title: Total Number Of Non Decreasing Numbers With N Digits
signature: func totalNumberOfNonDecreasingNumbersWithNDigits(n int) int64 {
test_code: package main
  
  import (
      "fmt"
      "reflect"
      "math"
      "sort"
  )
  
  // SOLUTION CODE
  // ===================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE
  // ===================================
  func validateSolution(actual int64, expected int64) bool {
      return reflect.DeepEqual(actual,expected)
  }
  
  func driver(n int, expected int64) string {
      if validateSolution(PLACEHOLDER_FN_NAME(n),expected) {
              return "PASSED"
      }
      return "FAILED"
  
  }
  
  func main() {
  
      // Use imports to avoid undefined errors
      var _ = reflect.DeepEqual
      _ = math.Abs
      _ = sort.Sort
      result := ""
      result = driver(21, 14307150)
      fmt.Printf("TEST-0...%s\n", result)
      
      result = driver(40, 2054455634)
      fmt.Printf("TEST-1...%s\n", result)
      
      result = driver(83, 868754947060)
      fmt.Printf("TEST-2...%s\n", result)
      
      result = driver(93, 2290415157800)
      fmt.Printf("TEST-3...%s\n", result)
      
      result = driver(43, 3679075400)
      fmt.Printf("TEST-4...%s\n", result)
      
      result = driver(98, 3585446225075)
      fmt.Printf("TEST-5...%s\n", result)
      
      result = driver(35, 708930508)
      fmt.Printf("TEST-6...%s\n", result)
      
      result = driver(86, 1174992339235)
      fmt.Printf("TEST-7...%s\n", result)
      
      result = driver(76, 411731930610)
      fmt.Printf("TEST-8...%s\n", result)
      
      result = driver(88, 1429144287220)
      fmt.Printf("TEST-9...%s\n", result)
      
          
  }
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;
  }