IterationIteration in practice: Cleaning teeth

A simple algorithm can be created for cleaning teeth. Suppose a person has ten top teeth. To make sure that every one of the top teeth is cleaned, the algorithm would look something like this:

1. put toothpaste on toothbrush
2. use toothbrush to clean tooth 1
3. use toothbrush to clean tooth 2
4. use toothbrush to clean tooth 3
5. use toothbrush to clean tooth 4
6. use toothbrush to clean tooth 5
7. use toothbrush to clean tooth 6
8. use toothbrush to clean tooth 7
9. use toothbrush to clean tooth 8
10. use toothbrush to clean tooth 9
11. use toothbrush to clean tooth 10
12. rinse toothbrush

Steps 2 through to 11 are essentially the same step repeated, just cleaning a different tooth every time. Iteration can be used to greatly simplify the algorithm. Look at this alternative:

1. put toothpaste on toothbrush
2. use toothbrush to clean a tooth
3. move onto next tooth
4. repeat steps 2 and 3 until all teeth are clean
5. rinse toothbrush

This algorithm is much simpler. However, there is a problem – how do we know when all teeth are clean (step 4)? A condition is needed to solve this problem.