this repo has no description
ft: add day 12.2022
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+320
2022/day12.livemd
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2022/day12.livemd
···
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<!-- livebook:{"persist_outputs":true} -->
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# Day 12
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```elixir
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Mix.install([
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{:kino_aoc, git: "https://github.com/ljgago/kino_aoc"},
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{:libgraph, ">= 0.0.0"}
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])
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```
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<!-- livebook:{"output":true} -->
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```
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:ok
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```
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## Section
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<!-- livebook:{"attrs":{"day":"12","session_secret":"ADVENT_OF_CODE_SESSION","variable":"puzzle_input","year":"2022"},"kind":"Elixir.KinoAOC.HelperCell","livebook_object":"smart_cell"} -->
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```elixir
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{:ok, puzzle_input} =
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KinoAOC.download_puzzle("2022", "12", System.fetch_env!("LB_ADVENT_OF_CODE_SESSION"))
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```
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<!-- livebook:{"output":true} -->
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```
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{:ok,
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"abccccaaacaccccaaaaacccccccaaccccccccaaaaaaccccccaaaaaccccccccccaaaaaaaaacccccccaaaaaaaaaaaaaaccaaaaaccccccccccccaccacccccccccccccccccccccccccccccccccccccccaaaaaa\nabccaacaaaaaccaaaaacccccaaaaaccccccccaaaaaaccccccaaaaaacccccccccaaaaaaaaaaaaacccaaaaaaaaaaaaaaaaaaaaaccccccccccccaaaacccccccccccccccccccccccccccccccccccccccaaaaaa\nabccaaaaaaaaccaaaaaacccccaaaaaccccccaaaaaaaacccccaaaaaaccccccccccaaaaaaaaaaaacccaaaaaacaaaaaacaaaaaaaaccccccccccaaaaacccccaccccccccccccccccccaaacccccccccccccaaaaa\nabcccaaaaaccccccaaaacccccaaaaacccccaaaaaaaaaaccccaaaaaacccccccccaaaaaaaaaaaaaacaaaaaaaaaaaaaacaaaaaaaaccccccccccaaaaaacccaaacccccccccccccccccaaaccccccccccccccaaaa\nabaaacaaaaacccccacccccccaaaaaccccccaaaaaaaaaaccccccaaaccccccccccaaaaaaaaacaaaaaaaaaaaaaaaaaaacccaaacaccaaaccccccaaaaaaaacaaacccccccccccaaccccaaacccccccccccccccaac\nabaaacaacaaaaccccccccccccccaaccccccacaaaaacccccaacccccccccccccccaaaacaaaaaaaaaacccaacccaaacaacccaaccccaaaaccccccccaacaaaaaaaaaaccccccccaaaaccaaaccccccccccccccaaac\nabaaccaaccaaacacccccccccccccccccccccccaaaacccaaaaaaccaaaccccccccccaacaaaaaaaaaacccaaccccccccccccccccccaaaaccccccccccccaaaaaaaaaccccccciiiiiaaaaacccccccccccccccccc\nabaaccccaaaaaaaacccccccccccccccccccccccaaccccaaaaaaccaaaaaccccacccaaccaaacaaaaacccccccccccccccaacccccccaaaccccccccccccccaaaaacccccccciiiiiiiiaaaaaccccccaaaccccccc\nabaaacccaaaaaaaacccccccccccccccccccccccccccccaaaaaacaaaaaccccaaaaaaaccaaccaaacccccccaaaaacacccaaccccccccccaacccccccccccaaaaaaccccccciiiiiiiiijjaaaaaccccaaacaccccc\nabaaaccccaaaaaaccccccccccccccccccccaaccccccccaaaaaccaaaaacccccaaaaaaaaccccccccccccccaaaaaaaaaaaaccccccccccaaacaaccccccaaaaaaaccccccciiinnnnoijjjjjjjjjjaaaaaaacccc\nabccccccccaaaaacccccaacccccccccccaaaacccccccccaaaacccaaaaaccccaaaaaaaaacccccccccccccaaaaaaaaaaaaaaccccccccaaaaaacccaacaaacaaacccccchhinnnnnoojjjjjjjjjkkaaaaaacccc\nabcccccccaaaaaacaaacaacccccccccccaaaaaaccccccccccccccaacccccccaaaaaaaaacaaccccccccccaaaaaaaaaaaaaaacccccaaaaaaacccaaaaccccccacaaccchhinnnnnoooojjjjjjkkkkaaaaccccc\nabaacccaccaaaccccaaaaaccccccccccccaaaaccccccccccccccccccccccccaaaaaaaacaaaaaaaccccccaaaaaaaaaaaaaaacccccaaaaaaacccaaaaccccaaacaaachhhnnntttuooooooooppkkkaaaaccccc\nabaacccaaaaaaaccccaaaaaacccccccccaaaaaccccccccccccccccccccccccaaaaaaacccaaaaacccccccccaaacaaaaaaaaccccccccaaaaacccaaaacccccaaaaacchhhnnnttttuooooooppppkkkaaaccccc\nabaacccaaaaaaccccaaaaaaacccccccccaacaaccccccccccccccccccccccaaaccaaaccaaaaaaacccccccccccccaaaaaaaccccccaacaacaaacccccccccccaaaaaahhhhnntttttuuouuuuupppkkkcccccccc\nabaaaacaaaaaaaaaaaaaaacccccccccccccccccccccccccccccccccccccaaaacccaaacaaaaaaaaccccccccccccaccaaaccccccaaacaaccccccccccccccaaaaaahhhhnnntttxxxuuuuuuupppkkkcccccccc\nabaaaacaaaaaaaaaaacaaacccaaacccccccccccccccccccccacccccccccaaaacccccccaaaaaaaaccccccccccccccccaaacccccaaacaaacccccccccccccaaaaaahhhhmnnttxxxxuuyuuuuuppkkkcccccccc\nabaaaccaaaaaaaaccccaaaccccaaaccacccccccccccaaaaaaaaccccccccaaaacccccccccaaacaacccccccccccccccccccccaaaaaaaaaacccccacccccccaacaghhhmmmmtttxxxxxxyyyuupppkkccccccccc\nabaaccaaaaaaaccccccccccccaaaaaaaacccccccccccaaaaaaccccccccccccccccccccccaaccccccaacccccccccccccccccaaaaaaaaacccccaaccccccccccagggmmmmttttxxxxxyyyyvvppkkkccccccccc\nabaacccaccaaacccccccccccaaaaaaaaccccccccccccaaaaaaccccccccccccccccccccccccccaaacaaaccccccccccccccccccaaaaaccccaaaaacaacccccccgggmmmmttttxxxxxyyyyvvpppiiiccccccccc\nSbaaaaaccccaaccccccccccaaaaaaaaacacccccccccaaaaaaaacccccccccccccccaacccccccccaaaaaccccccccccaaaacccccaaaaaacccaaaaaaaaccaaaccgggmmmsssxxxEzzzzyyvvvpppiiiccccccccc\nabaaaaaccccccccccccccccaaaaaaaaaaaaaaaaaccaaaaaaaaaacccccccccccaaaaacccccccccaaaaaaaccccccccaaaaaccccaaaaaaaccccaaaaacccaaaaagggmmmsssxxxxxyyyyyyvvqqqiiiccccccccc\nabaaaaacccccccccccccccccaaaaaaaacaaaaaacccaaaaaaaaaaccccccccccccaaaaacccccccaaaaaaaacccccccaaaaaaccccaaacaaacccaaaaacccaaaaaagggmmmssswwwwwyyyyyyyvvqqqiiicccccccc\nabaaaaccccccccccccccccccccaaaaaaaaaaaaacccacacaaacccccccccccccccaaaaacccccccaaaaaaaacccccccaaaaaaccccacccccccccaacaaaccaaaaaagggmmmsssswwwwyyyyyyyvvvqqiiicccccccc\nabaaaaacccccccccccccccccccaacccaaaaaaaaaccccccaaaccccccccccccccaaaaaccccccccaacaaacccccccccaaaaaacccccccccccccccccaaccccaaaaagggmmmmssssswwyywwvvvvvvqqiiicccccccc\nabaaaaacccccccccccccc" <> ...}
