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0. 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, _________”.
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
for every f:V→R
if and only if ∀u∈V, f(u) is positive
if and only if ∀u∈V, f(u) is negative
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