357 Count Numbers with Unique Digits

🔀 Pick One

Given an integer n, return the count of all numbers with unique digits, x, where 0 <= x < 10n.

Example 1:

Input: n = 2
Output: 91
Explanation: The answer should be the total numbers in the range of 0 ≤ x < 100,
excluding 11,22,33,44,55,66,77,88,99

Example 2:

Input: n = 0
Output: 1

Constraints:

  • 0 <= n <= 8
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20

class Solution:
    '''
    <x-digit num: y numbers with unique digits>
    0: 1
    1: 9
    2: 9*9
    3: 9*9*8
    4: 9*9*8*7
    '''
    def countNumbersWithUniqueDigits(self, n: int) -> int:
        res = 1
        acc = 9
        cur = 9
        i = 1
        while i <= n:
            res += acc
            acc *= cur
            cur -= 1
            i += 1
        return res