Can you give another example of dynamic programming?

Can you give another example of dynamic programming?

Sure! One classic example is the Fibonacci sequence. Instead of calculating each Fibonacci number recursively, which can be inefficient, we can use dynamic programming to store previously calculated values.

How does that work exactly?

We can use an array to store Fibonacci numbers. For instance, we start with F(0) = 0 and F(1) = 1, then calculate F(n) = F(n-1) + F(n-2) iteratively, storing each result.

What are the benefits of using dynamic programming for this?

The main benefits are improved efficiency and reduced time complexity. Instead of exponential time, we can achieve linear time complexity, making it much faster for larger values of n.

Are there other problems where dynamic programming is useful?

Absolutely! Problems like the Knapsack problem, longest common subsequence, and matrix chain multiplication are all great examples.