Add Elixir example for Dijkstra's algorithm

07_dijkstras_algorithm/elixir/01_dijkstras_algorithm.exs

@@ -0,0 +1,84 @@
+defmodule DijkstrasAlgorithm do
+  def find_shortest_path(graph, costs, parents),
+    do: do_find_shortest_path(graph, costs, parents, [])
+
+  defp do_find_shortest_path(graph, costs, parents, processed) do
+    find_lowest_cost_node(costs, processed)
+    |> process_node(processed, graph, costs, parents)
+  end
+
+  defp process_node(nil, _, _, costs, parents), do: {costs, parents}
+
+  defp process_node(node, processed, graph, costs, parents) do
+    node_cost = costs[node]
+    neighbors = for(neighbor_node_cost <- graph[node], do: neighbor_node_cost)
+
+    {new_costs, new_parents} = process_node_neighbors(node, node_cost, neighbors, costs, parents)
+
+    do_find_shortest_path(graph, new_costs, new_parents, [node | processed])
+  end
+
+  defp process_node_neighbors(node, node_cost, neighbors, costs, parents)
+
+  defp process_node_neighbors(_, _, [], costs, parents), do: {costs, parents}
+
+  defp process_node_neighbors(node, node_cost, [neighbor | tail], costs, parents) do
+    {neighbor_node, neighbor_cost} = neighbor
+    new_cost = node_cost + neighbor_cost
+
+    if costs[neighbor_node] > node_cost + neighbor_cost do
+      new_costs = %{costs | neighbor_node => new_cost}
+      new_parents = %{parents | neighbor_node => node}
+
+      process_node_neighbors(node, node_cost, tail, new_costs, new_parents)
+    else
+      process_node_neighbors(node, node_cost, tail, costs, parents)
+    end
+  end
+
+  defp find_lowest_cost_node(costs, processed) do
+    {lowest_cost_node, _} =
+      for({node, cost} <- costs, node not in processed, do: {node, cost})
+      |> find_lowest_cost
+
+    lowest_cost_node
+  end
+
+  defp find_lowest_cost([]), do: {nil, :infinity}
+
+  defp find_lowest_cost([node_cost | []]), do: node_cost
+
+  defp find_lowest_cost([node_cost = {_, cost} | tail]) do
+    (min_node_cost = {_, min_cost}) = find_lowest_cost(tail)
+
+    if cost < min_cost,
+      do: node_cost,
+      else: min_node_cost
+  end
+end
+
+# the graph
+graph = %{
+  "start" => %{"a" => 6, "b" => 2},
+  "a" => %{"fin" => 1},
+  "b" => %{"a" => 3, "fin" => 5},
+  "fin" => %{}
+}
+
+# the costs table
+costs = %{
+  "a" => 6,
+  "b" => 2,
+  "fin" => :infinity
+}
+
+# the parents table
+parents = %{
+  "a" => "start",
+  "b" => "start",
+  "fin" => nil
+}
+
+{costs, _} = DijkstrasAlgorithm.find_shortest_path(graph, costs, parents)
+IO.puts("Cost from the start to each node:")
+IO.inspect(costs)