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What does K (top most loop) in Floyd-Warshall Algorithm tells? I have confusion between 'k' tells number of intermediate vertex or K tells the kth vertex will be taken as intermediate vertex.

Abhishek Shukla
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Floyd-Warshall: 

for(every vertex k that could possibly make distance from i to j shorter)
        for(every possible vertex i)
            for(every possible vertex j)
                if(going through k can make the distance from i to j shorter)
                    you should go through k and update distance between i and j as you go