Count Numbers With Unique Digits II

Count Numbers With Unique Digits II - Problem

Given two positive integers a and b, return the count of numbers having unique digits in the range [a, b] (inclusive).

A number has unique digits if no digit appears more than once in the number. For example, 123 has unique digits, but 121 does not because the digit 1 appears twice.

Input & Output

Example 1 — Small Range

$ Input: a = 20, b = 25

› Output: 5

💡 Note: Numbers 20, 21, 23, 24, 25 all have unique digits. Number 22 has repeated digit '2', so it's not counted.

Example 2 — Single Digits

$ Input: a = 1, b = 10

› Output: 10

💡 Note: All single digit numbers (1-9) and 10 have unique digits. Total count is 10.

Example 3 — Range with Repeats

$ Input: a = 80, b = 120

› Output: 27

💡 Note: Count numbers from 80-120 where all digits are unique. Excludes numbers like 88, 99, 100, 101, 110, 111, etc.

Constraints

1 ≤ a ≤ b ≤ 10⁸
Both a and b are positive integers

Visualization

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Asked in

G Google 35 a Amazon 28 M Microsoft 22 f Facebook 18

The key insight is to efficiently check digit uniqueness using hash sets for O(1) lookup. For large ranges, mathematical approaches using combinatorics provide O(log n) time complexity. Best approach depends on range size: brute force for small ranges, mathematical for large ranges. Time: O(n×d) to O(log n), Space: O(1) to O(d).

Common Approaches

✓ Bit Manipulation

⏱️ Time: N/A Space: N/A

Brute Force - Check Each Number

⏱️ Time: O(n × d) Space: O(d)

For each number in the range [a,b], convert it to string and check if all digits are unique by counting their frequencies.

Hash Map Optimization

⏱️ Time: O(n × d) Space: O(d)

Same approach as brute force but uses hash set for O(1) digit lookup instead of scanning, making digit checking more efficient.

Mathematical Approach

⏱️ Time: O(log n) Space: O(1)

Instead of checking each number, calculate how many valid numbers exist by considering digit placement constraints and using mathematical formulas.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Medium Frequency

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Smart Actions

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