add problem 18 and 67

problems/18/solution.livemd

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+# Project Euler 18 and 67
+
+## Section
+
+```elixir
+defmodule PathSum do
+  defstruct data: %{}, depth: 0
+  def parse(input) do
+    data = input
+    |> String.trim()
+    |> String.split("\n")
+    |> Stream.with_index()
+    |> Stream.flat_map(fn {line, j} -> 
+      line
+      |> String.split(" ")
+      |> Stream.map(&String.to_integer/1)
+      |> Stream.with_index()
+      |> Stream.map(fn {n, i} -> {{j, i}, n} end)
+      end)
+    |> Enum.into(%{})
+
+    %__MODULE__{
+      data: data,
+      depth: data |> Enum.max_by(fn {{x, _}, _} -> x end) |> elem(0) |> elem(0)
+    }
+  end
+
+  defmacro with_val(coord, tree) do 
+    quote do
+      { unquote(coord), Map.get(unquote(tree).data, unquote(coord)) }
+    end
+  end
+
+  def above({0, 0}, _), do: nil
+  def above({1, _}, tree), do: {0, 0} |> with_val(tree)
+  def above({n, 0}, tree), do: {n - 1, 0} |> with_val(tree)
+  def above({n, n}, tree), do: {n - 1, n - 1} |> with_val(tree)
+  def above({n, m}, tree), do: [{n - 1, m - 1} |> with_val(tree), {n - 1, m} |> with_val(tree)]
+  
+  def best_path_to(tree, loc) do
+    case Process.get({tree, loc}) do
+      nil -> 
+        best = case above(loc, tree) do
+          nil -> 0
+          {c, n} -> n + best_path_to(tree, c)
+          [{lloc, left}, {rloc, right}] ->
+            ll = left + best_path_to(tree, lloc)
+            rr = right + best_path_to(tree, rloc)
+            if ll > rr do
+              ll
+            else
+              rr
+            end
+        end
+        Process.put({tree, loc}, best)
+        best
+      n -> n
+    end   
+  end
+
+  @doc """
+  
+  ## Example
+  iex> """
+  ...> 3
+  ...> 7 4
+  ...> 2 4 6
+  ...> 8 5 9 3
+  ...> """ |>
+  ...> PathSum.parse() |> PathSum.best_path()
+  23
+  """
+  def best_path(tree) do
+    for {{x, _} = coord, n} <- tree.data,
+      x == tree.depth,
+      reduce: 0 do
+      best -> 
+        max(best, n + best_path_to(tree, coord))
+    end
+  end
+end
+```

problems/67/solution.txt

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+See problem 18