2022 day 15 init

2022/day15/README.org

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+** --- Day 15: Beacon Exclusion Zone ---
+You feel the ground rumble again as the distress signal leads you to a
+large network of subterranean tunnels. You don't have time to search
+them all, but you don't need to: your pack contains a set of deployable
+/sensors/ that you imagine were originally built to locate lost Elves.
+
+The sensors aren't very powerful, but that's okay; your handheld device
+indicates that you're close enough to the source of the distress signal
+to use them. You pull the emergency sensor system out of your pack, hit
+the big button on top, and the sensors zoom off down the tunnels.
+
+Once a sensor finds a spot it thinks will give it a good reading, it
+attaches itself to a hard surface and begins monitoring for the nearest
+signal source /beacon/. Sensors and beacons always exist at integer
+coordinates. Each sensor knows its own position and can /determine the
+position of a beacon precisely/; however, sensors can only lock on to
+the one beacon /closest to the sensor/ as measured by the
+[[https://en.wikipedia.org/wiki/Taxicab_geometry][Manhattan distance]].
+(There is never a tie where two beacons are the same distance to a
+sensor.)
+
+It doesn't take long for the sensors to report back their positions and
+closest beacons (your puzzle input). For example:
+
+#+begin_example
+Sensor at x=2, y=18: closest beacon is at x=-2, y=15
+Sensor at x=9, y=16: closest beacon is at x=10, y=16
+Sensor at x=13, y=2: closest beacon is at x=15, y=3
+Sensor at x=12, y=14: closest beacon is at x=10, y=16
+Sensor at x=10, y=20: closest beacon is at x=10, y=16
+Sensor at x=14, y=17: closest beacon is at x=10, y=16
+Sensor at x=8, y=7: closest beacon is at x=2, y=10
+Sensor at x=2, y=0: closest beacon is at x=2, y=10
+Sensor at x=0, y=11: closest beacon is at x=2, y=10
+Sensor at x=20, y=14: closest beacon is at x=25, y=17
+Sensor at x=17, y=20: closest beacon is at x=21, y=22
+Sensor at x=16, y=7: closest beacon is at x=15, y=3
+Sensor at x=14, y=3: closest beacon is at x=15, y=3
+Sensor at x=20, y=1: closest beacon is at x=15, y=3
+#+end_example
+
+So, consider the sensor at =2,18=; the closest beacon to it is at
+=-2,15=. For the sensor at =9,16=, the closest beacon to it is at
+=10,16=.
+
+Drawing sensors as =S= and beacons as =B=, the above arrangement of
+sensors and beacons looks like this:
+
+#+begin_example
+               1    1    2    2
+     0    5    0    5    0    5
+ 0 ....S.......................
+ 1 ......................S.....
+ 2 ...............S............
+ 3 ................SB..........
+ 4 ............................
+ 5 ............................
+ 6 ............................
+ 7 ..........S.......S.........
+ 8 ............................
+ 9 ............................
+10 ....B.......................
+11 ..S.........................
+12 ............................
+13 ............................
+14 ..............S.......S.....
+15 B...........................
+16 ...........SB...............
+17 ................S..........B
+18 ....S.......................
+19 ............................
+20 ............S......S........
+21 ............................
+22 .......................B....
+#+end_example
+
+This isn't necessarily a comprehensive map of all beacons in the area,
+though. Because each sensor only identifies its closest beacon, if a
+sensor detects a beacon, you know there are no other beacons that close
+or closer to that sensor. There could still be beacons that just happen
+to not be the closest beacon to any sensor. Consider the sensor at
+=8,7=:
+
+#+begin_example
+               1    1    2    2
+     0    5    0    5    0    5
+-2 ..........#.................
+-1 .........###................
+ 0 ....S...#####...............
+ 1 .......#######........S.....
+ 2 ......#########S............
+ 3 .....###########SB..........
+ 4 ....#############...........
+ 5 ...###############..........
+ 6 ..#################.........
+ 7 .#########S#######S#........
+ 8 ..#################.........
+ 9 ...###############..........
+10 ....B############...........
+11 ..S..###########............
+12 ......#########.............
+13 .......#######..............
+14 ........#####.S.......S.....
+15 B........###................
+16 ..........#SB...............
+17 ................S..........B
+18 ....S.......................
+19 ............................
+20 ............S......S........
+21 ............................
+22 .......................B....
+#+end_example
+
+This sensor's closest beacon is at =2,10=, and so you know there are no
+beacons that close or closer (in any positions marked =#=).
+
+None of the detected beacons seem to be producing the distress signal,
+so you'll need to work out where the distress beacon is by working out
+where it /isn't/. For now, keep things simple by counting the positions
+where a beacon cannot possibly be along just a single row.
+
+So, suppose you have an arrangement of beacons and sensors like in the
+example above and, just in the row where =y=10=, you'd like to count the
+number of positions a beacon cannot possibly exist. The coverage from
+all sensors near that row looks like this:
+
+#+begin_example
+                 1    1    2    2
+       0    5    0    5    0    5
+ 9 ...#########################...
+10 ..####B######################..
+11 .###S#############.###########.
+#+end_example
+
+In this example, in the row where =y=10=, there are =26= positions where
+a beacon cannot be present.
+
+Consult the report from the sensors you just deployed. /In the row where
+=y=2000000=, how many positions cannot contain a beacon?/