commit b3c0ceca9f6e6b330b71c83b79fa1526f548963d · hauleth.dev/advent-of-code

+320

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

     

       245
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               distances ->

     

       246
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                 case distances do

     

       247
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                   %{^u => :infinity} ->

     

       248
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                     distances

     

       249
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       250
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                   %{^u => du, ^v => dv} when du + weight < dv ->

     

       251
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                     %{distances | v => du + weight}

     

       252
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       253
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                   _ ->

     

       254
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                     distances

     

       255
       +
                 end

     

       256
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             end

     

       257
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       258
       +
           if has_negative_cycle?(distances, weights) do

     

       259
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             nil

     

       260
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           else

     

       261
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             Map.new(distances, fn {k, v} -> {Map.fetch!(vertices, k), v} end)

     

       262
       +
           end

     

       263
       +
         end

     

       264
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       265
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         @spec init_distances(Graph.vertex(), Graph.vertices()) :: distance

     

       266
       +
         defp init_distances(vertex_id, vertices) do

     

       267
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           Map.new(vertices, fn

     

       268
       +
             {id, _vertex} when id == vertex_id -> {id, 0}

     

       269
       +
             {id, _} -> {id, :infinity}

     

       270
       +
           end)

     

       271
       +
         end

     

       272
       +
       

     

       273
       +
         @spec edge_weight(term) :: float

     

       274
       +
         defp edge_weight({e, edge_value}), do: {e, edge_value |> Map.values() |> List.first()}

     

       275
       +
       

     

       276
       +
         defp has_negative_cycle?(%{} = distances, meta) do

     

       277
       +
           Enum.any?(meta, fn {{u, v}, weight} ->

     

       278
       +
             %{^u => du, ^v => dv} = distances

     

       279
       +
       

     

       280
       +
             du != :infinity and du + weight < dv

     

       281
       +
           end)

     

       282
       +
         end

     

       283
       +
       end

     

       284
       +
       ```

     

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       +
       

     

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       <!-- livebook:{"output":true} -->

     

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       +
       

     

       288
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       ```

     

       289
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       {:module, BellmanFord, <<70, 79, 82, 49, 0, 0, 19, ...>>, {:has_negative_cycle?, 2}}

     

       290
       +
       ```

     

       291
       +
       

     

       292
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       ```elixir

     

       293
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       min_paths =

     

       294
       +
         tgraph

     

       295
       +
         # |> Graph.bellman_ford(stop)

     

       296
       +
         |> BellmanFord.call(stop)

     

       297
       +
         |> Map.take(lowest)

     

       298
       +
         |> Map.values()

     

       299
       +
       ```

     

       300
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       301
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       <!-- livebook:{"output":true} -->

     

       302
       +
       

     

       303
       +
       ```

     

       304
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       [:infinity, :infinity, :infinity, 454, :infinity, :infinity, :infinity, :infinity, :infinity,

     

       305
       +
        :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,

     

       306
       +
        :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,

     

       307
       +
        :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,

     

       308
       +
        :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity, :infinity,

     

       309
       +
        :infinity, :infinity, :infinity, :infinity, :infinity, ...]

     

       310
       +
       ```

     

       311
       +
       

     

       312
       +
       ```elixir

     

       313
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       Enum.min(min_paths)

     

       314
       +
       ```

     

       315
       +
       

     

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       <!-- livebook:{"output":true} -->

     

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       +
       

     

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       ```

     

       319
       +
       430

     

       320
       +
       ```