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I couldn’t think of anything to put here.

I couldn’t think of anything to put here. So have a cow. Or two. PotW Solution. Problem recap: Determine the ancestors of a node in an organization graph. Given a list of employee to boss relationships and a list of queries, determine who must obey whom from the list of queries.

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I couldn’t think of anything to put here.

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  1. I couldn’t think of anything to put here. So have a cow. Or two.

  2. PotW Solution Problem recap: • Determine the ancestors of a node in an organization graph. • Given a list of employee to boss relationships and a list of queries, determine who must obey whom from the list of queries.

  3. PotW Solution HashMap<String, String> boss = newHashMap<String, String>(); intgroupN = scan.nextInt(); for (inti = 0 ; i < groupN; i++) { intemployeeN = scan.nextInt(); String curBoss = scan.next(); for (int j = 0; j < employeeN; j++) { boss.put(scan.next(), curBoss); } } intqueryN = scan.nextInt(); for (inti = 0 ; i < queryN; i++) { String x = scan.next(), y = scan.next(); booleanisBoss = false; while (!isBoss && boss.containsKey(x)) { x = boss.get(x); isBoss = x.equals(y); } if (isBoss) { System.out.println("yes"); } else { System.out.println("no"); } }

  4. Gunn Programming Contest • Was last Saturday! • A Lynbrook team placed first! Congratulations to: • Steven Hao • Tony Jiang • Qingqi Zeng • Missed the Gunn contest? Fear not, because there’s still…

  5. Harker Invitational • March 17, 9AM – 4PM • Participation worth 30 points PotW credit (subject to change) • Register at http://bit.ly/harkerproco12 • Registration deadline - March 10 • If anyone’s has a parent willing to chaperone, email us (officers@lynbrookcs.com)!

  6. March USACO • Is this coming weekend (March 2-5) • You know what that means! • (yes, the usual 5 points PotW credit for a 3-hour contest) • Take it!

  7. February USACO Problems I could have used this on the title slide…

  8. Bronze – Rope Folding • Farmer John has a rope of length L (1 <= L <= 10,000) with N (1 <= N <= 100) knots tied at distinct locations, including at its two endpoints. • Count the number of locations where the rope can be folded such that the knots on opposite strands all line up exactly with each other. Example:

  9. Rope Folding - Solution • Sort the knot locations, build an array of differences • 0, 2, 4, 6, 10 would become 2, 2, 2, 4 • Any prefix or suffix of the difference array that is a palindrome corresponds to a valid fold (ex: 2, 2; 2, 2, 2) • Bounds are small enough to brute force check for palindromes

  10. Silver – Overplanting • Given N (1 <= N <= 1000) different axially-aligned, possibly overlapping rectangular regions (all coordinates between -108 and 108), determine the total area covered by these regions. (Result may be larger than a 32-bit int)

  11. Overplanting - Solution • Use a “sweep line” approach: • Sort all y-coordinates in scene, divide space into horizontal “slices” • Store the height of each slice as well as an “overlap count” for each slice • Sort all x-coordinates, sweep across plane from left to right • When leading vertical edge of rectangle hit, increment “overlap count” of all slices covered by rectangle • When trailing vertical edge hit, decrement overlap counts • Maintains current number of “active” rectangles within each slice • To compute total area, add up area of slices w/ positive overlap counts

  12. Gold – Symmetry • How many lines of symmetry are there between N < 1000 cows (with integer coordinates) on the 2D plane? First, how do we check if a certain line works? • Given a line, use vector geometry to reflect each point P over to a point Q • Use a set to check if point Q exists quickly • Let m be the center of mass of the points • Then simply check every line PM • In order to take care of special cases, also check the line that goes through M and is perpendicular to PM

  13. PotW– Juggling • 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.

  14. Juggling (cont.) • Example Input:33 2 1 • Output:6 • For 25 points, solve for N < 1,000 • For 50 points, solve for N < 100,000 • Time limit: 2 seconds

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