title: Total Number Of Non Decreasing Numbers With N Digits
signature: def totalNumberOfNonDecreasingNumbersWithNDigits(n: Int) = {
test_code: import scala.collection.mutable.HashMap
  import scala.collection.immutable.HashSet
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  
  // TESTING CODE 
  // ============================================
  def validateSolution(actual: Long , expected: Long): Boolean = {
      actual.toString == expected.toString
  }
  
  def driver(n: Int, expected: Long): String = {
      try {
          if (validateSolution(PLACEHOLDER_FN_NAME(n),expected)) {
              "PASSED"
          } else{
              "FAILED"
          }
      }catch{
          case e: Exception => {e.getClass.getName}
      }
  
  }
  object QuestionEvaluator extends App {
  
      println(s"TEST-0...${driver(
        21, 
        14307150L    
      )}")   
  
  
      println(s"TEST-1...${driver(
        40, 
        2054455634L    
      )}")   
  
  
      println(s"TEST-2...${driver(
        83, 
        868754947060L    
      )}")   
  
  
      println(s"TEST-3...${driver(
        93, 
        2290415157800L    
      )}")   
  
  
      println(s"TEST-4...${driver(
        43, 
        3679075400L    
      )}")   
  
  
      println(s"TEST-5...${driver(
        98, 
        3585446225075L    
      )}")   
  
  
      println(s"TEST-6...${driver(
        35, 
        708930508L    
      )}")   
  
  
      println(s"TEST-7...${driver(
        86, 
        1174992339235L    
      )}")   
  
  
      println(s"TEST-8...${driver(
        76, 
        411731930610L    
      )}")   
  
  
      println(s"TEST-9...${driver(
        88, 
        1429144287220L    
      )}")   
  
  }
  
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;
  }