My first instinct was brute force, just iterate over every split point and count shared characters each time.
Clarify the problem and constraints, then propose an efficient solution using prefix and suffix frequency arrays to track distinct character counts for each split point. Iterate through all possible split positions, compute the intersection of distinct characters from both sides, and count those where the intersection size exceeds k.
Pro tip: Demonstrate awareness of edge cases such as k being larger than the total distinct characters or the string length being too small, and discuss how to handle them gracefully. Also, mention the time and space complexity trade-offs, showing you consider scalability for large inputs.
Restate the problem in your own words and ask clarifying questions about input size, character set, and k's range. Confirm that substrings must be non-empty and contiguous.
Propose using prefix and suffix arrays to store the set of distinct characters for each position. Explain how to compute these in O(n) time by scanning from left and right.
For each split point i (from 1 to n-1), compute the intersection of distinct characters from prefix[0..i-1] and suffix[i..n-1]. Count splits where the intersection size > k.
State that the algorithm runs in O(n * σ) time where σ is the alphabet size, or O(n) with bitmasks if σ ≤ 64. Discuss space usage and potential optimizations.
Walk through a small example, then test edge cases like k=0, k greater than total distinct characters, and strings of length 1 or 2.
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