Mastering Manacher’s Algorithm: Find the Longest Palindromic Substring in O(N)

Manacher’s algorithm transforms the classic longest palindromic substring problem into a linear‑time solution by preprocessing the string with separators, tracking palindrome radii, and efficiently updating the center and right boundary using mirror positions, with detailed Python code and step‑by‑step illustrations.

Manacher algorithmPythonString processing

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Mastering Manacher’s Algorithm: Find the Longest Palindromic Substring in O(N)

Alibaba Cloud Developer

Aug 15, 2018 · Artificial Intelligence

How τ‑FPL Reduces False Positives in High‑Risk Classification Tasks

τ‑FPL introduces a novel ranking‑threshold approach that explicitly incorporates a false‑positive‑rate constraint into binary classifier training, offering linear‑time optimal solutions, theoretical error bounds, and superior experimental performance on high‑risk tasks such as disease monitoring and autonomous driving.

Neyman-Pearsonfalse-positive-ratelinear-time

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How τ‑FPL Reduces False Positives in High‑Risk Classification Tasks