid redundant calculations.

What are the main characteristics of problems that can be solved with dynamic programming?

The main characteristics are optimal substructure and overlapping subproblems. Optimal substructure means that the optimal solution to a problem can be constructed from optimal solutions of its subproblems. Overlapping subproblems mean that the same subproblems are solved multiple times.

How does dynamic programming differ from divide and conquer?

Dynamic programming solves overlapping subproblems by storing results, while divide and conquer breaks problems into independent subproblems and solves them separately. Dynamic programming is more efficient for problems with overlapping subproblems.