Consider the following greedy strategy for finding a shortest path from vertex start to vertex goal in a given connected graph. 1: Initialize path to start . 2: Initialize set visited to { start }. 3:...

Consider the following greedy strategy for finding a shortest path from

vertex
start
to vertex
goal
in a given connected graph.

1: Initialize
path
to
start.

2: Initialize set
visited
to {start}.

3: If
start=goal, return
path
and exit. Otherwise, continue.

4: Find the edge (start,v) of minimum weight such that
v
is adjacent to

start
and
v
is not in
visited.

5: Add
v
to
path.

6: Add
v
to
visited.

7: Set
start
equal to
v
and go to step 3.

Does this greedy strategy always find a shortest path from
start
to
goal?

Either explain intuitively why it works, or give a counterexample.