Advent of Code

--- Day 22: Mode Maze ---

   This is it, your final stop: the year -483. It's snowing and dark outside;
   the only light you can see is coming from a small cottage in the distance.
   You make your way there and knock on the door.

   A portly man with a large, white beard answers the door and invites you
   inside. For someone living near the North Pole in -483, he must not get many
   visitors, but he doesn't act surprised to see you. Instead, he offers you
   some milk and cookies.

   After talking for a while, he asks a favor of you. His friend hasn't come
   back in a few hours, and he's not sure where he is. Scanning the region
   briefly, you discover one life signal in a cave system nearby; his friend
   must have taken shelter there. The man asks if you can go there to retrieve
   his friend.

   The cave is divided into square regions which are either dominantly rocky,
   narrow, or wet (called its type). Each region occupies exactly one
   coordinate in X,Y format where X and Y are integers and zero or greater.
   (Adjacent regions can be the same type.)

   The scan (your puzzle input) is not very detailed: it only reveals the depth
   of the cave system and the coordinates of the target. However, it does not
   reveal the type of each region. The mouth of the cave is at 0,0.

   The man explains that due to the unusual geology in the area, there is a
   method to determine any region's type based on its erosion level. The
   erosion level of a region can be determined from its geologic index. The
   geologic index can be determined using the first rule that applies from the
   list below:

     • The region at 0,0 (the mouth of the cave) has a geologic index of 0.
     • The region at the coordinates of the target has a geologic index of 0.
     • If the region's Y coordinate is 0, the geologic index is its X
     coordinate times 16807. • If the region's X coordinate is 0, the geologic
     index is its Y coordinate times 48271. • Otherwise, the region's geologic
     index is the result of multiplying the erosion levels of the regions at
     X-1,Y and X,Y-1.

   A region's erosion level is its geologic index plus the cave system's depth,
   all modulo 20183. Then:

     • If the erosion level modulo 3 is 0, the region's type is rocky. • If the
     erosion level modulo 3 is 1, the region's type is wet. • If the erosion
     level modulo 3 is 2, the region's type is narrow.

   For example, suppose the cave system's depth is 510 and the target's
   coordinates are 10,10. Using % to represent the modulo operator, the cavern
   would look as follows:

     • At 0,0, the geologic index is 0. The erosion level is (0 + 510) % 20183
     = 510. The type is 510 % 3 = 0, rocky. • At 1,0, because the Y coordinate
     is 0, the geologic index is 1 * 16807 = 16807. The erosion level is (16807
     + 510) % 20183 = 17317. The type is 17317 % 3 = 1, wet. • At 0,1, because
     the X coordinate is 0, the geologic index is 1 * 48271 = 48271. The
     erosion level is (48271 + 510) % 20183 = 8415. The type is 8415 % 3 = 0,
     rocky. • At 1,1, neither coordinate is 0 and it is not the coordinate of
     the target, so the geologic index is the erosion level of 0,1 (8415) times
     the erosion level of 1,0 (17317), 8415
       * 17317 = 145722555. The erosion level is (145722555 + 510) % 20183 =
       * 1805. The type is 1805 % 3 = 2, narrow.
     • At 10,10, because they are the target's coordinates, the geologic index
     is 0. The erosion level is (0 + 510) % 20183 = 510. The type is 510 % 3 =
     0, rocky.

   Drawing this same cave system with rocky as ., wet as =, narrow as |, the
   mouth as M, the target as T, with 0,0 in the top-left corner, X increasing
   to the right, and Y increasing downward, the top-left corner of the map
   looks like this:

 M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

   Before you go in, you should determine the risk level of the area. For the
   rectangle that has a top-left corner of region 0,0 and a bottom-right corner
   of the region containing the target, add up the risk level of each
   individual region: 0 for rocky regions, 1 for wet regions, and 2 for narrow
   regions.

   In the cave system above, because the mouth is at 0,0 and the target is at
   10,10, adding up the risk level of all regions with an X coordinate from 0
   to 10 and a Y coordinate from 0 to 10, this total is 114.

   What is the total risk level for the smallest rectangle that includes 0,0
   and the target's coordinates?

   Your puzzle answer was 10603.

--- Part Two ---

   Okay, it's time to go rescue the man's friend.

   As you leave, he hands you some tools: a torch and some climbing gear. You
   can't equip both tools at once, but you can choose to use neither.

