Seemed straightforward at first, just iterate and check each number.
Clarify that the range bounds are inclusive and that we need to count numbers with three distinct digits. Then either iterate through the range and check each number's digits for uniqueness, or use a combinatorial counting approach to compute the count directly. Discuss trade-offs between the two methods based on range size and constraints.
Pro tip: Mention that a brute-force check is O(n) and fine for small ranges, but if the range is large or the function is called repeatedly, a precomputed prefix sum array of valid counts up to 999 allows O(1) queries. This shows you think about scalability and real-world usage.
Confirm that the range is inclusive, both bounds are three-digit numbers (100-999), and that numbers like 100 (digits 1,0,0) do not qualify. Ask if the range can be large or if multiple queries are expected.
Decide between a simple iteration with digit extraction and a combinatorial counting method. For a single query, iteration is straightforward; for multiple queries, precompute a prefix sum array.
For a given number, extract its hundreds, tens, and ones digits using division and modulo. Check that all three are distinct (e.g., h != t && h != o && t != o).
If iterating, loop from left to right, apply the check, and increment a counter. If using precomputation, build an array where prefix[i] = count of valid numbers from 100 to i, then answer = prefix[right] - prefix[left-1].
State the time complexity: O(n) for iteration where n = right - left + 1, or O(1) per query after O(900) precomputation. Discuss space trade-offs and when each method is preferable.
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