DECEMBER 8 TH, 2008 Lynbrook Computer Science

Announcements USACO December – tonight! ACSL #1 – next week TopCoder Marathon Match – Wednesday $5000 purse!

USACO: How to stay under time-limit Know when to brute force Use custom tester Identify slowest parts of program

When to brute-force? 1 sec = ~ 1 million operations/iterations Depends on size/complexity of each iteration Plug in max values, determine max possible states that will need to be tested

Example There are P (3 <= P <= 15) people. Given that the productivity of two people Pi and Pj working together is Wi_j (-1000 <= Wi_j <= 1000), what is the most productive group that can be formed? How many states will we need to test, at most?

There are 2^15 = 32,768 possible groups to be formed at most (with 15 people). In each group, each person can either be in the group, or not in the group. Thus with P people the number of possible groups is 2^P. We can brute-force!

USACO Custom Tester USACO allows you to test your program with custom test data Write a program to generate max size test data Run it on USACO server to see if your program is fast enough

Identifying slowest parts of a program Nested loops = BAD! Recursive functions: Check how many times they call themselves. E.g. Flood-fill recursion calls itself 8 times each time (once for each direction)

Improving algorithms? Nested loops: Devise a new algorithm that has fewer nested loops Recursion: Can the solution be found with an iterative algorithm? (Usually, it can)