Clarify the problem and constraints, then discuss a brute-force solution that checks each number in the range by extracting and comparing its digits. Optimize by either precomputing valid numbers or using combinatorics to count directly, and analyze time and space complexity.
Pro tip: Mention that since the range is at most 900 numbers, brute force is acceptable, but demonstrating an O(1) combinatorial solution shows deeper insight. Also, handle edge cases like when left > right or when the range includes numbers with leading zeros (though not applicable here).
Restate the problem in your own words and confirm constraints: left and right are three-digit numbers, and we need to count numbers with all distinct digits.
Explain a simple approach: iterate from left to right, for each number extract its hundreds, tens, and units digits, and check if all three are distinct. Count the valid ones.
State that the brute force runs in O(n) time where n = right - left + 1 (at most 900), and O(1) space. This is efficient enough for the given constraints.
If asked for optimization, propose a combinatorial approach: count valid numbers up to a given number using digit DP or precomputed counts, then answer queries in O(1).
Walk through a small example, e.g., left=100, right=120, and verify the count. Also consider edge cases like left=right or ranges with no valid numbers.
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