Add elixir longest common subsequence implementation (#306)

11_dynamic_programming/elixir/01_longest_common_subsequence.exs

@@ -1,12 +1,51 @@
-# `cell` is a map of maps here, e.g.
+defmodule LCSubsequence do
-# cell = %{
+  def generate_table(word_a, word_b) do
-#   0 => %{0 => 0, ...},
+    word_a
-#   1 => %{...},
+    |> Enum.with_index()
-#   ...
+    |> Enum.reduce(%{}, fn {_x, index}, acc ->
-# }
+      nested_map =
+        word_b
+        |> Enum.with_index()
+        |> Enum.reduce(%{}, fn {_x, index}, acc ->
+          Map.put(acc, index, 0)
+        end)
 
-if String.at(word_a, i) == String.at(word_a, j) do
+      Map.put(acc, index, nested_map)
-  put_in(cell[i - 1][j - 1], cell[i - 1][j - 1] + 1)
+    end)
-else
+  end
-  put_in(cell[i - 1][j - 1], max(cell[i - 1][j], cell[i][j - 1]))
+
+  def compute(table, word_a, word_b) do
+    for i <- 0..(length(word_a) - 1), reduce: table do
+      table ->
+        for j <- 0..(length(word_b) - 1), reduce: table do
+          table ->
+            if Enum.at(word_a, i) == Enum.at(word_b, j) do
+              value = (table[i - 1][j - 1] || 0) + 1
+              put_in(table[i][j], value)
+            else
+              first = table[i - 1][j] || 0
+              second = table[i][j - 1] || 0
+              put_in(table[i][j], max(first, second))
+            end
+        end
+    end
+  end
 end
+
+word_a = ["b", "l", "u", "e"]
+word_b = ["c", "l", "u", "e", "s"]
+
+result =
+  word_a
+  |> LCSubsequence.generate_table(word_b)
+  |> LCSubsequence.compute(word_a, word_b)
+
+Enum.each(result, fn {_index, value} ->
+  IO.inspect(Map.values(value))
+end)
+
+# Output
+# [0, 0, 0, 0, 0]
+# [0, 1, 1, 1, 1]
+# [0, 1, 2, 2, 2]
+# [0, 1, 2, 3, 3]