-module(yog@pathfinding).
-compile([no_auto_import, nowarn_unused_vars, nowarn_unused_function, nowarn_nomatch, inline]).
-define(FILEPATH, "src/yog/pathfinding.gleam").
-export([shortest_path/6, single_source_distances/5, a_star/7, bellman_ford/6, floyd_warshall/4]).
-export_type([path/1, bellman_ford_result/1]).

-if(?OTP_RELEASE >= 27).
-define(MODULEDOC(Str), -moduledoc(Str)).
-define(DOC(Str), -doc(Str)).
-else.
-define(MODULEDOC(Str), -compile([])).
-define(DOC(Str), -compile([])).
-endif.

-type path(KWB) :: {path, list(integer()), KWB}.

-type bellman_ford_result(KWC) :: {shortest_path, path(KWC)} |
    negative_cycle |
    no_path.

-file("src/yog/pathfinding.gleam", 96).
-spec compare_frontier(
    {KWT, list(integer())},
    {KWT, list(integer())},
    fun((KWT, KWT) -> gleam@order:order())
) -> gleam@order:order().
compare_frontier(A, B, Cmp) ->
    Cmp(erlang:element(1, A), erlang:element(1, B)).

-file("src/yog/pathfinding.gleam", 104).
-spec compare_distance_frontier(
    {KWW, integer()},
    {KWW, integer()},
    fun((KWW, KWW) -> gleam@order:order())
) -> gleam@order:order().
compare_distance_frontier(A, B, Cmp) ->
    Cmp(erlang:element(1, A), erlang:element(1, B)).

-file("src/yog/pathfinding.gleam", 112).
-spec compare_a_star_frontier(
    {KWX, KWX, list(integer())},
    {KWX, KWX, list(integer())},
    fun((KWX, KWX) -> gleam@order:order())
) -> gleam@order:order().
compare_a_star_frontier(A, B, Cmp) ->
    Cmp(erlang:element(1, A), erlang:element(1, B)).

-file("src/yog/pathfinding.gleam", 122).
?DOC(
    " Helper to determine if a node should be explored based on distance comparison.\n"
    " Returns True if the node hasn't been visited or if the new distance is shorter.\n"
).
-spec should_explore_node(
    gleam@dict:dict(integer(), KXA),
    integer(),
    KXA,
    fun((KXA, KXA) -> gleam@order:order())
) -> boolean().
should_explore_node(Visited, Node, New_dist, Compare) ->
    case gleam_stdlib:map_get(Visited, Node) of
        {ok, Prev_dist} ->
            case Compare(New_dist, Prev_dist) of
                lt ->
                    true;

                _ ->
                    false
            end;

        {error, nil} ->
            true
    end.

-file("src/yog/pathfinding.gleam", 53).
-spec do_dijkstra(
    yog@model:graph(any(), KWK),
    integer(),
    gleamy@pairing_heap:heap({KWK, list(integer())}),
    gleam@dict:dict(integer(), KWK),
    fun((KWK, KWK) -> KWK),
    fun((KWK, KWK) -> gleam@order:order())
) -> gleam@option:option(path(KWK)).
do_dijkstra(Graph, Goal, Frontier, Visited, Add, Compare) ->
    case gleamy@priority_queue:pop(Frontier) of
        {error, nil} ->
            none;

        {ok, {{Dist, [Current | _] = Path}, Rest_frontier}} ->
            case Current =:= Goal of
                true ->
                    {some, {path, lists:reverse(Path), Dist}};

                false ->
                    Should_explore = should_explore_node(
                        Visited,
                        Current,
                        Dist,
                        Compare
                    ),
                    case Should_explore of
                        false ->
                            do_dijkstra(
                                Graph,
                                Goal,
                                Rest_frontier,
                                Visited,
                                Add,
                                Compare
                            );

                        true ->
                            New_visited = gleam@dict:insert(
                                Visited,
                                Current,
                                Dist
                            ),
                            Next_frontier = begin
                                _pipe = yog@model:successors(Graph, Current),
                                gleam@list:fold(
                                    _pipe,
                                    Rest_frontier,
                                    fun(H, Neighbor) ->
                                        {Next_id, Weight} = Neighbor,
                                        gleamy@priority_queue:push(
                                            H,
                                            {Add(Dist, Weight),
                                                [Next_id | Path]}
                                        )
                                    end
                                )
                            end,
                            do_dijkstra(
                                Graph,
                                Goal,
                                Next_frontier,
                                New_visited,
                                Add,
                                Compare
                            )
                    end
            end;

        {ok, _} ->
            none
    end.

