As a reminder from last week, officer applications can be found here, and should be emailed to the officer team by the end of Monday, May 14. Good luck!

Last but not least, as many of you know already, it’s that time of the year! Officer applications for the 2012-2013 school year are now available here. Applications are due at the end of Monday, May 14, and should be submitted to officers [-at-] lynbrookcs [-dot-] com. The new officer team will be announced on May 23. Good luck everyone!

• Write a Befunge program that prints out a Brain**** program that prints out a HQ9+ program that prints out “Hello, world!”.
• Worth 30 points. The shortest version (in terms of non-whitespace characters) will receive 5 bonus points.
• As an easier version, for 15 points, write a Brain**** program that prints out a HQ9+ program that prints out “Hello, world!”.
• For access to compilers, use http://codeforces.com/problemset/customtest and http://ideone.com/
  We will be using the same system, so if your code works on it, it should easily get the points.
  Note that all of these programming languages work with ASCII values for representing characters.

Lastly, remember to take the last round of USACO this weekend and register for ProCo at http://proco.stanford.edu.

New PotW:

• Given a set of N cows on the 2D plane, find the closest pair of cows in terms of Euclidean distance (conveniently named Steven and Julia).
• For 20 points, N < 1000. For 45 points, N < 100,000.
• Input:            Output:
  3                   0 0 (Julia)
  0 0                1 3 (Steven)
  1 3
  4 0
• The pair will be unique, but since they are indistinguishable, their order does not matter.

Today we talked about cryptography, the science of information security. It is really interesting because it existed since ancient times. More details on the various types of cryptography and cracking ciphers can be found in our meeting slides.

Our new PotW is as follows:

• A repeating XOR cipher works by taking the key and XOR-ing every element with the corresponding element of the input to produce the output. If the input is longer than the key, you restart at the beginning of the key.
• E.g.: given a key of {1, 2}, and input of {3, 4, 5}, you get an output of {3 ^ 1, 4 ^ 2, 5 ^ 1} = {2, 6, 4}, where “^” is the XOR operator.
• Given corresponding input and output of length N, there may be multiple possible keys. Find all possible lengths of the key. Assume the key is at most N long.
• N < 500: worth 30 points
  N < 50,000: worth 50 points
  Time limit: 1 sec.
• Sample Input:
  5 (N)
  3 10 5 5 2 (input – integers within [0, 255])
  2 8 4 7 3 (output – integers within [0, 255])
• Sample Output:
  2 4 5
  Explanation: The key may be {1, 2}, {1, 2, 1, 2}, or {1, 2, 1, 2, 1}.
• Hints can be found in our meeting slides.

There is no PotW this week since many will be busy participating in HPI.

Meeting slides can be found here.

• Returning from your most recent adventures, you have noticed that there has been some pretty ridiculous inflation in the shop. Given N < 50 pieces of equipment available in the shop, maximize the total power of items you can buy with your X < 10^12 hard-earned coins. Each piece of equipment costs C < 10^10 and gives you P < 10^10 power, and you can only buy each at most once.
• Worth 40 points. If your answer is within 5% of the answer our awesome program gives, it will be deemed correct.
• Time limit: 2 seconds
• Sample Input:
  6 9001 (N, X)
  8980 3 (C, P)
  8940 2
  10 3
  20 4
  30 5
  40 6
• Sample Output:
  2 3 4 5 (indices of the bought items, not necessarily in order)

Lastly, sign up for Harker at http://bit.ly/harkerproco12 if you haven’t already.

Today we went over solutions to one bronze, one silver, and one gold division problem from the last USACO. We also went over the solution to last week’s PotW, and introduced the new problem, which is as follows:

• Bessie the cow is performing an elaborate juggling act that requires her to juggle many objects, but now that the act is ending, she needs to drop them in a certain order.
• Given the current order of the N objects, tell her how many moves she needs to drop all of the objects. A “move” is a left cyclic shift.
• For example, {3, 2, 1} is juggled to become {2, 1, 3}, {2, 1, 3} becomes {1, 3, 2}, 1 is dropped to make {3, 2}, which becomes {2, 3}, which becomes {3}, which becomes {}: 6 moves.
• Example Input:
  3
  3 2 1
• Output:
  6
• For 25 points, solve for N < 1,000
• For 50 points, solve for N < 100,000
• Time limit: 2 seconds
• Meeting slides can be found here.

Just a reminder to sign up for HPI at http://bit.ly/harkerproco12 by March 10th. The actual competition will be on March 17 from 9am to 4pm. We will be having a chaperone, so you guys can just put N/A under the chaperone section.

• Gunn Programming Contest

• Sign up at bit.ly/gunnproco12
• February 25th, 9am – 3pm

• Harker Invitational

• Sign up at bit.ly/harkerproco12
• March 17th, 8:30am – 3:30pm

Our full solution to last week’s PotW can be found at http://ideone.com/iC4F6, and our meeting slides can be found here. Today we presented some problems from last year’s Harker Invitational. If you wish to take a closer look to practice, the entire problem set can be found here.

The new PotW(9.2 from the packet) is as follows:

• Determine the ancestors of a node in an organization graph. Given a list of employee to boss relationships and a list of queries, determine which of the queries must be satisfied.  Each organizational line is composed of one team: the first element will be the number of employees in the group, the first name will be the boss, and each following name will be the direct employees. Each query is composed of two people: X and then Y. Determine if X must obey Y.
• The input is guaranteed to be valid: there will be no cyclic relationships, and all names will correspond properly.
• # of employees < 1000
• # of queries < 1000
• Worth 25 points
• Sample Input:
  4 (# of groups)
  2 BigBoss Amy Fred
  3 Amy Wilson Stoker Bubba
  4 Wilson James Marc Tim Alan
  2 Fred Wilma Dino
  3 (# of queries)
  Alan Dino
  Alan BigBoss
  Wilson James
• Sample Output:
  no
  yes
  no

• When: Feb. 25, 9AM – 3PM
• Teams of up to 3
• 2 hour round, 12 problems
• Will be worth PotW credit

The meeting discussion was on data compression. The presentation primarily focused on two different variations: loseless and lossy. Our meeting slides can be found here, and this week’s PotW is as follows:

• As part of a new compression algorithm, Bessie is trying to modify a sequence of data of length N so that it contains at most K distinct values. However, it costs |a – b| additional bits to change an integer a into an integer b. Tell her the optimal sequence she should modify the original sequence into. If there are multiple solutions, output any.
• For 30 points, solve for N < 20.
  For 50 points, solve for N < 100.
  For bragging rights, solve for N < 1000.
• Time Limit: 2 seconds.
  Note: The second and third tasks are very difficult
• Sample Input #1:
  3 2 (N K)
  7 6 3 (elements of the original sequence)
  Output:
  1 (minimal cost is 1)
  6 6 3 (7 7 3 is another option)
• Sample Input #2:
  7 2
  3 4 5 6 9 10 11
  Output:
  6
  4 4 4 4 10 10 10 (5 5 5 5 10 10 10 is another option)