adventofcode/2016/day13/problem

Advent of Code

--- Day 13: A Maze of Twisty Little Cubicles ---

   You arrive at the first floor of this new building to discover a much less
   welcoming environment than the shiny atrium of the last one. Instead, you
   are in a maze of twisty little cubicles, all alike.

   Every location in this area is addressed by a pair of non-negative integers
   (x,y). Each such coordinate is either a wall or an open space. You can't
   move diagonally. The cube maze starts at 0,0 and seems to extend infinitely
   toward positive x and y; negative values are invalid, as they represent a
   location outside the building. You are in a small waiting area at 1,1.

   While it seems chaotic, a nearby morale-boosting poster explains, the layout
   is actually quite logical. You can determine whether a given x,y coordinate
   will be a wall or an open space using a simple system:

     • Find x*x + 3*x + 2*x*y + y + y*y.

     • Add the office designer's favorite number (your puzzle input).

     • Find the binary representation of that sum; count the number of bits
       that are 1.

          • If the number of bits that are 1 is even, it's an open space.
          • If the number of bits that are 1 is odd, it's a wall.

   For example, if the office designer's favorite number were 10, drawing walls
   as # and open spaces as ., the corner of the building containing 0,0 would
   look like this:

   0123456789
 0 .#.####.##
 1 ..#..#...#
 2 #....##...
 3 ###.#.###.
 4 .##..#..#.
 5 ..##....#.
 6 #...##.###

   Now, suppose you wanted to reach 7,4. The shortest route you could take is
   marked as O:

   0123456789
 0 .#.####.##
 1 .O#..#...#
 2 #OOO.##...
 3 ###O#.###.
 4 .##OO#OO#.
 5 ..##OOO.#.
 6 #...##.###

   Thus, reaching 7,4 would take a minimum of 11 steps (starting from your
   current location, 1,1).

   What is the fewest number of steps required for you to reach 31,39?

   Your puzzle answer was 86.

   The first half of this puzzle is complete! It provides one gold star: *

--- Part Two ---

   How many locations (distinct x,y coordinates, including your starting
   location) can you reach in at most 50 steps?

   Your puzzle input is still 1364.

   Answer: 127

References

   Visible links
   . http://adventofcode.com/
   . http://adventofcode.com/2016/about
   . http://adventofcode.com/2016/support
   . http://adventofcode.com/2016/events
   . http://adventofcode.com/2016/settings
   . http://adventofcode.com/2016/auth/logout
   . http://adventofcode.com/2016
   . http://adventofcode.com/2016
   . http://adventofcode.com/2016/leaderboard
   . http://adventofcode.com/2016/stats
   . http://adventofcode.com/2016/sponsors
   . http://adventofcode.com/2016/sponsors
   . https://en.wikipedia.org/wiki/Binary_number
   . https://en.wikipedia.org/wiki/Bit