GATE | GATE CS 2020 | Question 50

Let G=(V,E) be a directed, weighted graph with weight function w:E→R. For some function f:V→R, for each edge (u,v)∈E, define w′(u,v) as w(u,v)+f(u)−f(v). Which one of the options completes the following sentence so that it is TRUE ? “The shortest paths in G under w are shortest paths under w′ too, _________”.

(A)

for every f:V→R

(B)

if and only if ∀u∈V, f(u) is positive

(C)

if and only if ∀u∈V, f(u) is negative

(D)

if and only if f(u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of G

Answer

Please comment below if you find anything wrong in the above post
Feeling lost in the world of random DSA topics, wasting time without progress? It's time for a change! Join our DSA course, where we'll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 geeks!

Last Updated :

Share your thoughts in the comments

GeeksforGeeks

Trending in News