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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).
This algorithm inputs 3 numbers, every number goes through successive division by 10 until its value is less than 1. An output is produced which comprise the number input and a val
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A binary search tree is used to locate the number 43. Which of the following probe sequences are possible and which are not? Explain. (a) 61 52 14 17 40 43 (b) 2 3 50 40 60 43 (c)
What is Assertions Introduction At every point in a program, there are generally constraints on the computational state that should hold for program to be correct. For ins
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It does not have any cycles (circuits, or closed paths), which would imply the existence of more than one path among two nodes. It is the most general kind of tree, and might be co
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