Lynbrook Computer Science December 8th, 2008
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)