What are the differences in complexity between greedy and dynamic programming?

What are the differences in complexity between greedy and dynamic programming?

Greedy algorithms make the locally optimal choice at each stage, while dynamic programming solves problems by breaking them down into simpler subproblems. This often leads to different time complexities.

Can you give an example of a problem where greedy is better than dynamic programming?

Sure! The activity selection problem is a classic example where a greedy approach is optimal, as it selects the next activity that finishes the earliest.

What about a problem where dynamic programming is necessary?

The knapsack problem is a great example. A greedy approach won't always yield the optimal solution, but dynamic programming can find the best combination of items.

How do I determine which approach to use for a given problem?

You can analyze the problem's structure. If it has overlapping subproblems and optimal substructure, dynamic programming is likely the way to go. Otherwise, a greedy approach might suffice.