-file("src/yog/pathfinding.gleam", 38).
?DOC(
    " Finds the shortest path between two nodes using Dijkstra's algorithm.\n"
    "\n"
    " Works with non-negative edge weights only. For negative weights, use `bellman_ford`.\n"
    "\n"
    " **Time Complexity:** O((V + E) log V) with heap\n"
    "\n"
    " ## Parameters\n"
    "\n"
    " - `zero`: The identity element for addition (e.g., 0 for integers)\n"
    " - `add`: Function to add two weights\n"
    " - `compare`: Function to compare two weights\n"
    "\n"
    " ## Example\n"
    "\n"
    " ```gleam\n"
    " pathfinding.shortest_path(\n"
    "   in: graph,\n"
    "   from: 1,\n"
    "   to: 5,\n"
    "   with_zero: 0,\n"
    "   with_add: int.add,\n"
    "   with_compare: int.compare\n"
    " )\n"
    " // => Some(Path([1, 2, 5], 15))\n"
    " ```\n"
).
-spec shortest_path(
    yog@model:graph(any(), KWE),
    integer(),
    integer(),
    KWE,
    fun((KWE, KWE) -> KWE),
    fun((KWE, KWE) -> gleam@order:order())
) -> gleam@option:option(path(KWE)).
shortest_path(Graph, Start, Goal, Zero, Add, Compare) ->
    Frontier = begin
        _pipe = gleamy@priority_queue:new(
            fun(A, B) -> compare_frontier(A, B, Compare) end
        ),
        gleamy@priority_queue:push(_pipe, {Zero, [Start]})
    end,
    do_dijkstra(Graph, Goal, Frontier, maps:new(), Add, Compare).

-file("src/yog/pathfinding.gleam", 197).
-spec do_single_source_dijkstra(
    yog@model:graph(any(), KXK),
    gleamy@pairing_heap:heap({KXK, integer()}),
    gleam@dict:dict(integer(), KXK),
    fun((KXK, KXK) -> KXK),
    fun((KXK, KXK) -> gleam@order:order())
) -> gleam@dict:dict(integer(), KXK).
do_single_source_dijkstra(Graph, Frontier, Distances, Add, Compare) ->
    case gleamy@priority_queue:pop(Frontier) of
        {error, nil} ->
            Distances;

        {ok, {{Dist, Current}, Rest_frontier}} ->
            Should_explore = should_explore_node(
                Distances,
                Current,
                Dist,
                Compare
            ),
            case Should_explore of
                false ->
                    do_single_source_dijkstra(
                        Graph,
                        Rest_frontier,
                        Distances,
                        Add,
                        Compare
                    );

                true ->
                    New_distances = gleam@dict:insert(Distances, Current, Dist),
                    Next_frontier = begin
                        _pipe = yog@model:successors(Graph, Current),
                        gleam@list:fold(
                            _pipe,
                            Rest_frontier,
                            fun(H, Neighbor) ->
                                {Next_id, Weight} = Neighbor,
                                gleamy@priority_queue:push(
                                    H,
                                    {Add(Dist, Weight), Next_id}
                                )
                            end
                        )
                    end,
                    do_single_source_dijkstra(
                        Graph,
                        Next_frontier,
                        New_distances,
                        Add,
                        Compare
                    )
            end
    end.