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```
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```elixir
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# puzzle_input = """
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# Sabqponm
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# abcryxxl
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# accszExk
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# acctuvwj
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# abdefghi
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# """
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```
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<!-- livebook:{"output":true} -->
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```
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nil
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```
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```elixir
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min = ?a - ?a
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max = ?z - ?a
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{map, start, stop} =
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puzzle_input
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|> String.split("\n", trim: true)
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|> Enum.map(&to_charlist/1)
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|> Enum.with_index()
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|> Enum.flat_map(fn {line, y} ->
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line
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|> Enum.with_index()
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|> Enum.map(fn {c, x} -> {{x, y}, c} end)
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end)
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|> Enum.reduce({%{}, nil, nil}, fn {p, v}, {map, s, e} ->
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case v do
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?S -> {Map.put(map, p, min), p, e}
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?E -> {Map.put(map, p, max), s, p}
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_ -> {Map.put(map, p, v - ?a), s, e}
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end
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end)
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graph =
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map
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|> Enum.reduce(Graph.new(), fn {p, v}, graph ->
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{x, y} = p
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graph =
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if map[{x - 1, y}] && v + 1 >= map[{x - 1, y}],
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do: Graph.add_edge(graph, {x, y}, {x - 1, y}, label: [v, map[{x - 1, y}]]),
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else: graph
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graph =
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if map[{x + 1, y}] && v + 1 >= map[{x + 1, y}],
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do: Graph.add_edge(graph, {x, y}, {x + 1, y}, label: [v, map[{x + 1, y}]]),
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else: graph
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graph =
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if map[{x, y - 1}] && v + 1 >= map[{x, y - 1}],
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do: Graph.add_edge(graph, {x, y}, {x, y - 1}, label: [v, map[{x, y - 1}]]),
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else: graph
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graph =
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if map[{x, y + 1}] && v + 1 >= map[{x, y + 1}],
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do: Graph.add_edge(graph, {x, y}, {x, y + 1}, label: [v, map[{x, y + 1}]]),
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else: graph
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end)
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```
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<!-- livebook:{"output":true} -->
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```
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warning: variable "graph" is unused (there is a variable with the same name in the context, use the pin operator (^) to match on it or prefix this variable with underscore if it is not meant to be used)
