title: Bell Numbers Number Of Ways To Partition A Set
signature: pub fn bell_numbers_number_of_ways_to_partition_a_set(n: i32) -> i32 {
test_code: use std::collections::HashMap;
  use std::collections::HashSet;
  use std::cmp::*;
  use std::collections::*;
  use std::fmt::*; 
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  pub fn validate_solution(actual: i32, expected: i32)->bool{
  return actual==expected
  }
  pub fn driver(n: i32, expected: i32)->String{
      if validate_solution(PLACEHOLDER_FN_NAME(n), expected) {
        return "PASSED".to_string();
      };
      return "FAILED".to_string();
  
  }
  
  fn main() {
      println!("TEST-0...{}", driver(
        9, 
        21147
      ));
      
      println!("TEST-1...{}", driver(
        4, 
        15
      ));
      
      println!("TEST-2...{}", driver(
        6, 
        203
      ));
      
  }
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 ];
  }