My first instinct was a brute force with nested loops and I just went with it.
Clarify the problem first: substrings must consist entirely of vowels and contain all five vowels. Then propose an efficient sliding window approach that expands and contracts to count valid substrings in O(n) time, explaining how to handle the 'all five vowels' condition with a frequency map.
Pro tip: Mention edge cases like strings with no vowels or fewer than five vowels, and discuss how the sliding window avoids redundant checks by leveraging the fact that once a window is valid, all larger windows ending at the same right pointer are also valid.
Confirm that substrings must consist only of vowels and contain all five vowels. Ask about input size, character set, and whether case matters.
Briefly describe the naive O(n^2) approach of checking every substring, noting it's inefficient for large inputs.
Explain using two pointers (left and right) to maintain a window of vowels, and a frequency map to track vowel counts. Expand right, and when all five vowels are present, count valid substrings ending at right and move left to find more.
When the window contains all five vowels, the number of valid substrings ending at right is (left - start + 1), where start is the first index after the last non-vowel. Increment count accordingly.
State O(n) time and O(1) space (since only 5 vowels). Discuss edge cases: empty string, no vowels, fewer than five distinct vowels, and uppercase letters.
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