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2022/day12.livemd#cell:7urrvoyk6ltuxa4kdqc63nncfh37x2fn:30
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```
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<!-- livebook:{"output":true} -->
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```
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#Graph<type: directed, num_vertices: 6642, num_edges: 24117>
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```
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## Task 1
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```elixir
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length(Graph.get_shortest_path(graph, start, stop)) - 1
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```
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<!-- livebook:{"output":true} -->
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```
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437
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```
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```elixir
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graph.vertices
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```
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<!-- livebook:{"output":true} -->
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```
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%{
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1148931603 => {118, 31},
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15476201 => {158, 33},
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3480980581 => {19, 26},
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513279067 => {86, 0},
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1642831488 => {111, 2},
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669567979 => {38, 18},
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1898334127 => {77, 28},
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2414760132 => {41, 27},
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1433989350 => {134, 33},
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4010762779 => {100, 37},
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1619384061 => {142, 27},
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2736818014 => {105, 29},
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3132807327 => {56, 13},
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1603662291 => {94, 23},
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183280155 => {35, 27},
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2518352043 => {127, 27},
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824501714 => {15, 33},
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1813555375 => {70, 18},
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733666720 => {72, 5},
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4293490381 => {13, 24},
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4037128590 => {87, 10},
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1287605231 => {99, 3},
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2697150767 => {19, 29},
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3345146674 => {78, 5},
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811252706 => {132, 14},
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3035418479 => {156, 5},
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2090318173 => {149, 1},
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1306366779 => {71, 39},
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113692275 => {158, 28},
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1809958846 => {4, 0},
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2979249361 => {95, 23},
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712034521 => {2, 34},
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838646858 => {127, 2},
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2636390019 => {97, 34},
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200998860 => {73, 23},
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2440897975 => {91, 7},
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2757930521 => {103, 38},
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2626031906 => {92, 21},
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4000959801 => {44, 20},
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2762901234 => {69, 16},
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3967362516 => {72, 9},
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1858208296 => {81, 16},
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3063825234 => {140, 14},
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1669140133 => {46, 21},
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684221776 => {146, 38},
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623366404 => {63, 40},
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3623360588 => {149, 6},
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2885933829 => {137, 14},
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3219344086 => {136, ...},
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3451324297 => {...},
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...
