Often people come up with new algorithms by taking inspiration from existing ones. For example, someone might see a sorting algorithm and think of a way to impr

Often people come up with new algorithms by taking inspiration from existing ones. For example, someone might see a sorting algorithm and think of a way to improve it, or they might see a search algorithm and think of a way to make it more efficient. There's no one way to design an algorithm, so it's often a matter of trial and error until something works well. One more thing: Don't forget that a lot of the time, people don't come up with new algorithms, they just implement existing ones. So while someone might not be coming up with a new algorithm, they might be coming up with a new way to implement an existing algorithm that is more efficient or more effective in some way.