···
1
+
<!-- livebook:{"persist_outputs":true} -->
7
+
{:kino_aoc, git: "https://github.com/ljgago/kino_aoc"}
11
+
<!-- livebook:{"output":true} -->
19
+
<!-- livebook:{"attrs":{"day":"15","session_secret":"ADVENT_OF_CODE_SESSION","variable":"puzzle_input","year":"2022"},"kind":"Elixir.KinoAOC.HelperCell","livebook_object":"smart_cell"} -->
22
+
{:ok, puzzle_input} =
23
+
KinoAOC.download_puzzle("2022", "15", System.fetch_env!("LB_ADVENT_OF_CODE_SESSION"))
26
+
<!-- livebook:{"output":true} -->
30
+
"Sensor at x=2288642, y=2282562: closest beacon is at x=1581951, y=2271709\nSensor at x=2215505, y=2975419: closest beacon is at x=2229474, y=3709584\nSensor at x=275497, y=3166843: closest beacon is at x=-626874, y=3143870\nSensor at x=1189444, y=2115305: closest beacon is at x=1581951, y=2271709\nSensor at x=172215, y=2327851: closest beacon is at x=-101830, y=2000000\nSensor at x=3953907, y=1957660: closest beacon is at x=2882446, y=1934422\nSensor at x=685737, y=2465261: closest beacon is at x=1581951, y=2271709\nSensor at x=1458348, y=2739442: closest beacon is at x=1581951, y=2271709\nSensor at x=3742876, y=2811554: closest beacon is at x=3133845, y=3162635\nSensor at x=437819, y=638526: closest beacon is at x=-101830, y=2000000\nSensor at x=2537979, y=1762726: closest beacon is at x=2882446, y=1934422\nSensor at x=1368739, y=2222863: closest beacon is at x=1581951, y=2271709\nSensor at x=2743572, y=3976937: closest beacon is at x=2229474, y=3709584\nSensor at x=2180640, y=105414: closest beacon is at x=3011118, y=-101788\nSensor at x=3845753, y=474814: closest beacon is at x=3011118, y=-101788\nSensor at x=2493694, y=3828087: closest beacon is at x=2229474, y=3709584\nSensor at x=2786014, y=3388077: closest beacon is at x=3133845, y=3162635\nSensor at x=3593418, y=3761871: closest beacon is at x=3133845, y=3162635\nSensor at x=856288, y=3880566: closest beacon is at x=2229474, y=3709584\nSensor at x=1757086, y=2518373: closest beacon is at x=1581951, y=2271709\nSensor at x=2853518, y=2939097: closest beacon is at x=3133845, y=3162635\nSensor at x=1682023, y=1449902: closest beacon is at x=1581951, y=2271709\nSensor at x=3360575, y=1739100: closest beacon is at x=2882446, y=1934422\nSensor at x=2904259, y=1465606: closest beacon is at x=2882446, y=1934422\nSensor at x=3078500, y=3564862: closest beacon is at x=3133845, y=3162635\nSensor at x=2835288, y=1011055: closest beacon is at x=2882446, y=1934422\nSensor at x=2998762, y=2414323: closest beacon is at x=2882446, y=1934422\n"}
36
+
|> String.split("\n", trim: true)
37
+
|> Enum.map(fn line ->
38
+
%{"sx" => sx, "sy" => sy, "bx" => bx, "by" => by} =
39
+
Regex.named_captures(
40
+
~r/x=(?<sx>-?\d+), y=(?<sy>-?\d+):.*x=(?<bx>-?\d+), y=(?<by>-?\d+)/,
45
+
sensor: {String.to_integer(sx), String.to_integer(sy)},
46
+
beacon: {String.to_integer(bx), String.to_integer(by)}
52
+
|> Enum.map(fn %{beacon: {bx, by}, sensor: {sx, sy}} ->
53
+
radius = abs(bx - sx) + abs(by - sy)
59
+
<!-- livebook:{"output":true} -->
63
+
{{2288642, 2282562}, 717544},
64
+
{{2215505, 2975419}, 748134},
65
+
{{275497, 3166843}, 925344},
66
+
{{1189444, 2115305}, 548911},
67
+
{{172215, 2327851}, 601896},
68
+
{{3953907, 1957660}, 1094699},
69
+
{{685737, 2465261}, 1089766},
70
+
{{1458348, 2739442}, 591336},
71
+
{{3742876, 2811554}, 960112},
72
+
{{437819, 638526}, 1901123},
73
+
{{2537979, 1762726}, 516163},
74
+
{{1368739, 2222863}, 262058},
75
+
{{2743572, 3976937}, 781451},
76
+
{{2180640, 105414}, 1037680},
77
+
{{3845753, 474814}, 1411237},
78
+
{{2493694, 3828087}, 382723},
79
+
{{2786014, 3388077}, 573273},
80
+
{{3593418, 3761871}, 1058809},
81
+
{{856288, 3880566}, 1544168},
82
+
{{1757086, 2518373}, 421799},
83
+
{{2853518, 2939097}, 503865},
84
+
{{1682023, 1449902}, 921879},
85
+
{{3360575, 1739100}, 673451},
86
+
{{2904259, 1465606}, 490629},
87
+
{{3078500, 3564862}, 457572},
88
+
{{2835288, 1011055}, 970525},
89
+
{{2998762, 2414323}, 596217}
94
+
defmodule RangeSet do
95
+
defstruct ranges: []
97
+
def new(), do: %__MODULE__{}
98
+
def new(%__MODULE__{} = set), do: set
99
+
def new(a..b//1) when a <= b, do: %__MODULE__{ranges: [a..b//1]}
100
+
def new(b..a//-1) when b > a, do: %__MODULE__{ranges: [a..b//1]}
