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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).
Assertions and Abstract Data Types Even though we have defined assertions in terms of programs, notion can be extended to abstract data types (which are mathematical entities).
In file access: what is the difference between serial, sequential and indexed sequential searching
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What is Class invariants assertion A class invariant is an assertion which should be true of any class instance before and after calls of its exported operations. Generally
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Write an algorithm for getting solution to the Tower's of Hanoi problem. Explain the working of your algorithm (with 4 disks) with appropriate diagrams. Ans: void Hanoi(int
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In this project you will write a program to produce a discrete time simulation of a queue as shown in Fig. 1. Time is slotted on the input and the output. Each input packet follows
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