Mazes are often simple puzzles for humans, but they present a great programming problem that we can solve using shortest-path techniques like Dijkstra’s algorithm.

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A Refresher on Dijkstra’s Algorithm

Dijkstra’s Algorithm is one of the more popular basic graph theory algorithms. It is used to find the shortest path between nodes on a directed graph. We start with a source node and known edge lengths between nodes.

We first assign a distance-from-source value to all the nodes. Node s receives a 0 value because it is the source; the rest receive values of ∞ to start.

Our node of interest is the smallest-value unprocessed node (shown in grey), which is s. First, we “relax” each adjacent vertex to our node of interest, updating their values to the minimum of their current value or the node of interest’s value plus the connecting edge length.

Node s is now finalized (black) and its neighbors _a _and _b _have taken on new values. The new node of interest is b, so we repeat the process of “relaxing” b’s adjacent nodes and finalizing the shortest-path value of b.

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