Dual problem

Okay kiddo, let me explain "dual problem" to you. Imagine you have to solve a problem, but you don't know how to do it. So what can you do? You can try to change the problem a little bit, so that it becomes easier to solve. That's what the dual problem is all about.

Here's an example: Let's say you're given the problem of finding the shortest distance between two cities while passing through three other cities in between. This might be a bit hard to solve! So what can you do? You can transform the problem into its dual form.

The dual form of the problem involves finding the longest path between two points, where the path is only allowed to pass through certain points, like the three cities in our example. Now, you might be wondering why we would want to solve the opposite problem: finding the longest path instead of the shortest one. Well, sometimes it's easier to solve the dual problem instead of the original problem. And once we solve the dual problem, we can use that information to solve the original problem.

So there you have it! The dual problem is like finding a different way to solve a problem that might be easier to handle. By thinking about a problem in a new light, we can come up with different strategies that are more efficient and help us find the solution we need.