I'm struggling with a programming challenge involving a map represented as an NxM grid. In this grid, non-walkable tiles are marked with '.', while walkable tiles are marked with '#'. The goal is to determine if I can traverse all the walkable tiles starting from the top-left corner (0, 0) without moving in certain directions—up, down, left, or right. I've tried several approaches, but so far I can only solve a few example cases, and my professor isn't providing any additional guidance. There's a mathematical concept involved, but I'm not sure how to apply it. I've attempted using a reachability matrix, but that alone doesn't ensure that I walk on every tile. I'm seeking a more dependable method to solve this issue, especially since my recursive attempts lead to branching problems causing incorrect outputs. Here are a couple of examples that illustrate where my logic fails:
1.
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..#
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#.#
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2.
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..#
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#..
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2 Answers
I feel your pain! It sounds like the crux of your issue is that reachability only tells you if you can get from one point to another, not if you can cover every single tile on your path. I’d suggest creating a breadth-first search or depth-first search to systematically explore each tile while respecting the movement constraints. That way, you can track which tiles you've visited and ensure you hit them all without missing any. It might also be helpful to backtrack if you find yourself stuck!
It looks like you might be misinterpreting the reachability matrix. Just because every node (or tile) is reachable, it doesn't imply that you can traverse all tiles in one go without leaving some behind. Try visualizing or sketching out the paths to see how moving in one direction impacts your ability to touch all tiles. Sometimes, certain paths can block access to others, so breaking down the problem into simpler parts could really help you out.
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