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Unformatted text preview: el across one edge to a gas station where we reﬁll our tank, and then travel two edges to the
destination, arriving with an empty gas tank. Notice that we are unable to continue the journey to
u5 if we wanted to, because even though there is a gas station there, we have to traverse a third
edge to get to it.) u3 u4
$3 Toll: $7 t Toll: $3
Toll: $10 s Gas:
Toll: $2 Toll: $1 Toll: $4
Toll: $5 Toll: $2
GAS u1 Toll: $1 NO
GAS Toll: $9 u2 Toll: $1 Gas:
$1 u5 There are some extra copies of this graph at the end of the exam (for your convenience). 6.006 Quiz 2 Solutions Name (a) [5 points] The valid path given in the description above is not the best path. Find a
least-expensive path from s to t in the graph above.
Solution: (s, u1 , u3 , u2 , t) (b) [5 points] Find the least-expensive path from s to u5 in the graph above.
Solution: (s, u1 , u3 , u2 , u4 , t, u5 ) (c) [15 points] Give an O(V log V + E ) algorithm to ﬁnd, in a given graph G = (V, E, w),
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.006 at MIT.
- Fall '11