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State-Space Searches
The states of Pac-Man
The ghosts in Pac-Man
Other uses of states
The Pac-Man game as a whole can be described
by a state machine
States are: Title screen, instructions screen,
various game levels, high scores screen
Designing "by states" is a useful techinque for all
kinds of programs, not just games
State-space searches
Many problems in Artificial Intelligence can be
describes as a search through a space of states
There is a start state and one or more goal
states; the object is to navigate a path from the
start state to some goal state
If you have an opponent, this isn't just a matter
of finding a path
Rules control the transition from one state to the
next
Tic-Tac-Toe (Naughts and Crosses)
Basic searches
There are two fundamental kinds of search:
Breadth-first search
Depth-first search
There are many variations on search methods
The most important in AI is the
A* search
When alternating moves with an opponent, a
different kind of search is needed
The most important kind is the alpha-beta search
Breadth-first search
Depth-first search
The basic search algorithm
Initialize: put the start node into OPEN
while OPEN is not empty
take a node N from OPEN
if N is a goal node, report success
put the children of N onto OPEN
Report failure
If OPEN is a stack, this is a depth-first search
If OPEN is a queue, this is a breadth-first search
OPEN may be a fancier structure
Breadth-first searching
queue: 1
2, 3, 4
3, 4, 5, 6, 7, ...
Put 1 on queue
Take 1 off queue; not a
goal
Put 2, 3, 4 on queue
Take 2 off queue; not
a goal
Put 5, 6, 7 on queue
Take 3 off queue...
search order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Depth-first searching
stack: 1
4, 3, 2
13, 12, 11, 3, 2, ...
Put 1 on stack
Take 1 off stack; not a
goal
Put 2, 3, 4 on stack
Take 4 off stack; not a
goal
Put 11, 12, 13 on stack
Take 13 off stack...
search order: 1, 4, 13, 12, 11, 3, 10, 9, 8, 2, 7, 6, 5
Depth-first searches and stacks
A breadth-first search uses a queue; a depth-first
search uses a stack
Recursive routines automatically use a stack
It is possible (and easy) to write a depth-first
search using the automatic stack
If you do a breadth-first search, you have to
implement the queue yourself
Recursive depth-first search
boolean search (node N)
if N is a goal node, return true
for each child C of N
if search(C) succeeds, return true
return false
Advantages/disadvantages
If a breadth-first search succeeds, it finds the
nearest possible goal
If a depth-first search succeeds, it may find an
arbitrarily bad path to a goal
A depth-first search requires an amount of
memory that is linear in the search depth
A breadth-first search requires an amount of
memory that is exponential in the search depth
Best-first searches
Initialize: put the start node into OPEN
while OPEN is not empty
take a node N from OPEN
if N is a goal node, report success
put the children of N onto OPEN
Report failure
If OPEN is neither a stack nor a queue, but is
sorted according to most promising, we have a
best-first search
Heuristic searches
How do we know which nodes are most
promising?
Answer 1: it depends on the problem
Answer 2: we don't; we have to guess
A heuristic is a "rule of thumb"
It uses incomplete information to evaluate our
possible choices
Algorithms guarantee a solution; heuristics don't
It's (almost) always better to have an algorithm
The A* search
The A* search combines the advantages of
breadth-first search (good solutions) with the
advantages of depth-first search (low memory
requirements)
A* is a kind of heuristic search
We won't get to it today
The End