The teacher runs an after$-$school computing club and stores the names of children who belong to this club in a list, which at present is unsorted.

She is considering ways to sort the list and is interested in a sorting algorithm she has recently heard about and which is new to her. The algorithm is called exchange sort, and she explains it like this.

In the first pass through the list you compare the name at position $1$ with that at position $2$: if they are out of order then you swap them. Then you compare the name at position $1$ with that at position $3$: if they are out of order then you swap them, and so on for the names at positions $4,5$ etc. You continue in this way until the name at position $1$ has been compared with the name at all other positions and swapped whenever necessary. When the first pass is complete the name that ends up at position $1$ will be the first in alphabetical order.

The second pass is similar, except that you begin with the name at position $2,$ comparing it with the names at positions $3,4$ etc. When pass two is complete the names at $1$ and $2$ will be the first and second in alphabetical order.

In the third pass you compare the name at position $3$ with those at positions $4,5$ etc. When pass three is complete the names at $1,2$ and $3$ will be the first, second and third in alphabetical order.

Continuing in this way we will eventually compare the name in the next$-$to$-$last position with that in the last position, swapping them if necessary, and at that point the entire list will be sorted.

This might sound a bit like bubble sort at first but if you look at the pairs that are compared in the first pass you can see that the pattern of comparisons is quite different.