title: Total Number Of Non Decreasing Numbers With N Digits
signature: fun totalNumberOfNonDecreasingNumbersWithNDigits(n: Int): Long {
test_code: package main
  
  import kotlin.text.*
  import kotlin.math.*
  
  
  // SOLUTION CODE
  // ===================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE
  // ===================================
  fun validateSolution(actual:Long, expected:Long):Boolean{
    return actual.equals(expected)
  }
  fun driver(n: Int, expected:Long):String {
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME(n), expected)) {
                return "PASSED"
        }
        return "FAILED"
      } catch (e: Exception){
        return e::class.simpleName as String
      }
  
  }
  
  fun main() {
      var result: String = ""
      result = driver(21, 14307150)
      println("TEST-0...${result}")
      
      result = driver(40, 2054455634)
      println("TEST-1...${result}")
      
      result = driver(83, 868754947060)
      println("TEST-2...${result}")
      
      result = driver(93, 2290415157800)
      println("TEST-3...${result}")
      
      result = driver(43, 3679075400)
      println("TEST-4...${result}")
      
      result = driver(98, 3585446225075)
      println("TEST-5...${result}")
      
      result = driver(35, 708930508)
      println("TEST-6...${result}")
      
      result = driver(86, 1174992339235)
      println("TEST-7...${result}")
      
      result = driver(76, 411731930610)
      println("TEST-8...${result}")
      
      result = driver(88, 1429144287220)
      println("TEST-9...${result}")
      
          
  }
  
  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;
  }