add solution for problem 19

problems/19/solution.livemd

@@ -0,0 +1,68 @@
+# Project Euler Problem 19
+
+```elixir
+defmodule CountingSundays do
+  defguard is_leap_year(y) when rem(y, 4) == 0 and (rem(y, 100) != 0 or rem(y, 400) == 0)
+  
+  @days %{
+    0 => :sun,
+    1 => :mon,
+    2 => :tue,
+    3 => :wed,
+    4 => :thur,
+    5 => :fri,
+    6 => :sat,
+  }
+  
+  @months %{
+    0 => :jan,
+    1 => :feb,
+    2 => :mar,
+    3 => :apr,
+    4 => :may,
+    5 => :jun,
+    6 => :jul,
+    7 => :aug,
+    8 => :sep,
+    9 => :oct,
+    10 => :nov,
+    11 => :dec
+  }
+
+  def days_in_month(year, month) do
+    case month do
+      m when m in [:apr, :jun, :nov, :sep] -> 30
+      :feb when is_leap_year(year) -> 29
+      :feb -> 28
+      _ -> 31
+    end
+  end
+  
+  def add_days(d, days), do: rem(d + days, 7)
+
+  defp count_sundays_between(year, month, fin_year, fin_month, _, acc) 
+    when fin_month < month and fin_year == year or year > fin_year do
+    acc
+  end
+  
+  defp count_sundays_between(year, month, fin_year, fin_month, d, acc) do
+    next = add_days(d, days_in_month(year, @months[month]))
+
+    acc = if @days[next] == :sun, do: acc + 1, else: acc
+    {year, month} = case month do
+      11 -> { year + 1, 0}
+      n -> { year, n + 1}
+    end
+    
+    count_sundays_between(year, month, fin_year, fin_month, next, acc)
+  end
+
+  def count_sundays() do
+    count_sundays_between(1900, 0, 2000, 11, 1, 0) - count_sundays_between(1900, 0, 1900, 11, 1, 0)
+  end
+end
+```
+
+```elixir
+CountingSundays.count_sundays()
+```