title: Total Number Of Non Decreasing Numbers With N Digits
signature: pub fn total_number_of_non_decreasing_numbers_with_n_digits(n: i32) -> i64 {
test_code: use std::collections::HashMap;
  use std::collections::HashSet;
  use std::cmp::*;
  use std::collections::*;
  use std::fmt::*; 
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  pub fn validate_solution(actual: i64, expected: i64)->bool{
  return actual==expected
  }
  pub fn driver(n: i32, expected: i64)->String{
      if validate_solution(PLACEHOLDER_FN_NAME(n), expected) {
        return "PASSED".to_string();
      };
      return "FAILED".to_string();
  
  }
  
  fn main() {
      println!("TEST-0...{}", driver(
        21, 
        14307150
      ));
      
      println!("TEST-1...{}", driver(
        40, 
        2054455634
      ));
      
      println!("TEST-2...{}", driver(
        83, 
        868754947060
      ));
      
      println!("TEST-3...{}", driver(
        93, 
        2290415157800
      ));
      
      println!("TEST-4...{}", driver(
        43, 
        3679075400
      ));
      
      println!("TEST-5...{}", driver(
        98, 
        3585446225075
      ));
      
      println!("TEST-6...{}", driver(
        35, 
        708930508
      ));
      
      println!("TEST-7...{}", driver(
        86, 
        1174992339235
      ));
      
      println!("TEST-8...{}", driver(
        76, 
        411731930610
      ));
      
      println!("TEST-9...{}", 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;
  }