Added day 18 problem

2016/day18/problem

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+Advent of Code
+
+--- Day 18: Like a Rogue ---
+
+   As you enter this room, you hear a loud click! Some of the tiles in the floor here seem to be
+   pressure plates for traps, and the trap you just triggered has run out of... whatever it tried
+   to do to you. You doubt you'll be so lucky next time.
+
+   Upon closer examination, the traps and safe tiles in this room seem to follow a pattern. The
+   tiles are arranged into rows that are all the same width; you take note of the safe tiles (.)
+   and traps (^) in the first row (your puzzle input).
+
+   The type of tile (trapped or safe) in each row is based on the types of the tiles in the same
+   position, and to either side of that position, in the previous row. (If either side is off
+   either end of the row, it counts as "safe" because there isn't a trap embedded in the wall.)
+
+   For example, suppose you know the first row (with tiles marked by letters) and want to
+   determine the next row (with tiles marked by numbers):
+
+ ABCDE
+ 12345
+
+   The type of tile 2 is based on the types of tiles A, B, and C; the type of tile 5 is based on
+   tiles D, E, and an imaginary "safe" tile. Let's call these three tiles from the previous row
+   the left, center, and right tiles, respectively. Then, a new tile is a trap only in one of the
+   following situations:
+
+     • Its left and center tiles are traps, but its right tile is not.
+     • Its center and right tiles are traps, but its left tile is not.
+     • Only its left tile is a trap.
+     • Only its right tile is a trap.
+
+   In any other situation, the new tile is safe.
+
+   Then, starting with the row ..^^., you can determine the next row by applying those rules to
+   each new tile:
+
+     • The leftmost character on the next row considers the left (nonexistent, so we assume
+       "safe"), center (the first ., which means "safe"), and right (the second ., also "safe")
+       tiles on the previous row. Because all of the trap rules require a trap in at least one of
+       the previous three tiles, the first tile on this new row is also safe, ..
+     • The second character on the next row considers its left (.), center (.), and right (^)
+       tiles from the previous row. This matches the fourth rule: only the right tile is a trap.
+       Therefore, the next tile in this new row is a trap, ^.
+     • The third character considers .^^, which matches the second trap rule: its center and
+       right tiles are traps, but its left tile is not. Therefore, this tile is also a trap, ^.
+     • The last two characters in this new row match the first and third rules, respectively, and
+       so they are both also traps, ^.
+
+   After these steps, we now know the next row of tiles in the room: .^^^^. Then, we continue on
+   to the next row, using the same rules, and get ^^..^. After determining two new rows, our map
+   looks like this:
+
+ ..^^.
+ .^^^^
+ ^^..^
+
+   Here's a larger example with ten tiles per row and ten rows:
+
+ .^^.^.^^^^
+ ^^^...^..^
+ ^.^^.^.^^.
+ ..^^...^^^
+ .^^^^.^^.^
+ ^^..^.^^..
+ ^^^^..^^^.
+ ^..^^^^.^^
+ .^^^..^.^^
+ ^^.^^^..^^
+
+   In ten rows, this larger example has 38 safe tiles.
+
+   Starting with the map in your puzzle input, in a total of 40 rows (including the starting
+   row), how many safe tiles are there?
+
+   Your puzzle answer ________.
+
+--- Part Two ---
+
+   How many safe tiles are there in a total of 400000 rows?
+
+   Your puzzle answer was ________.
+
+References
+
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+   . https://nethackwiki.com/wiki/Trap
+   . http://adventofcode.com/2016
+   . http://adventofcode.com/2016/day/18/input