Dijkstra’s algorithm: Correctness by induction
Since d(x) is the length of the shortest s-to-xpath by the I.H., d(x) ‘(Q x), giving us d(x) + ‘(xy) ‘(Q x): Since yis adjacent to x, d(y) must have been updated by the algorithm, so d(y) d(x) + ‘(xy): Finally, since uwas picked by the algorithm, umust have the smallest distance label: d(u) d(y):
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