Design a Score for Imperfect Palindromes

Design a scoring method for how closely a string resembles a palindrome when it is not an exact palindrome. Identify the aspects of resemblance you would measure, assign weights to them, and explain what the resulting score means. The goal is an interpretable score that can compare imperfect strings. There is no single required scoring formula. Your answer must provide one complete proposal with defined preprocessing, a score range, boundary behavior, worked examples, and a way to assess whether the weighting is useful. ### Constraints and Clarifying Questions - Decide whether comparison uses exact characters or normalized text, including the treatment of case, spaces, and punctuation. - Clarify whether a mismatch in a mirrored position and an inserted or missing character should be penalized in the same way. - State how length affects the score and what empty and one-character strings receive. - If arbitrary Unicode is in scope, specify the unit being compared and the normalization policy; a narrow character domain is also acceptable if explicit. - Do not treat your proposed weights as a uniquely correct answer or a supplied business requirement. ```hint Compare kinds of imperfection A substituted character can break one mirrored pair. An extra character can shift several pairs even when removing it restores symmetry. Consider whether those cases should receive similar scores. ``` ### What a Strong Answer Covers - At least one precisely defined resemblance feature and an explanation of any additional feature's distinct purpose. - A normalized, interpretable scoring rule with explicit weights and boundary cases. - Examples that distinguish exact palindromes, mirrored mismatches, and disruption caused by an extra or missing character. - Computational cost and a practical plan to evaluate or revise the weights without claiming unsupported accuracy. ### Follow-up Questions - Could a long string score well despite containing several defects, and is that desirable for your use case? - How would your score change if substitutions were allowed but insertions and deletions were forbidden? - What examples would reveal that two selected features are redundant or that their weights produce an unintuitive ranking?