Question

What are real-world problems where a recursive approach is the natural solution besides depth-first search (DFS)?

(I don’t consider Tower of Hanoi, Fibonacci number, or factorial real-world problems. They are a bit contrived in my mind.)

Answer 1

There are lots of mathy examples here, but you wanted a real world example, so with a bit of thinking, this is possibly the best I can offer:

You find a person who has contracted a given contageous infection, which is non fatal, and fixes itself quickly( Type A) , Except for one in 5 people ( We’ll call these type B ) who become permanently infected with it and shows no symptoms and merely acts a spreader.

This creates quite annoying waves of havoc when ever type B infects a multitude of type A.

Your task is to track down all the type Bs and immunise them to stop the backbone of the disease. Unfortunately tho, you cant administer a nationwide cure to all, because the people who are typeAs are also deadly allergic to the cure that works for type B.

The way you would do this, would be social discovery, given an infected person(Type A), choose all their contacts in the last week, marking each contact on a heap. When you test a person is infected, add them to the ‘follow up’ queue. When a person is a type B, add them to the ‘follow up’ at the head ( because you want to stop this fast ).

After processing a given person, select the person from the front of the queue and apply immunization if needed. Get all their contacts previously unvisited, and then test to see if they’re infected.

Repeat until the queue of infected people becomes 0, and then wait for another outbreak..

( Ok, this is a bit iterative, but its an iterative way of solving a recursive problem, in this case, breadth first traversal of a population base trying to discover likely paths to problems, and besides, iterative solutions are often faster and more effective, and I compulsively remove recursion everywhere so much its become instinctive. …. dammit! )