-file("src/yog/pathfinding.gleam", 183).
?DOC(
    " Computes shortest distances from a source node to all reachable nodes.\n"
    "\n"
    " Returns a dictionary mapping each reachable node to its shortest distance\n"
    " from the source. Unreachable nodes are not included in the result.\n"
    "\n"
    " This is useful when you need distances to multiple destinations, or want\n"
    " to find the closest target among many options. More efficient than running\n"
    " `shortest_path` multiple times.\n"
    "\n"
    " **Time Complexity:** O((V + E) log V) with heap\n"
    "\n"
    " ## Parameters\n"
    "\n"
    " - `zero`: The identity element for addition (e.g., 0 for integers)\n"
    " - `add`: Function to add two weights\n"
    " - `compare`: Function to compare two weights\n"
    "\n"
    " ## Example\n"
    "\n"
    " ```gleam\n"
    " // Find distances from node 1 to all reachable nodes\n"
    " let distances = pathfinding.single_source_distances(\n"
    "   in: graph,\n"
    "   from: 1,\n"
    "   with_zero: 0,\n"
    "   with_add: int.add,\n"
    "   with_compare: int.compare\n"
    " )\n"
    " // => dict.from_list([#(1, 0), #(2, 5), #(3, 8), #(4, 15)])\n"
    "\n"
    " // Find closest target among many options\n"
    " let targets = [10, 20, 30]\n"
    " let closest = targets\n"
    "   |> list.filter_map(fn(t) { dict.get(distances, t) })\n"
    "   |> list.sort(int.compare)\n"
    "   |> list.first\n"
    " ```\n"
    "\n"
    " ## Use Cases\n"
    "\n"
    " - Finding nearest target among multiple options\n"
    " - Computing distance maps for game AI\n"
    " - Network routing table generation\n"
    " - Graph analysis (centrality measures)\n"
    " - Reverse pathfinding (with `transform.transpose`)\n"
).
-spec single_source_distances(
    yog@model:graph(any(), KXE),
    integer(),
    KXE,
    fun((KXE, KXE) -> KXE),
    fun((KXE, KXE) -> gleam@order:order())
) -> gleam@dict:dict(integer(), KXE).
single_source_distances(Graph, Source, Zero, Add, Compare) ->
    Frontier = begin
        _pipe = gleamy@priority_queue:new(
            fun(A, B) -> compare_distance_frontier(A, B, Compare) end
        ),
        gleamy@priority_queue:push(_pipe, {Zero, Source})
    end,
    do_single_source_dijkstra(Graph, Frontier, maps:new(), Add, Compare).

-file("src/yog/pathfinding.gleam", 294).
-spec do_a_star(
    yog@model:graph(any(), LDV),
    integer(),
    gleamy@pairing_heap:heap({LDS, LDS, list(integer())}),
    gleam@dict:dict(integer(), LDS),
    fun((LDS, LDV) -> LDS),
    fun((LDS, LDS) -> gleam@order:order()),
    fun((integer(), integer()) -> LDV)
) -> gleam@option:option(path(LDS)).
do_a_star(Graph, Goal, Frontier, Visited, Add, Compare, H) ->
    case gleamy@priority_queue:pop(Frontier) of
        {error, nil} ->
            none;

        {ok, {{_, Dist, [Current | _] = Path}, Rest_frontier}} ->
            case Current =:= Goal of
                true ->
                    {some, {path, lists:reverse(Path), Dist}};

                false ->
                    Should_explore = should_explore_node(
                        Visited,
                        Current,
                        Dist,
                        Compare
                    ),
                    case Should_explore of
                        false ->
                            do_a_star(
                                Graph,
                                Goal,
                                Rest_frontier,
                                Visited,
                                Add,
                                Compare,
                                H
                            );

                        true ->
                            New_visited = gleam@dict:insert(
                                Visited,
                                Current,
                                Dist
                            ),
                            Next_frontier = begin
                                _pipe = yog@model:successors(Graph, Current),
                                gleam@list:fold(
                                    _pipe,
                                    Rest_frontier,
                                    fun(Acc_h, Neighbor) ->
                                        {Next_id, Weight} = Neighbor,
                                        Next_dist = Add(Dist, Weight),
                                        F_score = Add(
                                            Next_dist,
                                            H(Next_id, Goal)
                                        ),
                                        gleamy@priority_queue:push(
                                            Acc_h,
                                            {F_score,
                                                Next_dist,
                                                [Next_id | Path]}
                                        )
                                    end
                                )
                            end,
                            do_a_star(
                                Graph,
                                Goal,
                                Next_frontier,
                                New_visited,
                                Add,
                                Compare,
                                H
                            )
                    end
            end;

        _ ->
            none
    end.

