title: Bell Numbers Number Of Ways To Partition A Set
signature: bellNumbersNumberOfWaysToPartitionASet(n) {
test_code: import 'dart:convert';
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  bool validateSolution(int actual, int expected){
      return actual.toString() == expected.toString();
  }
  
  String driver(n, int expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(n), expected)){
              return "PASSED";
          }
          return "FAILED";
      }catch(exception_object){
          return exception_object.runtimeType.toString();
      }
  }
  
  int main() {
  
      print("TEST-0...${driver(
          9, 
          21147)
      }");
  
      print("TEST-1...${driver(
          4, 
          15)
      }");
  
      print("TEST-2...${driver(
          6, 
          203)
      }");
  
      return 0;
  }
source_py: def bell_numbers_number_of_ways_to_partition_a_set(n):
      bell = [[0 for i in range((n + 1))] for j in range((n + 1))]
      bell[0][0] = 1
      for i in range(1, (n + 1)):
          bell[i][0] = bell[(i - 1)][(i - 1)]
          for j in range(1, (i + 1)):
              bell[i][j] = (bell[(i - 1)][(j - 1)] + bell[i][(j - 1)])
      return bell[n][0]
source_cpp: int bell_numbers_number_of_ways_to_partition_a_set(int n) {
    int bell [ n + 1 ] [ n + 1 ];
    bell [ 0 ] [ 0 ] = 1;
    for ( int i = 1;
    i <= n;
    i ++ ) {
      bell [ i ] [ 0 ] = bell [ i - 1 ] [ i - 1 ];
      for ( int j = 1;
      j <= i;
      j ++ ) bell [ i ] [ j ] = bell [ i - 1 ] [ j - 1 ] + bell [ i ] [ j - 1 ];
    }
    return bell [ n ] [ 0 ];
  }