I spent way too long trying to think of something clever before realizing the key insight is pretty mechanical once you see it: strip out the dots and the relative order of L/R/X tokens must match exactly between start and target, and walls must be in identical positions.
First, clarify the problem constraints and define the invariants: the sequence of non-wall characters must be identical in both strings, and each 'L' in the start must not be to the left of its corresponding 'L' in the target, while each 'R' must not be to the right. Then, design a single-pass algorithm that checks these conditions in O(n) time and O(1) space, and discuss edge cases and correctness.
Pro tip: Emphasize that the relative order of tokens is invariant because tokens cannot pass through each other or walls. This simplifies the problem to checking positions of corresponding tokens, which you can do in one pass without extra space.
Restate the movement rules: 'L' moves left only, 'R' moves right only, cannot jump over walls or other tokens. Identify key invariants: the sequence of non-wall characters must match, and the relative order of tokens is preserved.
Verify that the strings of non-wall characters (ignoring '.') are identical. If not, transformation is impossible.
For each corresponding 'L' in start and target, ensure start index >= target index (since 'L' can only move left). For each 'R', ensure start index <= target index (since 'R' can only move right).
Use two pointers to traverse both strings simultaneously, skipping '.', and check the conditions in a single pass without extra data structures.
Cover cases like mismatched walls, tokens separated by walls, consecutive tokens with no room to move, and argue why the invariants guarantee feasibility.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.