State Space Search 2Chapter 3

Three Algorithms

Backtracking

SupposeWe are searching depth-firstNo further progress is possible (i.e., we

can only generate nodes we’ve already generated)

Backtrack

The algorithm: First Pass

1. Pursue path until goal is reached or dead end

2. If goal, quit and return the path3. If dead end, backtrack until you reach

the most recent node whose children have not been fully examined

BT maintains Three Lists and A State

SL◦List of nodes in current path being tried. If goal

is found, SL contains the pathNSL

◦List of nodes whose descendents have not been generated and searched

DE◦List of dead end nodes

All lists are treated as stacksCS

◦Current state of the search

The Algorithm

State Space

a

b

e

g

c

a

d

h

i

j

A as a child of C is intentional

Trace

At Home Exercise:

Trace with Goal j, Start AShow SL, NSL, DE, CS at each step of the algorithm

Depth-First: A Simplification of BT

Eliminate saved path (SL)Results in Depth-First search

◦Goes as deeply as possible◦Is not guaranteed to find a shortest path◦Maintains two lists

Open List◦Contains states generated◦Children have not been examined (like NSL)◦Open is implemented as a stack

Closed List◦Contains states already examined◦Union of SL and DE

bool Depth-First(Start){

open = [Start];closed = [];while (!isEmpty.open()){

CS = open.pop();if (CS == goal)

return true; else { generate children of CS; closed.push(CS); eliminate children from CS that are on open or closed;

while (CS has more children) open.push(child of CS);

} } return false;}

Trace

At Home Exercise:

Trace graph on slide 6 with Goal j, Start aShow Open, Close, CS at each step of the algorithm

Breadth-First Search: DF but with a Queue

bool Breadth-First(Start){

open = [Start];closed = [];while (!isEmpty.open()){

CS = open.dequeue();if (CS == goal)

return true; else { generate children of CS; closed.enqueue(CS); eliminate children from CS that are on open or closed;

while (CS has more children) open.enqueue(child of CS);

} } return false;}

Trace

At Home Exercise:

Trace graph on slide 6 with Goal j, Start aShow Open, Close, CS at each step of the algorithm

Both Algorithms

1. Open forms frontier of search2. Path can be easily reconstructed

Each node is an ordered pair (x,y) X is the node name Y is the parent When goal is found, search closed for

parent, the parent of the parent, etc., until start is reached.

Breadth-FirstFinds shortest solutionIf branching factor is high, could require a

lot of storageDepth-FirstIf it is known that the solution path is long,

DF will not waste time searching shallow states

DF can get lost going too deep and miss a shallow solution

DF and BF follow for the 8-puzzle

8 Puzzle—DF (p. 105)

Depth First Search of 8-Puzzle (p. 105)Depth Bound = 5