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}
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```
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## Task 2
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```elixir
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tgraph = Graph.transpose(graph)
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```
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<!-- livebook:{"output":true} -->
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```
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#Graph<type: directed, num_vertices: 6642, num_edges: 24117>
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```
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```elixir
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lowest =
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Enum.flat_map(map, fn
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{p, 0} -> [p]
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_ -> []
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end)
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```
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<!-- livebook:{"output":true} -->
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```
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[32256290, 409066827, 186924390, 1502865800, 887663648, 2543466388, 697356458, 1070575781,
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1659702078, 4000784021, 1947564743, 2361038489, 3904452243, 3615669650, 270460033, 1281654811,
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3153535741, 2393890474, 3946102901, 2210758189, 2982223724, 2654353783, 2656280720, 3935389969,
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2818948768, 4279780723, 3595206681, 3496428192, 2269119594, 2583881244, 3997991000, 520325395,
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457672928, 1453390554, 3289433936, 2574402082, 1560492086, 3242480874, 389839366, 4176230802,
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1147783117, 2469841095, 2034019869, 438932546, 1799582666, 1100008137, 467060197, 162439868,
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3928107970, 800548913, ...]
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```
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```elixir
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# Copied BF implementation from `libgraph` to optimise it
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defmodule BellmanFord do
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@moduledoc """
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The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single
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source vertex to all of the other vertices in a weighted digraph.
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It is capable of handling graphs in which some of the edge weights are negative numbers
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Time complexity: O(VLogV)
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"""
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@type distance :: %{Graph.vertex_id() => integer}
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@doc """
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Returns nil when graph has negative cycle.
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"""
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@spec call(Graph.t(), Graph.vertex()) :: [Graph.vertex()] | nil
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def call(%Graph{vertices: vs, edges: meta}, source) do
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distances = source |> Graph.Utils.vertex_id() |> init_distances(vs)
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weights = Enum.map(meta, &edge_weight/1)
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distances =
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for _ <- 1..map_size(vs),
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{{u, v}, weight} <- weights,
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reduce: distances do
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distances ->
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case distances do
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%{^u => :infinity} ->
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distances
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%{^u => du, ^v => dv} when du + weight < dv ->
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%{distances | v => du + weight}
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_ ->
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distances
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end
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end
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if has_negative_cycle?(distances, weights) do
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nil
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else
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Map.new(distances, fn {k, v} -> {Map.fetch!(vertices, k), v} end)
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end
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end
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@spec init_distances(Graph.vertex(), Graph.vertices()) :: distance
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defp init_distances(vertex_id, vertices) do
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Map.new(vertices, fn
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{id, _vertex} when id == vertex_id -> {id, 0}
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{id, _} -> {id, :infinity}
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end)
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end
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@spec edge_weight(term) :: float
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defp edge_weight({e, edge_value}), do: {e, edge_value |> Map.values() |> List.first()}
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defp has_negative_cycle?(%{} = distances, meta) do
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Enum.any?(meta, fn {{u, v}, weight} ->
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%{^u => du, ^v => dv} = distances
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+
280
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du != :infinity and du + weight < dv
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end)
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end
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end
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```
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<!-- livebook:{"output":true} -->
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```
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{:module, BellmanFord, <<70, 79, 82, 49, 0, 0, 19, ...>>, {:has_negative_cycle?, 2}}
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```
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```elixir
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min_paths =
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tgraph
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# |> Graph.bellman_ford(stop)
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|> BellmanFord.call(stop)
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|> Map.take(lowest)
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|> Map.values()
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```
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<!-- livebook:{"output":true} -->
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```
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[:infinity, :infinity, :infinity, 454, :infinity, :infinity, :infinity, :infinity, :infinity,
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:infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,
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:infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,
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:infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,
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:infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,
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:infinity, :infinity, :infinity, :infinity, :infinity, ...]
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```
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```elixir
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Enum.min(min_paths)
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```
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+
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<!-- livebook:{"output":true} -->
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+
318
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```
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430
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```