Challenge: Frequency-Balanced Window

Start with the idea

Solve the exact task, not just the visible example: With at most one replacement, return the longest equal-character substring length. On input AABABBA, predict the output before opening the answer reveal. The revealed output is a test oracle for this case, while private checks exercise other legal cases. Start by stating the input grammar and output format in your own words. Parse the complete input, including surrounding whitespace, before relying on any convenient positions in the example.

Build the solution around one maintained claim: Track the dominant count so replacements needed equal window length minus that count. Decide what state represents that claim, how it is initialized, what a single update does, and when the algorithm stops. A window is a contiguous interval with a maintained summary. Describe what entering the right edge adds and what leaving the left edge removes. Trace the visible input by hand and record at least two intermediate states, not only the final answer. If the trace cannot justify your predicted output, there is a gap between the idea and the implementation.

Use the Rust sketch as a guide, not a substitute for a complete solve function. The supplied Rust sketch is a starting point. Identify what it stores, how one iteration changes it, and whether it already solves the exact task or only demonstrates a related operation. Represent bounds as a half-open range when possible.