title: Eulerian Number 1
signature: def eulerianNumber1(n: Int, m: Int) = {
test_code: import scala.collection.mutable.HashMap
  import scala.collection.immutable.HashSet
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  
  // TESTING CODE 
  // ============================================
  def validateSolution(actual: Int , expected: Int): Boolean = {
      actual.toString == expected.toString
  }
  
  def driver(n: Int, m: Int, expected: Int): String = {
      try {
          if (validateSolution(PLACEHOLDER_FN_NAME(n, m),expected)) {
              "PASSED"
          } else{
              "FAILED"
          }
      }catch{
          case e: Exception => {e.getClass.getName}
      }
  
  }
  object QuestionEvaluator extends App {
  
      println(s"TEST-0...${driver(
        6, 10, 
        0    
      )}")   
  
  
      println(s"TEST-1...${driver(
        26, 33, 
        0    
      )}")   
  
  
      println(s"TEST-2...${driver(
        74, 86, 
        0    
      )}")   
  
  
      println(s"TEST-3...${driver(
        65, 97, 
        0    
      )}")   
  
  }
  
source_py: def eulerian_number_1(n, m):
      dp = [[0 for x in range((m + 1))] for y in range((n + 1))]
      for i in range(1, (n + 1)):
          for j in range(0, (m + 1)):
              if (i > j):
                  if (j == 0):
                      dp[i][j] = 1
                  else:
                      dp[i][j] = (((i - j) * dp[(i - 1)][(j - 1)]) + ((j + 1) * dp[(i - 1)][j]))
      return dp[n][m]
source_cpp: int eulerian_number_1(int n, int m) {
    int dp [ n + 1 ] [ m + 1 ];
    memset ( dp, 0, sizeof ( dp ) );
    for ( int i = 1;
    i <= n;
    i ++ ) {
      for ( int j = 0;
      j <= m;
      j ++ ) {
        if ( i > j ) {
          if ( j == 0 ) dp [ i ] [ j ] = 1;
          else dp [ i ] [ j ] = ( ( i - j ) * dp [ i - 1 ] [ j - 1 ] ) + ( ( j + 1 ) * dp [ i - 1 ] [ j ] );
        }
      }
    }
    return dp [ n ] [ m ];
  }