Author

Andrew Au

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Preprint Oct 2026

Many Scores Force Many Reads: An Optimality Proof for Score of Parentheses

LeetCode Problem 856, Score of Parentheses, admits a one-pass algorithm using $O(n)$ time and $O(1)$ auxiliary registers. Its correctness follows from a local interpretation: every occurrence of () contributes a power of two determined by its nesting depth. The space bound is immediately optimal in the usual programmin...

Andrew Au · 0 citations

Preprint Aug 2026

Do We Really Need to Read the Input? An Optimality Proof for Stone Game III

This work extends the argument to positive but unbounded values, obtaining the same linear lower bound without zeros or ties, and establishes the asymptotic optimality of the standard $O(n)$-time, $O(1)$-space solution in several increasingly restrictive variants.

Andrew Au · 0 citations