## Floyd–Warshall algorithm |

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In **Floyd–Warshall algorithm** is an ^{[1]}^{[2]} A single execution of the algorithm will find the lengths (summed weights) of shortest paths between *all* pairs of vertices. Although it does not return details of the paths themselves, it is possible to reconstruct the paths with simple modifications to the algorithm.Versions of the algorithm can also be used for finding the

- history and naming
- algorithm
- example
- behavior with negative cycles
- path reconstruction
- analysis
- applications and generalizations
- implementations
- comparison with other shortest path algorithms
- references
- external links

The Floyd–Warshall algorithm is an example of ^{[3]} However, it is essentially the same as algorithms previously published by ^{[4]} and also by ^{[5]} for finding the transitive closure of a graph,^{[6]} and is closely related to ^{[7]} The modern formulation of the algorithm as three nested for-loops was first described by Peter Ingerman, also in 1962.^{[8]}

The algorithm is also known as **Floyd's algorithm**, the **Roy–Warshall algorithm**, the **Roy–Floyd algorithm**, or the **WFI algorithm**.

Other Languages

العربية: خوارزمية فلويد-مارشل

čeština: Floydův–Warshallův algoritmus

Deutsch: Algorithmus von Floyd und Warshall

español: Algoritmo de Floyd-Warshall

فارسی: الگوریتم فلوید-وارشال

français: Algorithme de Floyd-Warshall

한국어: 플로이드-워셜 알고리즘

Bahasa Indonesia: Algoritme Floyd-Warshall

italiano: Algoritmo di Floyd-Warshall

עברית: אלגוריתם פלויד-וורשאל

日本語: ワーシャル–フロイド法

polski: Algorytm Floyda-Warshalla

português: Algoritmo de Floyd-Warshall

русский: Алгоритм Флойда — Уоршелла

српски / srpski: Флојд-Воршалов алгоритам

українська: Алгоритм Флойда — Воршелла

Tiếng Việt: Thuật toán Floyd-Warshall

中文: Floyd-Warshall算法