My first instinct was brute force, check every prefix, reverse it, see if the whole thing is a palindrome.
Clarify the problem and edge cases, then explain that the shortest palindrome is formed by finding the longest palindromic prefix of the string and prepending the reverse of the remaining suffix. Present an efficient algorithm such as KMP-based pattern matching, and analyze time and space complexity.
Pro tip: Mention that this problem reduces to finding the longest palindromic prefix, and that KMP is preferred over brute force for large inputs. Also, relate it to real-world applications like DNA sequence analysis or text processing, which can impress interviewers.
Restate the problem in your own words and ask clarifying questions about input constraints, character set, and expected output. Discuss edge cases like empty string, single character, and already palindromic strings.
Explain that the shortest palindrome is obtained by finding the longest palindromic prefix of the original string. The characters after this prefix need to be reversed and prepended.
Describe a linear-time approach using the Knuth-Morris-Pratt (KMP) algorithm: compute the failure function on the string s + '#' + reverse(s), and the value at the last position gives the length of the longest palindromic prefix.
State that the KMP approach runs in O(n) time and O(n) space. Compare with a naive O(n^2) approach and explain why KMP is better for large inputs.
Walk through a simple example like 'abac' to verify the algorithm. Mention possible extensions, such as allowing insertions at both ends or finding the shortest palindrome by appending characters.
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