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.