title: Eulerian Number 1
signature: function eulerian_number_1(n, m)
test_code: using Printf
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  function validate_solution(actual, expected)
      return actual == expected
  end
  
  function driver(n, m, expected)
      try
  
          if validate_solution(PLACEHOLDER_FN_NAME(n, m), expected)
              return "PASSED";
          end
          return "FAILED";
      catch exception_obj
          return string(Base.typename(typeof(exception_obj)).wrapper);
      end
  end
  
  function main()
      
      result = driver(6, 10, 0);
      @printf("TEST-0...%s\n",result);
      
      result = driver(26, 33, 0);
      @printf("TEST-1...%s\n",result);
      
      result = driver(74, 86, 0);
      @printf("TEST-2...%s\n",result);
      
      result = driver(65, 97, 0);
      @printf("TEST-3...%s\n",result);
      
  end
  
  main()
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 ];
  }