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Pseudocode

$1. \;\;$ Floyd-Warshall(W)
$2. \;\;\;\;\;\;$ n = rows(W)
$3. \;\;\;\;\;\;$ D⁽⁰⁾ = W
$4. \;\;\;\;\;\;$ for k = 1 to n
$5. \;\;\;\;\;\;\;\;\;$ for i = 1 to n
$6. \;\;\;\;\;\;\;\;\;\;\;\;$ for j = 1 to n
$7. \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ $d_{ij}^{(k)} \;=\; min(d_{ij}^{(k-1)}, \;d_{ik}^{(k-1)} \;+\; d_{kj}^{(k-1)})$
$8. \;\;\;\;\;\;$ return D⁽ⁿ⁾

Three nested for loops: $\Theta(n^3)$ , n = $\mid$ V $\mid$
Better than O(V³ lg V) and O(V⁴) of SSSP

Floyd-Warshall Applet

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