-file("src/yog/pathfinding.gleam", 276).
?DOC(
    " Finds the shortest path using A* search with a heuristic function.\n"
    "\n"
    " A* is more efficient than Dijkstra when you have a good heuristic estimate\n"
    " of the remaining distance to the goal. The heuristic must be admissible\n"
    " (never overestimate the actual distance) to guarantee finding the shortest path.\n"
    "\n"
    " **Time Complexity:** O((V + E) log V), but often faster than Dijkstra in practice\n"
    "\n"
    " ## Parameters\n"
    "\n"
    " - `heuristic`: A function that estimates distance from any node to the goal.\n"
    "   Must be admissible (h(n) ≤ actual distance) to guarantee shortest path.\n"
    "\n"
    " ## Example\n"
    "\n"
    " ```gleam\n"
    " // Manhattan distance heuristic for grid\n"
    " let h = fn(node, goal) {\n"
    "   int.absolute_value(node.x - goal.x) + int.absolute_value(node.y - goal.y)\n"
    " }\n"
    "\n"
    " pathfinding.a_star(\n"
    "   in: graph,\n"
    "   from: start,\n"
    "   to: goal,\n"
    "   with_zero: 0,\n"
    "   with_add: int.add,\n"
    "   with_compare: int.compare,\n"
    "   heuristic: h\n"
    " )\n"
    " ```\n"
).
-spec a_star(
    yog@model:graph(any(), KXT),
    integer(),
    integer(),
    KXT,
    fun((KXT, KXT) -> KXT),
    fun((KXT, KXT) -> gleam@order:order()),
    fun((integer(), integer()) -> KXT)
) -> gleam@option:option(path(KXT)).
a_star(Graph, Start, Goal, Zero, Add, Compare, H) ->
    Initial_f = H(Start, Goal),
    Frontier = begin
        _pipe = gleamy@priority_queue:new(
            fun(A, B) -> compare_a_star_frontier(A, B, Compare) end
        ),
        gleamy@priority_queue:push(_pipe, {Initial_f, Zero, [Start]})
    end,
    do_a_star(Graph, Goal, Frontier, maps:new(), Add, Compare, H).

-file("src/yog/pathfinding.gleam", 425).
-spec relaxation_passes(
    yog@model:graph(any(), KYM),
    list(integer()),
    gleam@dict:dict(integer(), KYM),
    gleam@dict:dict(integer(), integer()),
    integer(),
    fun((KYM, KYM) -> KYM),
    fun((KYM, KYM) -> gleam@order:order())
) -> {gleam@dict:dict(integer(), KYM), gleam@dict:dict(integer(), integer())}.
relaxation_passes(
    Graph,
    Nodes,
    Distances,
    Predecessors,
    Remaining,
    Add,
    Compare
) ->
    case Remaining =< 0 of
        true ->
            {Distances, Predecessors};

        false ->
            {New_distances, New_predecessors} = gleam@list:fold(
                Nodes,
                {Distances, Predecessors},
                fun(Acc, U) ->
                    {Dists, Preds} = Acc,
                    case gleam_stdlib:map_get(Dists, U) of
                        {error, nil} ->
                            Acc;

                        {ok, U_dist} ->
                            Neighbors = yog@model:successors(Graph, U),
                            gleam@list:fold(
                                Neighbors,
                                {Dists, Preds},
                                fun(Inner_acc, Edge) ->
                                    {V, Weight} = Edge,
                                    {Curr_dists, Curr_preds} = Inner_acc,
                                    New_dist = Add(U_dist, Weight),
                                    case gleam_stdlib:map_get(Curr_dists, V) of
                                        {error, nil} ->
                                            {gleam@dict:insert(
                                                    Curr_dists,
                                                    V,
                                                    New_dist
                                                ),
                                                gleam@dict:insert(
                                                    Curr_preds,
                                                    V,
                                                    U
                                                )};

                                        {ok, V_dist} ->
                                            case Compare(New_dist, V_dist) of
                                                lt ->
                                                    {gleam@dict:insert(
                                                            Curr_dists,
                                                            V,
                                                            New_dist
                                                        ),
                                                        gleam@dict:insert(
                                                            Curr_preds,
                                                            V,
                                                            U
                                                        )};

                                                _ ->
                                                    Inner_acc
                                            end
                                    end
                                end
                            )
                    end
                end
            ),
            relaxation_passes(
                Graph,
                Nodes,
                New_distances,
                New_predecessors,
                Remaining - 1,
                Add,
                Compare
            )
    end.

