1. Houyang 3/25/13

2. USACO March Contest Congrats to Johnny Ho for scoring over 900 points in the Gold Division o 7th place in US Kudos to Jonathan Uesato too, for a score of 878 o Almost slayed the Ho

3. Bronze: Breed Proximity N (1 <= N <= 50000) cows in a line. o Each has a breed (breeds are integers 0...1000000) Cows can be crowded: o Two cows of the same breed are said to be "crowded" if their positions within the line differ by no more than K (1 <= K <= N) Find the maximum breed of a pair of crowded cows. Sample: N = 6, K = 3 Breeds: 7 3 4 2 3 4 Output: 4

4. Bronze: Breed Proximity Solution Iterate over the cows from left to right. For each breed, store the position of the last cow of that breed. o Use an array, because 1000000 is small enough. o Could also use a map. Runtime: O(N)

5. Silver/Gold: The Cow Run N (1 <= N <= 1000) cows on a number line. o Each has a coordinate P (|P| <= 500000) o Each minute, a rampaging cow causes one dollar worth of damage. Farmer John can walk over to a cow and calm it. o He starts at the origin and walks 1 unit per minute. Farmer John wants to minimize the total damage. Compute the minimum. Sample: N = 4 Positions: -2, -12, 3, 7 Output: 50 (visit -2, then 3, then 7, then -12)

6. Silver/Gold: The Cow Run Solution Separate the cows into two arrays: positive / negative coordinates. Sort each. Then "merge" the two arrays, visiting the next positive or next negative cow each step. After N steps, all cows will be calmed. DP state: #negative cows, #positive cows, and a flag to represent FJ's location o If flag is 1, FJ is on the positive side. o Else, FJ is on the negative side. This is O(N^2).

7. Gold: Necklace Bessie has string A of length N (N <= 10000) and string B of length M (M <= 1000) Bessie wants to remove some characters from A so that B is not a substring of A. Find the minimum number of characters to remove. Sample: A = ababaa, B = aba Output: 1. (remove an a to make abbaa)

8. Gold: Necklace Solution DP State: Position in A, Position in B To transition in amortized O(1), use a KMP string matching algorithm failure function table. Each step, you can either keep the character in A, or delete it. o If you delete it, Position in B doesn't change. o If you keep it, you compute the new position in B using the table. O(NM) states.

9. POTW You have N nodes, M bidirectional edges. How many groups of 3 nodes are all connected to each other or all not connected? Input Format: o Line 1: N, M o Line 2...M+1: a, b: edge from a to b (1 <= a,b <= N) Sample: N = 6, M = 3 Edges: 1 2, 1 3, 2 3 Output: 2 (123 are all connected, 456 are all not) Constraints: 1 <= N,M <= 100000 o Partial Credit if it passes for small cases.