My first instinct was to just brute force every prefix and suffix reversal and track the minimum, which works fine for small inputs.
First, clarify the problem: reversing a prefix means choosing an index i and reversing s[0..i], and reversing a suffix means choosing an index j and reversing s[j..n-1]. The set of possible strings includes the original string (by reversing the entire string twice or choosing empty prefix/suffix). To find the lexicographically smallest, we can analyze the effect of each operation: reversing a prefix of length k yields s[k-1] + reverse(s[0..k-2]) + s[k..n-1], and reversing a suffix starting at j yields s[0..j-1] + reverse(s[j+1..n-1]) + s[j]. We can generate all candidates efficiently by considering each possible prefix and suffix reversal, but we can optimize by noting that the smallest string will start with the minimum character in the string, and we only need to consider reversals that bring that minimum character to the front. Then compare candidates lexicographically.
Pro tip: Don't jump into coding immediately; first discuss the brute-force approach and its complexity, then propose an optimization. Interviewers at Meta value clear communication and the ability to iterate from a naive solution to an efficient one.
Confirm that reversing a prefix means reversing the first k characters (k from 1 to n), and reversing a suffix means reversing the last m characters (m from 1 to n). Also consider empty reversals (k=0 or m=0) which yield the original string. Discuss edge cases like empty string, single character, and strings with repeated characters.
Generate all possible strings by reversing every possible prefix and every possible suffix. There are 2n such operations (including the original string). Compare them lexicographically to find the smallest. This takes O(n^2) time due to string creation and comparison, but it's a good starting point.
The lexicographically smallest string must start with the smallest character in the original string. Identify all positions where this minimum character occurs. Only reversals that bring this character to the front can produce the smallest string. For prefix reversals, the minimum character must be at the end of the prefix; for suffix reversals, it must be at the start of the suffix.
For each candidate reversal that places the minimum character at the front, construct the resulting string and compare it with the current best. Use efficient string comparison (e.g., in Python, direct string comparison is O(n) but optimized). Keep track of the smallest string found.
The optimized approach may still be O(n^2) in the worst case (e.g., all characters are the same), but it reduces the number of candidates. Discuss potential further optimizations (e.g., using suffix arrays or rolling hashes) if needed. Test with examples like 'cba', 'abac', and 'aaaa'.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.