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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).
solve the following relation by recursive method: T(n)=2T(n^1/2)+log n
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The following formula is used to calculate n: n = x * x/(1 - x) . Value x = 0 is used to stop algorithm. Calculation is repeated using values of x until value x = 0 is input. There
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Program of sun series
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1) The set of the algorithms whose order is O (1) would run in the identical time. True/False 2) Determine the complexity of the following program into big O notation:
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