Palindrome

Naive substring search compares the pattern against every position in the text, restarting from scratch on each mismatch, for `O(n * m)` worst-case time. KMP, by precomputing where to resume after a mismatch, never restarts. The text pointer moves forward strictly monotonically, the pattern pointer is corrected by a failure function, and the whole search runs in `O(n + m)`. That single insight defines a family of linear-time string algorithms that power editors, search engines, and bioinformatics pipelines. **String Algorithms** covers that family. KMP teaches you to build the failure function (prefix function) and use it to skip redundant comparisons. The Z algorithm offers an alternative `O(n)` framework based on the Z-array. Rabin-Karp introduces rolling hashes for multi-pattern search and is the backbone of plagiarism detection. Manacher's algorithm finds the longest palindromic substring in linear time using a clever transform with separators. Aho-Corasick generalizes KMP to multiple patterns simultaneously by adding failure links to a trie, producing a finite automaton that scans the text once. In **Arrays & Strings**, you treated strings as arrays of characters with `O(1)` indexed access. **Hash Map (Dictionary) Basics** gave you the `O(1)` lookup used by Rabin-Karp. This lesson layers algorithmic structure on top of those primitives. Next, **Pattern Matching Algorithms** extends the toolkit with Boyer-Moore, DFA-based matching, and 2D pattern search.