Stable marriage problem

The Stable Marriage Problem is like a big game of matchmaking! Imagine you have a group of boys and a group of girls who want to get married, but they don't know who to marry. The problem is to find a way to pair them up so that everyone is happy with their match and nobody wants to switch!

To do this, each boy makes a list of the girls he likes in order from most to least, and each girl does the same with the boys. Then, we pair up each boy with his top choice girl and each girl with her top choice boy. Now we have some pairs, but this might not be a stable solution.

Here's where it gets tricky. If there are any boys or girls who would rather be with someone else, we let them "cheat" and swap partners. But we can't just let anyone switch to anyone else willy-nilly – we need to make sure that everyone is still happy with their match.

So we keep letting people switch until no one wants to switch anymore! That means we've found a stable solution. In this solution, each person is with their preferred partner and no one wants to leave their partner for someone else.

This problem is important because it can be applied to many real-life situations where we want to pair up people or things based on their preferences. It's used in everything from matching medical students with residency programs to pairing kidney donors with recipients. By finding a stable solution, we can ensure that everyone involved is satisfied with the outcome!