Improving the Running Time

An easy change to the algorithm improves the running time to .

• How can we make the search for a free man (boy) take constant time?
• How can we implement RANK to run in constant time? It needs to, for example, take a boy b and a girl g and tell us where b is on g's ROL. With some preprocessing, can do this with a single array lookup.

Therefore, each iteration of the while loop takes constant time. Total time.