title: Total Number Of Non Decreasing Numbers With N Digits
signature: function totalNumberOfNonDecreasingNumbersWithNDigits($n) {
test_code: <?php
  
  
  // SOLUTION CODE 
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function validateSolution($actual, $expected){
      return serialize($actual) == serialize($expected);
  }
  
  function driver($n, $expected){
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME($n), $expected)){
          return "PASSED";
        }
        return "FAILED";
      }
      catch (Exception $exception_obj) {
        return get_class($exception_obj);
      }
  }
  
  function main(){
      printf("TEST-0...%s\n",driver(
        21, 
        14307150));
      
      printf("TEST-1...%s\n",driver(
        40, 
        2054455634));
      
      printf("TEST-2...%s\n",driver(
        83, 
        868754947060));
      
      printf("TEST-3...%s\n",driver(
        93, 
        2290415157800));
      
      printf("TEST-4...%s\n",driver(
        43, 
        3679075400));
      
      printf("TEST-5...%s\n",driver(
        98, 
        3585446225075));
      
      printf("TEST-6...%s\n",driver(
        35, 
        708930508));
      
      printf("TEST-7...%s\n",driver(
        86, 
        1174992339235));
      
      printf("TEST-8...%s\n",driver(
        76, 
        411731930610));
      
      printf("TEST-9...%s\n",driver(
        88, 
        1429144287220));
      
  }
  
  main();
  ?>
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;
  }