GATE | GATE MOCK 2017 | Question 48

Consider a graph where all edge weights are positive. We have computed shortest path using Dijkstra’s shortest path algorithm and total weight of shortest path is W.

Consider below two statements about a shortest path from a source to a destination.

i) If the graph is modified and all edge weights are multiplied with x, then the shortest path remains same and weight of shortest path becomes W*x (W multiplied by x).

ii) If the graph is modified and x is added to all edge weights, then the shortest path remains same and weight of shortest path becomes W + n*x. Where n is number of edges on the shortest path.

(A) Only (i) is always True

(B) Only (ii) is always True

(C) Both are always True

(D) Neither (i) nor (ii) is always True

Answer: (A)

Explanation:

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