Question

 Consider the following undirected weighted graph where 
you want to find a path from A to G.

              A
            /   \
           B --- C
            \   /  \
              G --- H

Weights (costs) of the edges are
W(AB) = 1; W(AC) = 3; W(BC) = 1; W(BG) = 9; W(CG) = 5; W(CH) = 2; 
W(GH) = 1,
and the heuristic estimates (h(n)) to the goal node, G, are
h(A) = 5, h(B) = 4, h(C) = 1, h(G) = 0, h(H) = 1.

Simulate A* search. At each step, show the path to the node that is being 
expanded, the length of that path, the total estimated cost (actual + heuristic) 
and the expanded list of nodes (all nodes visited so far in the order in which 
they were visited). Provide the answer in the following table.

Path to node expanded   Length of Path   Total Estimated Cost   Expanded list

         A                    0                  5                   (A)

....... finish the table as suggested.

Is the given h(n) function an admissible heuristic? Explain.

Answer 1

for admissible heuristic,

h(n) is admissible for all n i.e.

h(n)<=h*(n)

h*(n) is the actual cost.here the actual cost is 7.while h(n) is i.e h(A) is 5

hence 5<7.hence it is admissible.

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