title: Number Of Binary Trees For Given Preorder Sequence Length
signature: numberOfBinaryTreesForGivenPreorderSequenceLength :: Integer -> Integer
  numberOfBinaryTreesForGivenPreorderSequenceLength n = 
test_code: import Text.Printf
  import Control.Exception (catch, SomeException)
  import Data.Typeable
  import qualified Data.List as List
  import qualified Data.Map as Map
  import qualified Data.Set as Set
  
  -- SOLUTION CODE
  -- ============================================
  
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  validateSolution :: Integer -> Integer -> Bool
  validateSolution actual expected = do
      actual == expected
  
  
  driver :: Integer -> Integer -> String
  driver n expected = do
      if (validateSolution (PLACEHOLDER_FN_NAME n) expected)
          then "PASSED"
      else "FAILED"
  
  main = do
      printf "TEST-0...%s\n" (driver (15) (9694845) )
  
      printf "TEST-1...%s\n" (driver (11) (58786) )
  
      printf "TEST-2...%s\n" (driver (11) (58786) )
  
      printf "TEST-3...%s\n" (driver (15) (9694845) )
  
source_py: def number_of_binary_trees_for_given_preorder_sequence_length(n):
      BT = ([0] * (n + 1))
      BT[0] = BT[1] = 1
      for i in range(2, (n + 1)):
          for j in range(i):
              BT[i] += (BT[j] * BT[((i - j) - 1)])
      return BT[n]
source_cpp: int number_of_binary_trees_for_given_preorder_sequence_length(int n) {
    int BT [ n + 1 ];
    memset ( BT, 0, sizeof ( BT ) );
    BT [ 0 ] = BT [ 1 ] = 1;
    for ( int i = 2;
    i <= n;
    ++ i ) for ( int j = 0;
    j < i;
    j ++ ) BT [ i ] += BT [ j ] * BT [ i - j - 1 ];
    return BT [ n ];
  }