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breadth-ﬁrst search ﬁnds it.
(g) T F [2 points] In a weighted undirected tree G = (V, E, w), depth-ﬁrst search from
a vertex s ﬁnds single-source shortest paths from s (via parent pointers) in O(V +
E ) time.
Solution: True. In a tree, there is only one path between two vertices, and
depth-ﬁrst search ﬁnds it.
(h) T F [2 points] If a graph represents tasks and their interdependencies (i.e., an edge
(u, v ) indicates that u must happen before v happens), then the breadth-ﬁrst
search order of vertices is a valid order in which to tackle the tasks.
Solution: No, you’d prefer depth-ﬁrst search, which can easily be used to produce a topological sort of the graph, which would correspond to a valid task
order. BFS can produce incorrect results.
(i) T F [2 points] Dijkstra’s shortest-path algorithm may relax an edge more than once
in a graph with a cycle.
Solution: False. Dijkstra’s algorithm always visits each node at most once; this
is why it produces an incorrect result in the presence of negative-weight edges. (j) T F [2 points] Given a weighted directed graph G = (V, E, w) and a source s ∈ V ,
if G has a negative-weight cycle somewhere, then the Bellman-Ford algorithm...
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- Fall '11