In Problem 9.8.10 you carried out a uniform-cost search to find the driving distance from Keene to each of the other towns on the map. In this problem we will use A^* search, with two different heuristics, to find the driving distance from Keene to Vernon.

(a) Carry out an A^* search with start node Keene and goal node Vernon,
using a heuristic h_1 such that h_1(x) is 10 times the smallest number of edges
in any path from x to Vernon.

(b) Carry out an A^* search from Keene to Vernon, using the heuristic h_2 such
that h_2(x) is the distance "as the crow flies" from x to Vernon:

Bernardston 11
Brattleboro 11
Chesterfield 16
Hinsdale 3
Keene 27
Northfield 9
Vernon 0
Winchester 11

(c) Which heuristic saved more computation? The greatest difference in the
two values is for Hinsdale, which is separated from Vernon by an unbridged
river. Did this difference greatly affect the behavior of the two searches?