State-Space Search: Depth-First and Breadth-First Algorithms, Study notes of Algorithms and Programming

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State

Space

Search

COMP

Oct

Graph

Traversal

Many

problems

require

processing

all

graph

vertices

(and

edges)

in

systematic

fashion

Graph

traversal

algorithms:

Depth

first

search

(DFS)

Breadth

first

search

(BFS)

REVIEW

Depth

First

Search

REVIEW

Depth

First

Search

a

b

e

f

c

d

g

h

a b

f e

g c d h

tree edgeback edge

DFS traversal stack:

h(8)d(7)

e(4) c(6)f(3) g(5)b(2)a(1)

REVIEW

Breadth

First

Search

REVIEW

Breadth

First

Search

BFS tree: a b

e f

g c h d

tree edgecross edge

a

b

e

f

c

d

g

h

BFS

traversal

queue:

a(1) b(2) e(3) f(4)

b(2) e(3) f(4) g(5)

g(5) c(6) h(7)

c(6) h(7) d(8)

REVIEW

FIX THIS

State

space

Search

Problems

A

state

space

search

problem

consists

of:

an

initial

state

a

set

of

possible

actions

-^

an

action

transforms

a

state

into

a

new

state

A

goal

state

(or

states)

path

costs

-^

cost

of

moving

from

one

state

to

another

A

solution

consists

of

a

sequence

of

actions

leading

from

initial

state

to

a

goal

state

Example

Problem:

Vacuum

World

Vacuum world has two cells (left and right),which can be dirty or clean.The vacuum robot which can do any of the following:

• move to left cell• move right cell• suck (clean the current cell)

The goal is to have both cells clean.

State

Space:

Vacuum

World

State

space

graph

shows

all

possible

states

and

the

state

transitions

caused

by

all

possible

actions

State

space

graph

is

usually

not

explicit,

rather

it

is

implicitly

defined

by

a

successor

function

8 possible statesdue to3 boolean valuedstate variables

Successor

Functions

A

successor

function

maps

a

state

and

action

to

a

new

state

<state,

action>

Æ

state

It

may

be

explicit

(i.e.

a

lookup

table)

or

implicit

(defined

as

a

function)

Example:

The

puzzle

states? locations

of

tiles

actions? move

blank

left,

right,

up,

down

goal

test? goal

state

(see

figure)

path

cost?

1

per

move

Example:

The

puzzle

The

successor

function

is

best

defined

by

a

function

a

table

would

be

excessively

large

How

many

possible

states

are

there

for

this

problem?

Tree

search

algorithms

explore

the

state

space

by

generating

successors

of

already

explored

states

The strategy for selecting the next nodeto expand determines the type of search

Example:

Romania

In this case, we do have an explicit graph of the state space.