   Tools can only be used in certain regions:

     • In rocky regions, you can use the climbing gear or the torch. You cannot
     use neither (you'll likely slip and fall). • In wet regions, you can use
     the climbing gear or neither tool. You cannot use the torch (if it gets
     wet, you won't have a light source). • In narrow regions, you can use the
     torch or neither tool. You cannot use the climbing gear (it's too bulky to
     fit).

   You start at 0,0 (the mouth of the cave) with the torch equipped and must
   reach the target coordinates as quickly as possible. The regions with
   negative X or Y are solid rock and cannot be traversed. The fastest route
   might involve entering regions beyond the X or Y coordinate of the target.

   You can move to an adjacent region (up, down, left, or right; never
   diagonally) if your currently equipped tool allows you to enter that region.
   Moving to an adjacent region takes one minute. (For example, if you have the
   torch equipped, you can move between rocky and narrow regions, but cannot
   enter wet regions.)

   You can change your currently equipped tool or put both away if your new
   equipment would be valid for your current region. Switching to using the
   climbing gear, torch, or neither always takes seven minutes, regardless of
   which tools you start with. (For example, if you are in a rocky region, you
   can switch from the torch to the climbing gear, but you cannot switch to
   neither.)

   Finally, once you reach the target, you need the torch equipped before you
   can find him in the dark. The target is always in a rocky region, so if you
   arrive there with climbing gear equipped, you will need to spend seven
   minutes switching to your torch.

   For example, using the same cave system as above, starting in the top left
   corner (0,0) and moving to the bottom right corner (the target, 10,10) as
   quickly as possible, one possible route is as follows, with your current
   position marked X:

 Initially: X=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Down: M=.|=.|.|=.|=|=. X|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Right: M=.|=.|.|=.|=|=. .X=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Switch from using the torch to neither tool: M=.|=.|.|=.|=|=. .X=|=|||..|.=...
 .==|....||=..|== =.|....|.==.|==. =|..==...=.|==.. =||.=.=||=|=..|=
 |.=.===|||..=..| |..==||=.|==|=== .=..===..=|.|||. .======|||=|=.|=
 .===|=|===T===|| =|||...|==..|=.| =.=|=.=..=.||==| ||=|=...|==.=|==
 |=.=||===.|||=== ||.|==.|.|.||=||

 Right 3: M=.|=.|.|=.|=|=. .|=|X|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Switch from using neither tool to the climbing gear: M=.|=.|.|=.|=|=.
 .|=|X|||..|.=... .==|....||=..|== =.|....|.==.|==. =|..==...=.|==..
 =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|=== .=..===..=|.|||.
 .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.| =.=|=.=..=.||==|
 ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Down 7: M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..X==..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Right: M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..=X=..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Down 3: M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||.X.|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Right: M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||..X|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Down: M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.X..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Right 4: M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===T===|| =|||...|==..|=.|
 =.=|=.=..=X||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Up 2: M=.|=.|.|=.|=|=. .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==.
 =|..==...=.|==.. =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|===
 .=..===..=|.|||. .======|||=|=.|= .===|=|===X===|| =|||...|==..|=.|
 =.=|=.=..=.||==| ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

 Switch from using the climbing gear to the torch: M=.|=.|.|=.|=|=.
 .|=|=|||..|.=... .==|....||=..|== =.|....|.==.|==. =|..==...=.|==..
 =||.=.=||=|=..|= |.=.===|||..=..| |..==||=.|==|=== .=..===..=|.|||.
 .======|||=|=.|= .===|=|===X===|| =|||...|==..|=.| =.=|=.=..=.||==|
 ||=|=...|==.=|== |=.=||===.|||=== ||.|==.|.|.||=||

   This is tied with other routes as the fastest way to reach the target: 45
   minutes. In it, 21 minutes are spent switching tools (three times, seven
   minutes each) and the remaining 24 minutes are spent moving.

   What is the fewest number of minutes you can take to reach the target?

   Your puzzle answer was 952.

   Both parts of this puzzle are complete! They provide two gold stars: **

   At this point, you should return to your Advent calendar and try another
   puzzle.

   If you still want to see it, you can get your puzzle input.

References

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   . https://en.wikipedia.org/wiki/Modulo_operation
   . https://adventofcode.com/2018
   . https://adventofcode.com/2018/day/22/input
