Knight's Travails — the shortest way across a board

moves

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squares examined

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Nothing yet.

Show the distance to every square from the knight

Why breadth first

Depth-first search would pick a move, then a move from there, and charge on until it stumbled into the target. It would find a route. It would not find the shortest one.

Breadth-first visits every square one move away, then every square two moves away, and so on. So the first time it reaches a square it has reached it by the shortest route there is, and it never has to go back and improve on an answer.

The board is not stored

There is no array of sixty-four things. A square's neighbours are worked out from the square itself. The graph is implied by how the piece moves.