Is Count Numbers with Unique Digits easy or hard?

The problem is rated Medium because the brute force idea is straightforward but recognizing the permutation pattern requires combinatorial reasoning. Once the pattern is identified, the implementation becomes very short and efficient.

How to solve Count Numbers with Unique Digits in O(n)?

Iterate over digit lengths from 1 to n and compute permutations. For length k, the count is 9 × 9 × 8 × ... for k digits because each new digit has fewer choices. Accumulate these counts to get the total number of valid integers.

Count Numbers with Unique Digits Python or Java solution?

Python solutions commonly implement backtracking with a visited set or use a simple loop to compute permutations. Java and C++ implementations often use the mathematical approach with iterative multiplication to maintain O(n) time and O(1) space.

What is the best approach for Count Numbers with Unique Digits?

The mathematical permutation approach is the most efficient. It counts how many valid digit permutations exist for each length instead of generating numbers. This runs in O(n) time with O(1) space and stops after 10 digits because only 10 unique digits exist.

Is Count Numbers with Unique Digits asked at Google/Amazon/Meta?

Permutation and combinatorics counting problems like this appear in interviews at large companies including Google and Amazon. The question tests understanding of digit constraints, permutations, and recognizing when enumeration can be replaced by counting.

What data structure is used in Count Numbers with Unique Digits?

The optimal solution mainly uses mathematical counting and does not require complex data structures. A backtracking implementation typically uses a boolean array or set to track which digits have already been used.

What is the time complexity of Count Numbers with Unique Digits?

The optimal permutation-based solution runs in O(n) time and O(1) space since it only multiplies decreasing digit choices for each length up to n. A backtracking solution can take up to O(10!) time because it explores permutations of digits.

Talentd/FleetCode/Problems/

357. Count Numbers with Unique Digits

Medium

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357. Count Numbers with Unique Digits

Medium56.1% Acceptance

Math Dynamic Programming Backtracking

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

Asked by 5 companies

Amazon

Microsoft