Spencer R. Shimko
CMSC 471-0101
Homework #3
II.
3.8
1) Consider a state space where the start state is number 1
and the successor function for state
n
returns two states,
numbers 2
n
and 2
n
+ 1.
a) Draw the portion of the state space for states 1 to 15.
b) Suppose the goal state is 11.
List the order in which
nodes will be visited for a breadth-first search, depth-
limited search with limit 3, and iterative deepening search.
Breadth-first: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Depth-first w/ limit of 3: 1, 2, 4, 8, 9, 5, 10, 11
Iterative deepending: 1, 2, 3, 1, 2, 4, 5, 3, 6, 7, 1, 2,
4, 8, 9, 5, 10, 11
3.17
On page 62, we said that we would no consider problems with
negative path costs.
In this exercise, we explore this in
more depth.
a) Suppose that actions can have arbitrarily large negative
costs; explain why this possibility would force any optimal
algorithm to explore the entire state space.
Any algorithm that is optimal must find the path with the