Algorithm for Human Towering

Question

In Cracking the Coding Interview, Fourth Edition, there is such a problem:

A circus is designing a tower routine consisting of people standing atop

Answer 1

For example

(3,2) (5,9) (6,7) (7,8)

Obviously, (6,7) is an unfit item, but how about (7,8)?

In answer to your Question - the algorithm first runs starting with 3,2 and gets the sequence (3,2) (5,9) marking (6,7) and (7,8) as unfit.

It then starts again on (6,7) (the first unfit) and gets (6,7) (7,8), and that makes the answer 2. Since there are no more "unfit" items, the sequence terminates with maximum length 2.