17. Transitive closure of a Graph
The problem can be found at the following link: Question Link
My Approach
This is the standard Floyd-Warshall graph problem for finding the transitive closure of a graph.
Initialize a transitive closure matrix with the given graph
Set all diagonal elements to 1
Use the Floyd-Warshall algorithm to compute the transitive closure by considering all pairs of vertices and updating the matrix based on the existence of a path between them through a third vertex.
For better understanding, refer to the following video: Floyd-Warshall Algorithm
Time and Auxiliary Space Complexity
Time Complexity:
O(N^3)
, whereN
is the number of vertices in the graphAuxiliary Space Complexity:
O(N^2)
is the number of vertices in the graph
Code (C++)
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