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Shortest Path Problem Has Optimal Substructure

Lemma 24.1

If shortest path p from s to v can be decomposed into \(s \stackrel{p'}{\leadsto} u \rightarrow v\), then p' is a shortest path from s to u, and \(\delta(s,v) \;=\; \delta(s,u) \;+\; w(u,v)\).



Because the problem has optimal substructure, we can try to use dynamic programming and greedy algorithms.


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