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 _____.

   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: _____________________

References

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   . https://en.wikipedia.org/wiki/Binary_number
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