The SECOND Meeting Or: How I learned exciting new things in CS Club

As you all know… The best way to learn is to do. o It’s true! Thus we will be giving you awesome problems to do o They’re awesome! o There’ll be one each week! o Thus they’re called Problems of the Week! (PotW) Concepts and tricks for USACO and other contests! Prizes!

The PotW Process* Problem presented at meeting o Will be posted online Submit solutions to by 11:59PM the day before the next o Feel free to give any feedback about difficulty o Or suggest your own problems Solution presented at next meeting o Will be posted online after it’s presented See how you and others are doing at lynbrookcs.com! lynbrookcs.com Prizes at end of semester! *subject to change

The Problems Any programming language accepted Graded based on guidelines specified in problem o Officers reserve the right to grade as they please :] Console input/output (System.in, System.out) unless otherwise specified Java input: Use Scanner (easier) or BufferedReader (faster)

Reading Input in JAVA import java.io.*; import java.util.*; Scanner s = new Scanner(System.in); int n = s.nextInt(); BufferedReader r = new BufferedReader( new InputStreamReader(System.in)); int n = Integer.parseInt(r.readLine());

PotW #1: The Ninja Cow Farmer John (get used to the cow theme) has quite a few cows, "conveniently" numbered 1 to N, inclusive. Except, one day, one cow became a ninja and "disappeared" from the herd. Your job is to figure out which cow became a ninja. To avoid arousing the suspicions of the ninja cow, you cannot use arrays, you cannot use longs, and you cannot allow integer overflow. For 10 points, implement your solution for N = 3 For 15 points, implement your solution for 2 ≤ N ≤ 1000 For 20 points, implement your solution for 2 ≤ N ≤ 10 6 Sample Input: Sample Output: 4 (number of cows) 2 (ID of ninja cow) 3 (1st visible cow) 4 (2nd) 1 (etc.)

Hints Note that the input list is not always going to be sorted Note that completing a later task encompasses previous tasks For the first task, “if” statements will work For the second task, calculate the missing cow by using sums o You'll need a "for" loop and a sum variable o Hint: N-1 + N For the third task, you can't use sums anymore because that would overflow an int (and long is not allowed) o The limit of a signed int is o Instead, use the xor operator: “^” instead of “+” o Hint: (a^b)^b always equals a