-file("src/yog/pathfinding.gleam", 489).
-spec has_negative_cycle(
    yog@model:graph(any(), KYZ),
    list(integer()),
    gleam@dict:dict(integer(), KYZ),
    fun((KYZ, KYZ) -> KYZ),
    fun((KYZ, KYZ) -> gleam@order:order())
) -> boolean().
has_negative_cycle(Graph, Nodes, Distances, Add, Compare) ->
    gleam@list:any(Nodes, fun(U) -> case gleam_stdlib:map_get(Distances, U) of
                {error, nil} ->
                    false;

                {ok, U_dist} ->
                    _pipe = yog@model:successors(Graph, U),
                    gleam@list:any(
                        _pipe,
                        fun(Edge) ->
                            {V, Weight} = Edge,
                            New_dist = Add(U_dist, Weight),
                            case gleam_stdlib:map_get(Distances, V) of
                                {error, nil} ->
                                    false;

                                {ok, V_dist} ->
                                    case Compare(New_dist, V_dist) of
                                        lt ->
                                            true;

                                        _ ->
                                            false
                                    end
                            end
                        end
                    )
            end end).

-file("src/yog/pathfinding.gleam", 521).
-spec reconstruct_path(
    gleam@dict:dict(integer(), integer()),
    integer(),
    integer(),
    list(integer())
) -> {ok, list(integer())} | {error, nil}.
reconstruct_path(Predecessors, Start, Current, Acc) ->
    case Current =:= Start of
        true ->
            {ok, Acc};

        false ->
            case gleam_stdlib:map_get(Predecessors, Current) of
                {error, nil} ->
                    {error, nil};

                {ok, Pred} ->
                    reconstruct_path(Predecessors, Start, Pred, [Pred | Acc])
            end
    end.

-file("src/yog/pathfinding.gleam", 379).
?DOC(
    " Finds shortest path with support for negative edge weights using Bellman-Ford.\n"
    "\n"
    " Unlike Dijkstra and A*, this algorithm can handle negative edge weights.\n"
    " It also detects negative cycles reachable from the source node.\n"
    "\n"
    " **Time Complexity:** O(VE) where V is vertices and E is edges\n"
    "\n"
    " ## Returns\n"
    "\n"
    " - `ShortestPath(path)`: If a valid shortest path exists\n"
    " - `NegativeCycle`: If a negative cycle is reachable from the start node\n"
    " - `NoPath`: If no path exists from start to goal\n"
    "\n"
    " ## Example\n"
    "\n"
    " ```gleam\n"
    " pathfinding.bellman_ford(\n"
    "   in: graph,\n"
    "   from: 1,\n"
    "   to: 5,\n"
    "   with_zero: 0,\n"
    "   with_add: int.add,\n"
    "   with_compare: int.compare\n"
    " )\n"
    " // => ShortestPath(Path([1, 3, 5], -2))  // Can have negative total weight\n"
    " // or NegativeCycle                       // If cycle detected\n"
    " // or NoPath                              // If unreachable\n"
    " ```\n"
).
-spec bellman_ford(
    yog@model:graph(any(), KYH),
    integer(),
    integer(),
    KYH,
    fun((KYH, KYH) -> KYH),
    fun((KYH, KYH) -> gleam@order:order())
) -> bellman_ford_result(KYH).
bellman_ford(Graph, Start, Goal, Zero, Add, Compare) ->
    All_nodes = yog@model:all_nodes(Graph),
    Initial_distances = maps:from_list([{Start, Zero}]),
    Initial_predecessors = maps:new(),
    Node_count = erlang:length(All_nodes),
    {Distances, Predecessors} = relaxation_passes(
        Graph,
        All_nodes,
        Initial_distances,
        Initial_predecessors,
        Node_count - 1,
        Add,
        Compare
    ),
    case has_negative_cycle(Graph, All_nodes, Distances, Add, Compare) of
        true ->
            negative_cycle;

        false ->
            case gleam_stdlib:map_get(Distances, Goal) of
                {error, nil} ->
                    no_path;

                {ok, Dist} ->
                    case reconstruct_path(Predecessors, Start, Goal, [Goal]) of
                        {ok, Path} ->
                            {shortest_path, {path, Path, Dist}};

                        {error, nil} ->
                            no_path
                    end
            end
    end.

