Algorithmic way of Sorting

One approach (not necessarily best) uses the following main idea.

Check for out-of-order pairs and swap them!

What is an out-of-order pair?

• Compare $a(i)$ with $a(i+1)$.
• More general: compare $a(i)$ with $a(j)$ for some pair $i,j$ with $i < j$.

Variants of the ``bubble sort'' approach.

Let the biggest number sink to bottom (alternatively- let smallest number ``bubble'' to top).