Exercise 3.32

Consider the unbounded version of the regular 2D grid shown in . The start state is at the origin, (0,0), and the goal state is at $(x,y)$.

1. What is the branching factor $b$ in this state space?

2. How many distinct states are there at depth $k$ (for $k>0$)?

3. What is the maximum number of nodes expanded by breadth-first tree search?

4. What is the maximum number of nodes expanded by breadth-first graph search?

5. Is $h = |u-x| + |v-y|$ an admissible heuristic for a state at $(u,v)$? Explain.

6. How many nodes are expanded by A graph search using $h$?

7. Does $h$ remain admissible if some links are removed?

8. Does $h$ remain admissible if some links are added between nonadjacent states?