-file("src/yog/pathfinding.gleam", 718).
?DOC(" Detects if there's a negative cycle by checking if any node has negative distance to itself\n").
-spec detect_negative_cycle(
    gleam@dict:dict({integer(), integer()}, KZT),
    list(integer()),
    KZT,
    fun((KZT, KZT) -> gleam@order:order())
) -> boolean().
detect_negative_cycle(Distances, Nodes, Zero, Compare) ->
    _pipe = Nodes,
    gleam@list:any(
        _pipe,
        fun(I) -> case gleam_stdlib:map_get(Distances, {I, I}) of
                {ok, Dist} ->
                    case Compare(Dist, Zero) of
                        lt ->
                            true;

                        _ ->
                            false
                    end;

                {error, nil} ->
                    false
            end end
    ).

-file("src/yog/pathfinding.gleam", 624).
?DOC(
    " Computes shortest paths between all pairs of nodes using the Floyd-Warshall algorithm.\n"
    "\n"
    " Returns a nested dictionary where `distances[i][j]` gives the shortest distance from node `i` to node `j`.\n"
    " If no path exists between two nodes, the pair will not be present in the dictionary.\n"
    "\n"
    " Returns `Error(Nil)` if a negative cycle is detected in the graph.\n"
    "\n"
    " **Time Complexity:** O(V³)\n"
    " **Space Complexity:** O(V²)\n"
    "\n"
    " ## Parameters\n"
    "\n"
    " - `zero`: The identity element for addition (e.g., `0` for integers, `0.0` for floats)\n"
    " - `add`: Function to add two weights\n"
    " - `compare`: Function to compare two weights\n"
    "\n"
    " ## Example\n"
    "\n"
    " ```gleam\n"
    " import gleam/dict\n"
    " import gleam/int\n"
    " import gleam/io\n"
    " import yog\n"
    " import yog/pathfinding\n"
    "\n"
    " pub fn main() {\n"
    "   let graph =\n"
    "     yog.directed()\n"
    "     |> yog.add_node(1, \"A\")\n"
    "     |> yog.add_node(2, \"B\")\n"
    "     |> yog.add_node(3, \"C\")\n"
    "     |> yog.add_edge(from: 1, to: 2, with: 4)\n"
    "     |> yog.add_edge(from: 2, to: 3, with: 3)\n"
    "     |> yog.add_edge(from: 1, to: 3, with: 10)\n"
    "\n"
    "   case pathfinding.floyd_warshall(\n"
    "     in: graph,\n"
    "     with_zero: 0,\n"
    "     with_add: int.add,\n"
    "     with_compare: int.compare\n"
    "   ) {\n"
    "     Ok(distances) -> {\n"
    "       // Query distance from node 1 to node 3\n"
    "       let assert Ok(row) = dict.get(distances, 1)\n"
    "       let assert Ok(dist) = dict.get(row, 3)\n"
    "       // dist = 7 (via node 2: 4 + 3)\n"
    "       io.println(\"Distance from 1 to 3: \" <> int.to_string(dist))\n"
    "     }\n"
    "     Error(Nil) -> io.println(\"Negative cycle detected!\")\n"
    "   }\n"
    " }\n"
    " ```\n"
    "\n"
    " ## Handling Negative Weights\n"
    "\n"
    " Floyd-Warshall can handle negative edge weights and will detect negative cycles:\n"
    "\n"
    " ```gleam\n"
    " let graph_with_negative_cycle =\n"
    "   yog.directed()\n"
    "   |> yog.add_node(1, \"A\")\n"
    "   |> yog.add_node(2, \"B\")\n"
    "   |> yog.add_edge(from: 1, to: 2, with: 5)\n"
    "   |> yog.add_edge(from: 2, to: 1, with: -10)\n"
    "\n"
    " case pathfinding.floyd_warshall(\n"
    "   in: graph_with_negative_cycle,\n"
    "   with_zero: 0,\n"
    "   with_add: int.add,\n"
    "   with_compare: int.compare\n"
    " ) {\n"
    "   Ok(_) -> io.println(\"No negative cycle\")\n"
    "   Error(Nil) -> io.println(\"Negative cycle detected!\")  // This will execute\n"
    " }\n"
    " ```\n"
    "\n"
    " ## Use Cases\n"
    "\n"
    " - Computing distance matrices for all node pairs\n"
    " - Finding transitive closure of a graph\n"
    " - Detecting negative cycles\n"
    " - Preprocessing for queries about arbitrary node pairs\n"
    " - Graph metrics (diameter, centrality)\n"
).
-spec floyd_warshall(
    yog@model:graph(any(), KZM),
    KZM,
    fun((KZM, KZM) -> KZM),
    fun((KZM, KZM) -> gleam@order:order())
) -> {ok, gleam@dict:dict({integer(), integer()}, KZM)} | {error, nil}.
floyd_warshall(Graph, Zero, Add, Compare) ->
    Nodes = maps:keys(erlang:element(3, Graph)),
    Initial_distances = begin
        _pipe = Nodes,
        gleam@list:fold(_pipe, maps:new(), fun(Distances, I) -> _pipe@1 = Nodes,
                gleam@list:fold(
                    _pipe@1,
                    Distances,
                    fun(Distances@1, J) -> case I =:= J of
                            true ->
                                case gleam_stdlib:map_get(
                                    erlang:element(4, Graph),
                                    I
                                ) of
                                    {ok, Neighbors} ->
                                        case gleam_stdlib:map_get(Neighbors, J) of
                                            {ok, Weight} ->
                                                case Compare(Weight, Zero) of
                                                    lt ->
                                                        gleam@dict:insert(
                                                            Distances@1,
                                                            {I, J},
                                                            Weight
                                                        );

