Count Vowels Permutation

HardDynamic Programming1d dp

Solve this the way you would in the interview: out loud, on a timer, with an AI interviewer asking follow-ups while you code. You get a scored report at the end.

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Problem

Count the strings of length n built only from the vowels 'a', 'e', 'i', 'o', 'u' that obey these rules about which letter may come **immediately after** each letter: - after 'a' only 'e', - after 'e' only 'a' or 'i', - after 'i' any vowel except another 'i', - after 'o' only 'i' or 'u', - after 'u' only 'a'. Return the count modulo 10^9 + 7.

Examples

Input: n = 1
Output: 5
Each single vowel is valid.
Input: n = 2
Output: 10
ae, ea, ei, ia, ie, io, iu, oi, ou, ua.
Input: n = 5
Output: 68
Applying the rules for five letters gives 68 strings.

Constraints

  • 1 <= n <= 2 * 10^4

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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