357. Count Numbers with Unique Digits

Update time

Given a non-negative integer n, count all numbers with unique digits, x, where 0 ≤ x < 10n.

Example:

Input: 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

Constraints:

0 <= n <= 8

# @lc code=start
using LeetCode

function count_numbers_with_unique_digits(n::Int)
    n > 10 && return count_numbers_with_unique_digits(10)
    n == 0 && return 1
    return 9 * binomial(9, n - 1) * factorial(n - 1) +
           count_numbers_with_unique_digits(n - 1)
end
# @lc code=end

count_numbers_with_unique_digits (generic function with 1 method)

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