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Use a sliding window (two-pointer) technique to maintain a window with at most k distinct characters, expanding the right pointer and shrinking the left pointer when the distinct count exceeds k. Track the maximum window length seen. This yields an O(n) time solution with O(k) space.
Pro tip: Clarify edge cases upfront (e.g., k=0, empty string, k >= distinct characters) and mention that the window size never needs to decrease, so you can avoid shrinking below the current max length. This shows attention to optimization and robustness.
Restate the problem in your own words and ask clarifying questions about input size, character set, and edge cases. Confirm that the substring must be contiguous.
Explain that a brute-force check of all substrings would be O(n^2) or worse, so a sliding window with a hash map to count characters gives O(n) time.
Describe initializing left and right pointers, a frequency map, and a variable for max length. Expand right, update the map, and while the map size exceeds k, shrink from left. Update max length after each valid window.
State that time complexity is O(n) because each character is visited at most twice, and space is O(k) for the map. Mention handling k=0, empty string, and k >= number of distinct characters.
Walk through a small example (e.g., 'eceba', k=2) to demonstrate correctness, and optionally discuss how to modify for at most k distinct with other constraints.
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