title: Total Number Of Non Decreasing Numbers With N Digits
signature: totalNumberOfNonDecreasingNumbersWithNDigits(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(
          21, 
          14307150)
      }");
  
      print("TEST-1...${driver(
          40, 
          2054455634)
      }");
  
      print("TEST-2...${driver(
          83, 
          868754947060)
      }");
  
      print("TEST-3...${driver(
          93, 
          2290415157800)
      }");
  
      print("TEST-4...${driver(
          43, 
          3679075400)
      }");
  
      print("TEST-5...${driver(
          98, 
          3585446225075)
      }");
  
      print("TEST-6...${driver(
          35, 
          708930508)
      }");
  
      print("TEST-7...${driver(
          86, 
          1174992339235)
      }");
  
      print("TEST-8...${driver(
          76, 
          411731930610)
      }");
  
      print("TEST-9...${driver(
          88, 
          1429144287220)
      }");
  
      return 0;
  }
source_py: def total_number_of_non_decreasing_numbers_with_n_digits(n):
      dp = [[0 for i in range((n + 1))] for i in range(10)]
      for i in range(10):
          dp[i][1] = 1
      for digit in range(10):
          for len in range(2, (n + 1)):
              for x in range((digit + 1)):
                  dp[digit][len] += dp[x][(len - 1)]
      count = 0
      for i in range(10):
          count += dp[i][n]
      return count
source_cpp: long long int total_number_of_non_decreasing_numbers_with_n_digits(int n) {
    long long int dp [ 10 ] [ n + 1 ];
    memset ( dp, 0, sizeof dp );
    for ( int i = 0;
    i < 10;
    i ++ ) dp [ i ] [ 1 ] = 1;
    for ( int digit = 0;
    digit <= 9;
    digit ++ ) {
      for ( int len = 2;
      len <= n;
      len ++ ) {
        for ( int x = 0;
        x <= digit;
        x ++ ) dp [ digit ] [ len ] += dp [ x ] [ len - 1 ];
      }
    }
    long long int count = 0;
    for ( int i = 0;
    i < 10;
    i ++ ) count += dp [ i ] [ n ];
    return count;
  }