Editing Dijkstra's algorithm (section)

=== Dynamic programming perspective ===
From a [[dynamic programming]] point of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the '''Reaching''' method.<ref name="sniedovich_062">{{cite journal |last=Sniedovich |first=M. |year=2006 |title=Dijkstra's algorithm revisited: the dynamic programming connexion |url=http://matwbn.icm.edu.pl/ksiazki/cc/cc35/cc3536.pdf |journal=Journal of Control and Cybernetics |volume=35 |issue=3 |pages=599–620}} [http://www.ifors.ms.unimelb.edu.au/tutorial/dijkstra_new/index.html Online version of the paper with interactive computational modules.]</ref><ref name="denardo_032">{{cite book |last=Denardo |first=E.V. |title=Dynamic Programming: Models and Applications |publisher=[[Dover Publications]] |year=2003 |isbn=978-0-486-42810-9 |location=Mineola, NY}}</ref><ref name="sniedovich_102">{{cite book |last=Sniedovich |first=M. |title=Dynamic Programming: Foundations and Principles |publisher=[[Francis & Taylor]] |year=2010 |isbn=978-0-8247-4099-3}}</ref>

In fact, Dijkstra's explanation of the logic behind the algorithm:{{sfn|Dijkstra|1959|p=270}} 
{{blockquote|'''Problem 2.''' Find the path of minimum total length between two given nodes {{mvar|P}} and {{mvar|Q}}.

We use the fact that, if {{mvar|R}} is a node on the minimal path from {{mvar|P}} to {{mvar|Q}}, knowledge of the latter implies the knowledge of the minimal path from {{mvar|P}} to {{mvar|R}}.}}
is a paraphrasing of [[Richard Bellman|Bellman's]] [[Bellman equation#Bellman's principle of optimality|Principle of Optimality]] in the context of the shortest path problem.