tasks a-s

Task/Catalan-numbers/Fantom/catalan-numbers.fantom

@@ -0,0 +1,52 @@
+class Main
+{
+  static Int factorial (Int n)
+  {
+    Int res := 1
+    if (n>1)
+      (2..n).each |i| { res *= i }
+    return res
+  }
+
+  static Int catalanA (Int n)
+  {
+    return factorial(2*n)/(factorial(n+1) * factorial(n))
+  }
+
+  static Int catalanB (Int n)
+  {
+    if (n == 0)
+    {
+      return 1
+    }
+    else
+    {
+      sum := 0
+      n.times |i| { sum += catalanB(i) * catalanB(n-1-i) }
+      return sum
+    }
+  }
+
+  static Int catalanC (Int n)
+  {
+    if (n == 0)
+    {
+      return 1
+    }
+    else
+    {
+      return catalanC(n-1)*2*(2*n-1)/(n+1)
+    }
+  }
+
+  public static Void main ()
+  {
+    (1..15).each |n|
+    {
+      echo (n.toStr.padl(4) +
+            catalanA(n).toStr.padl(10) +
+            catalanB(n).toStr.padl(10) +
+            catalanC(n).toStr.padl(10))
+    }
+  }
+}