My first instinct was to just alternate characters evenly and call it a day.
Use a greedy approach with a max-heap to always pick the character with the highest remaining count, ensuring we don't place three identical characters consecutively. At each step, choose the most frequent character that isn't the same as the last two characters, append it, decrement its count, and push it back if still positive. This yields the longest possible string because it maximizes the use of the most abundant characters while respecting the constraint.
Pro tip: Discuss the time and space complexity upfront: O(n log 3) time (effectively O(n)) and O(1) space since the heap size is at most 3. Also, mention that the greedy choice is optimal because any deviation would only reduce the length by wasting a high-frequency character.
Clarify that we need to use all characters if possible, but the constraint may force us to leave some unused. The goal is to maximize the length of the resulting string.
Use a max-heap (priority queue) to efficiently retrieve the character with the highest remaining count. Since there are only three characters, the heap size is constant.
At each step, pick the character with the largest count that is not the same as the last two characters in the result. If the most frequent character is blocked, pick the next most frequent.
Iterate until no valid character can be added. Handle cases where counts are zero or where the last two characters force a different choice. Return the constructed string.
Argue that the greedy choice is optimal: always using the most frequent available character maximizes the length. Analyze time complexity as O(n log 3) = O(n) and space as O(1).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.