title: Total Number Of Non Decreasing Numbers With N Digits
signature: totalNumberOfNonDecreasingNumbersWithNDigits :: Integer -> Integer
  totalNumberOfNonDecreasingNumbersWithNDigits n = 
test_code: import Text.Printf
  import Control.Exception (catch, SomeException)
  import Data.Typeable
  import qualified Data.List as List
  import qualified Data.Map as Map
  import qualified Data.Set as Set
  
  -- SOLUTION CODE
  -- ============================================
  
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  validateSolution :: Integer -> Integer -> Bool
  validateSolution actual expected = do
      actual == expected
  
  
  driver :: Integer -> Integer -> String
  driver n expected = do
      if (validateSolution (PLACEHOLDER_FN_NAME n) expected)
          then "PASSED"
      else "FAILED"
  
  main = do
      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) )
  
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;
  }