Dynamic problem (algorithms)

Imagine you are playing a game where you have to climb up a mountain. But here's the tricky part - the mountain is filled with obstacles like rocks and cliffs. You want to find the best way to reach the top without falling or getting stuck.

To tackle this problem, you can break it down into smaller parts. Instead of looking at the whole mountain at once, you focus on each step. You start at the very bottom and figure out the best way to take the first step. Once you've figured that out, you move on to the second step, and then the third, and so on.

The cool thing is that as you take each step, you remember the best way to get there. So, when you're deciding how to take the second step, you already know the best way to reach the first step. This way, you don't have to re-think everything from the beginning each time.

This strategy of breaking down a big problem into smaller sub-problems and remembering the solutions for future steps is called dynamic programming.

In our climbing game example, you can think of dynamic programming as a way to save time and effort. By reusing the solutions found for smaller steps, you can quickly find the best way to climb the entire mountain.

Dynamic programming is used in many areas, not just games. It's especially useful for solving problems that can be broken down into smaller, overlapping sub-problems. By solving and remembering these sub-problems, you can find the overall solution more efficiently.