The base scoring wasn't hard to wrap my head around but the 'change one character' part is where I fumbled for a bit.
First, clarify the scoring rules and constraints, then propose an efficient algorithm that computes the base score and evaluates the impact of changing each character. Use a sliding window or dynamic programming to count valid adjacent pairs, and for each position, consider all possible replacement characters to maximize the score.
Pro tip: Demonstrate awareness of edge cases such as single-character strings or when no change improves the score, and discuss time/space complexity trade-offs. Mention that you would test with small inputs and compare against a brute-force solution to validate correctness.
Restate the scoring: 1 point per character plus 1 bonus point for each adjacent pair where the absolute difference in alphabet positions is at most 1. Confirm that you can change at most one character to any lowercase letter.
Calculate the initial score by summing the length of the string and the number of valid adjacent pairs (where |c_i - c_{i+1}| <= 1).
For each position i, consider changing s[i] to any letter from 'a' to 'z'. The change affects only the pairs (i-1, i) and (i, i+1). Compute the new score by adjusting the base score: subtract the old contributions of these pairs and add the new contributions.
Track the maximum score over all positions and all possible replacement characters. Also consider the option of not changing any character (i.e., the base score).
The naive approach is O(n * 26) which is O(n). Explain that this is optimal since you must consider each position. Discuss potential optimizations like precomputing prefix/suffix scores or using a sliding window, but note that O(n) is already efficient.
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