                                                    _ ->
                                                        gleam@dict:insert(
                                                            Distances@1,
                                                            {I, J},
                                                            Zero
                                                        )
                                                end;

                                            {error, nil} ->
                                                gleam@dict:insert(
                                                    Distances@1,
                                                    {I, J},
                                                    Zero
                                                )
                                        end;

                                    {error, nil} ->
                                        gleam@dict:insert(
                                            Distances@1,
                                            {I, J},
                                            Zero
                                        )
                                end;

                            false ->
                                case gleam_stdlib:map_get(
                                    erlang:element(4, Graph),
                                    I
                                ) of
                                    {ok, Neighbors@1} ->
                                        case gleam_stdlib:map_get(
                                            Neighbors@1,
                                            J
                                        ) of
                                            {ok, Weight@1} ->
                                                gleam@dict:insert(
                                                    Distances@1,
                                                    {I, J},
                                                    Weight@1
                                                );

                                            {error, nil} ->
                                                Distances@1
                                        end;

                                    {error, nil} ->
                                        Distances@1
                                end
                        end end
                ) end)
    end,
    Final_distances = begin
        _pipe@2 = Nodes,
        gleam@list:fold(
            _pipe@2,
            Initial_distances,
            fun(Distances@2, K) -> _pipe@3 = Nodes,
                gleam@list:fold(
                    _pipe@3,
                    Distances@2,
                    fun(Distances@3, I@1) -> _pipe@4 = Nodes,
                        gleam@list:fold(
                            _pipe@4,
                            Distances@3,
                            fun(Distances@4, J@1) ->
                                case gleam_stdlib:map_get(Distances@4, {I@1, K}) of
                                    {error, nil} ->
                                        Distances@4;

                                    {ok, Dist_ik} ->
                                        case gleam_stdlib:map_get(
                                            Distances@4,
                                            {K, J@1}
                                        ) of
                                            {error, nil} ->
                                                Distances@4;

                                            {ok, Dist_kj} ->
                                                New_dist = Add(Dist_ik, Dist_kj),
                                                case gleam_stdlib:map_get(
                                                    Distances@4,
                                                    {I@1, J@1}
                                                ) of
                                                    {error, nil} ->
                                                        gleam@dict:insert(
                                                            Distances@4,
                                                            {I@1, J@1},
                                                            New_dist
                                                        );

                                                    {ok, Current_dist} ->
                                                        case Compare(
                                                            New_dist,
                                                            Current_dist
                                                        ) of
                                                            lt ->
                                                                gleam@dict:insert(
                                                                    Distances@4,
                                                                    {I@1, J@1},
                                                                    New_dist
                                                                );

                                                            _ ->
                                                                Distances@4
                                                        end
                                                end
                                        end
                                end
                            end
                        ) end
                ) end
        )
    end,
    case detect_negative_cycle(Final_distances, Nodes, Zero, Compare) of
        true ->
            {error, nil};

        false ->
            {ok, Final_distances}
    end.