05

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Day 5: Doesn't He Have InternElves For This?

Part 1

Santa needs help figuring out which strings in his text file are naughty or nice.

A nice string is one with all of the following properties:

• It contains at least three vowels (aeiou only), like aei, xazegov, or aeiouaeiouaeiou.
• It contains at least one letter that appears twice in a row, likexx, abcdde (dd), or aabbccdd (aa, bb, cc, or dd).
• It does_not_ contain the strings ab, cd, pq, or xy, even if they are part of one of the other requirements.

For example:

• ugknbfddgicrmopn is nice because it has at least three vowels (u...i...o...), a double letter (...dd...), and none of the disallowed substrings.
• aaa is nice because it has at least three vowels and a double letter, even though the letters used by different rules overlap.
• jchzalrnumimnmhp is naughty because it has no double letter.
• haegwjzuvuyypxyu is naughty because it contains the string xy.
• dvszwmarrgswjxmb is naughty because it contains only one vowel.

How many strings are nice?

Part 2

Realizing the error of his ways, Santa has switched to a better model of determining whether a string is naughty or nice. None of the old rules apply, as they are all clearly ridiculous.

Now, a nice string is one with all of the following properties:

• It contains a pair of any two letters that appears at least twice in the string without overlapping, likexyxy (xy) or aabcdefgaa (aa), but not like aaa (aa, but it overlaps).
• It contains at least one letter which repeats with exactly one letter between them, likexyx, abcdefeghi (efe), or even aaa.

For example:

• qjhvhtzxzqqjkmpb is nice because is has a pair that appears twice (qj) and a letter that repeats with exactly one letter between them (zxz).
• xxyxx is nice because it has a pair that appears twice and a letter that repeats with one between, even though the letters used by each rule overlap.
• uurcxstgmygtbstg is naughty because it has a pair (tg) but no repeat with a single letter between them.
• ieodomkazucvgmuy is naughty because it has a repeating letter with one between (odo), but no pair that appears twice.

How many strings are nice under these new rules?