101
+
def new(list), do: %__MODULE__{ranges: list |> Enum.sort_by(& &1.first) |> squash()}
103
+
def min(%__MODULE__{ranges: [a.._ | _]}), do: a
105
+
def max(%__MODULE__{ranges: ranges}) do
106
+
_..a = List.last(ranges)
111
+
def gaps(%__MODULE__{ranges: ranges}) do
114
+
|> Enum.chunk_every(2, 1, :discard)
115
+
|> Enum.flat_map(fn [_..a, b.._] -> [(a + 1)..(b - 1)] end)
118
+
%__MODULE__{ranges: gaps}
121
+
def empty?(%__MODULE__{ranges: ranges}), do: ranges == []
123
+
def has?(%__MODULE__{ranges: ranges}, value), do: Enum.any?(ranges, &(value in &1))
125
+
def length(%__MODULE__{ranges: ranges}),
126
+
do: Enum.reduce(ranges, 0, fn r, acc -> acc + Range.size(r) end)
128
+
def to_list(%__MODULE__{ranges: ranges}),
129
+
do: Enum.flat_map(ranges, & &1)
131
+
def remove(%__MODULE__{ranges: ranges}, int) when is_integer(int) do
133
+
Enum.flat_map(ranges, fn a..b ->
135
+
a == int -> [(int + 1)..b]
136
+
b == int -> [a..(int - 1)]
137
+
int in a..b -> [a..(int - 1), (int + 1)..b]
142
+
%__MODULE__{ranges: new_ranges}
145
+
def remove(%__MODULE__{ranges: ranges}, c..d//1) when c <= d do
147
+
Enum.flat_map(ranges, fn a..b ->
149
+
a in c..d and b in c..d -> []
150
+
a < c and b in c..d -> [a..(c - 1)]
151
+
a in c..d and b > d -> [(d + 1)..b]
152
+
c in a..b and d in a..b -> [a..(c - 1), (d + 1)..b]
157
+
%__MODULE__{ranges: new_ranges}
160
+
def remove(%__MODULE__{} = set, %__MODULE__{ranges: ranges}),
161
+
do: Enum.reduce(ranges, set, &remove(&2, &1))
163
+
def remove(%__MODULE__{} = set, list),
164
+
do: Enum.reduce(list, set, &remove(&2, &1))
166
+
def add(set, int) when is_integer(int), do: add(set, int..int//1)
168
+
def add(set, a..b//-1), do: add(set, b..a//1)
170
+
def add(%__MODULE__{} = set, a..b//1) when a > b, do: set
172
+
def add(%__MODULE__{ranges: ranges}, a..b//1 = range) when a <= b do
175
+
|> insert_sorted(range)
178
+
%__MODULE__{ranges: ranges}
181
+
defp insert_sorted([], val), do: [val]
183
+
defp insert_sorted([a.._ = x | rest], b.._ = y) when a < b,
184
+
do: [x | insert_sorted(rest, y)]
186
+
defp insert_sorted(rest, y),
189
+
defp squash([]), do: []
190
+
defp squash([_] = list), do: list
192
+
defp squash([a..b, c..d | rest]) when b >= c - 1,
193
+
do: squash([a..max(b, d) | rest])
195
+
defp squash([x | rest]), do: [x | squash(rest)]
199
+
<!-- livebook:{"output":true} -->
202
+
{:module, RangeSet, <<70, 79, 82, 49, 0, 0, 37, ...>>, {:squash, 1}}
206
+
RangeSet.new([6..10, -8..26])
209
+
<!-- livebook:{"output":true} -->
212
+
%RangeSet{ranges: [-8..26]}
215
+
Our list can be change into list of radii of the circles (in Taxicab metric these will be visually squares), so then using inequality for circle
221
+
where $d(a, b)$ is distance function for given metric, we can compute possible ranges of values at given line in constant time. In Taxicab metric $d$ is defined as:
224
+
d(a, b) = |a_x - b_x| + |a_y - b_y|
227
+
So after substitution at the above inequality we get:
230
+
r \ge |C_x - a_x| + |C_y - a_y|
233
+
In the task $a_y = const$ and $C = const$, so we need to solve only for $a_x$. So we can define $d_y = |C_y - a_y| = const$ as well.
238
+
|a_x - C_x| \le r - d_y
243
+
\therefore&\ -r + d_y &\le&\ a_x - C_x &\le&\ r - d_y \\
244
+
\therefore&\ -r + d_y + C_x &\le&\ a_x &\le&\ r - d_y + C_x
249
+
defmodule Beacons do
250
+
def covered_at_line(circles, a_y) do
251
+
Enum.reduce(circles, RangeSet.new(), fn {{c_x, c_y}, r}, set ->
252
+
d_y = abs(c_y - a_y)
253
+
RangeSet.add(set, (-r + d_y + c_x)..(r - d_y + c_x)//1)
259
+
<!-- livebook:{"output":true} -->
262
+
{:module, Beacons, <<70, 79, 82, 49, 0, 0, 9, ...>>, {:covered_at_line, 2}}
271
+
Enum.flat_map(points, fn %{beacon: {x, y}} -> if y == a_y, do: [x], else: [] end)
274
+
|> Beacons.covered_at_line(a_y)
275
+
|> RangeSet.remove(beacons_at_line)
276
+
|> RangeSet.length()
279
+
<!-- livebook:{"output":true} -->
288
+
range = 4_000_000..0//-1
289
+
# range = 0..4_000_000
293
+
|> Enum.find_value(fn y ->
294
+
covered = Beacons.covered_at_line(circles, y)
296
+
gaps = RangeSet.gaps(covered)
298
+
if not RangeSet.empty?(gaps) do
299
+
{y, RangeSet.to_list(gaps)}
306
+
<!-- livebook:{"output":true} -->
hauleth.dev