title: Count Sum Of Digits In Numbers From 1 To N
signature: function count_sum_of_digits_in_numbers_from_1_to_n(n)
test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return isCorrect(actual,expected)
  end
  
  function driver(n, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(n) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver(29, 165)
      print(string.format("TEST-0...%s",result))
  
      result = driver(97, 865)
      print(string.format("TEST-1...%s",result))
  
      result = driver(71, 540)
      print(string.format("TEST-2...%s",result))
  
      result = driver(82, 667)
      print(string.format("TEST-3...%s",result))
  
      result = driver(69, 525)
      print(string.format("TEST-4...%s",result))
  
      result = driver(30, 168)
      print(string.format("TEST-5...%s",result))
  
      result = driver(82, 667)
      print(string.format("TEST-6...%s",result))
  
      result = driver(32, 177)
      print(string.format("TEST-7...%s",result))
  
      result = driver(77, 609)
      print(string.format("TEST-8...%s",result))
  
      result = driver(39, 240)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def count_sum_of_digits_in_numbers_from_1_to_n(n):
      if (n < 10):
          return ((n * (n + 1)) / 2)
      d = int(math.log10(n))
      a = ([0] * (d + 1))
      a[0] = 0
      a[1] = 45
      for i in range(2, (d + 1)):
          a[i] = ((a[(i - 1)] * 10) + (45 * int(math.ceil(math.pow(10, (i - 1))))))
      p = int(math.ceil(math.pow(10, d)))
      msd = (n // p)
      return int(((((msd * a[d]) + (((msd * (msd - 1)) // 2) * p)) + (msd * (1 + (n % p)))) + count_sum_of_digits_in_numbers_from_1_to_n((n % p))))
source_cpp: int count_sum_of_digits_in_numbers_from_1_to_n(int n) {
    if ( n < 10 ) return n * ( n + 1 ) / 2;
    int d = log10 ( n );
    int * a = new int [ d + 1 ];
    a [ 0 ] = 0, a [ 1 ] = 45;
    for ( int i = 2;
    i <= d;
    i ++ ) a [ i ] = a [ i - 1 ] * 10 + 45 * ceil ( pow ( 10, i - 1 ) );
    int p = ceil ( pow ( 10, d ) );
    int msd = n / p;
    return msd * a [ d ] + ( msd * ( msd - 1 ) / 2 ) * p + msd * ( 1 + n % p ) + count_sum_of_digits_in_numbers_from_1_to_n ( n % p );
  }