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We have discussed that the above Dijkstra's single source shortest-path algorithm works for graphs along with non-negative edges (like road networks). Given two scenarios can emerge out of negative cost edges into a graph:
Figure: A Graph with negative edge & non-negative weight cycle
The net weight of the cycle is 2(non-negative)
Figure: A graph with negative edge and negative weight cycle
The net weight of the cycle is 3(negative) (refer to above figure). The shortest path from A to B is not well defined as the shortest path to this vertex are infinite, that means , by traveling each cycle we can reduced the cost of the shortest path by 3, like (S, A, B) is path (S, A, B, A, B) is a path with less cost and so forth.
Dijkstra's Algorithm works only for directed graphs along non-negative weights (cost).
What is the time complexity of Merge sort and Heap sort algorithms? Time complexity of merge sort is O(N log2 N) Time complexity of heap sort is O(nlog2n)
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Consider the digraph G with three vertices P1,P2 and P3 and four directed edges, one each from P1 to P2, P1 to P3, P2 to P3 and P3 to P1. a. Sketch the digraph. b. Find the a
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