Dijkstra's algorithm: why does it work? (not how)

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Published on 2010-05-18T11:17:27Z Indexed on 2010/05/18 11:20 UTC
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I understand what Dijkstra's algorithm is but I don't understand why it works.

When selecting the next vertice to examine, why does Dijkstra's algorithm select the one with the smallest weight? Why not just select a vertex arbitrarily, since the algorithm visits all vertices anyway?

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