Reason About Character Paths in a Grid

# Reason About Character Paths in a Grid A two-dimensional array has a path beginning at the top-left cell. Cells on the path contain either a marker or a character; collect the characters encountered along the path into a string. Explain a depth-first traversal for the single-path case, then extend the design to return every character string when the path can branch. ### Constraints & Assumptions - The source identifies the top-left start, path markers, character cells, and a branching follow-up. - It does not define which neighboring cells connect, how a path ends, or how multiple results are ordered. - Cycles and revisiting behavior must be clarified before traversal. ### Clarifying Questions to Ask - Are moves orthogonal, diagonal, or supplied explicitly? - Which cells are traversable, and does a character cell also continue the path? - At a branch, what marks a completed result and may the returned strings appear in any order? ```hint Track path-local state When branches are possible, keep the collected characters and visited state associated with the current traversal path. ``` ### What a Strong Answer Covers - A precise cell and adjacency contract before implementation. - DFS state for position, collected characters, and cycle prevention. - The difference between one unbranched path and enumerating every branch result. - Complexity in terms of cells, edges, path length, and total output size. ### Follow-up Questions 1. How would shared suffixes affect copying and memory use? 2. What should happen if the top-left cell is not part of any valid path?