String Functions in Contiguous Memory — Alternative¶
Problem setter's solution; implementation organized by Codex (GPT-6). Keep a contiguous byte array and prefix sums, scan for the terminating zero, and apply modifications byte by byte.
The main solution specifies the error and warning order: validate everything before mutation, and reject overlapping copy intervals including their terminators. Scanning finds the exact string length. Every binary string is a run of ones followed by zero, so writing that sequence reproduces the source exactly. The array equals the specified memory byte for byte before and after every operation; induction proves all outputs correct.
Prefix sums and initial memory take \(O(n+S)\) time. An operation takes worst-case \(O(S)\) , giving total time \(O(n+S+kS)\) and space \(O(n+S)\) . This method is direct and has small storage constants; the segment tree has better asymptotic time for query-heavy inputs. This program passes the current full data within the estimated limit and is a useful simple alternative.