## Tournament rankings – a K-ary sort problem

I was working on some programming projects then I suddenly got stuck at a particular problem that took me a whole day still unable to solve. When simplified, it looks like this:

**Background**

Consider a tournament where we want to find out the ranking of N contestants. In each competition, M contestants compete with each other at the same time to generate a ranking order. How many such competitions S are required in the tournament to fully rank all contestants given M” title=”N => M”/>?

Did some search online and it turns out that this is an ongoing research problem more officially known as the K-ary sort algorithm, although the it is formulated slightly differently where (which would become regular binary sort) and .

There are a few things that are obvious:

1. Inherently at atomic level, the act of ranking involves comparing 2 contestants, which is a binary case.

2. We do not need every contestant to have had competed with every other contestant. Between 2 contestants, the winner wins every other person that the loser wins and vice versa.

3. We must have information of combination(N, 2) rankings between any 2 contestants.

To be continued…

#### Jake See

Jake See is the thinker, philosopher and a source of new perspectives, and sometimes controversies, for his family and people around him. Jake currently earn his living as an IT Professional, juggling both technical and business aspects of his trade as an employee and freelancer. He has more than 16 years of experience in Business Analysis, Software Engineering, Project Management and Business Development.