357. Count Numbers with Unique Digits

Problem

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

Solution

class Solution {
    public int countNumbersWithUniqueDigits(int n) {
        int ans = 1;
        for (int i = 1; i <= n; i++) {
            int mul = 1;
            for (int j = 1; j < i; j++) {
                mul *= (10 - j);
            }
            ans = ans + 9 * mul;
        }
        return ans;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).