Ch. 4 – Informed Search
Supplemental slides for CSE 327
Prof. Jeff Heflin
A* Example
• Use A* to solve the 8-puzzle:
initial state:
1
4
7
2
6
5
3
8
goal state:
1
4
7
2
5
8
3
6
path cost is the total number of moves made
• Consider these heuristics
– H1: The number of tiles out of place
– H2: Sum of distances of tiles from goal positions
• Ignore moves that return you to the previous state
A* on 8-puzzle
Heuristic = H1
2
1 2 3
4
8
7 6 5
1 2 3
4 6 8
7
5
f=2+3=5
Whether or not this node is
expanded depends on how you
break ties. It could be expanded at
any time or not at all.
1
1 2 3
4 6 8
7 5
f=0+3=3
3
f=1+3=4
1 2 3
4 6 8
7 5
f=2+4=6
1
3 f=3+3=6
4 2 6
7 5 8
4
1 2 3
4
6
7 5 8
1 2 3
4 6
7 5 8
1 2 3
4 6
7 5 8
f=2+2=4
f=3+3=6
f=1+3=4
1 2
4 6 3
7 5 8
f=2+4=6
5 1 2 3 f=3+1=4
4 5 6
7
8
1 2 3
4 5 6
7 8
f=4+2=6 6 1 2 3 f=4+0=4
4 5 6
7 8
A* on 8-puzzle
1
Heuristic = H2
1 2 3
4 6 8
7
5
1 2 3
4 6 8
7 5
f=0+4=4
2
f=1+5=6
3
1
3
4 2 6
7 5 8
f=3+3=6
1 2 3
4
6
7 5 8
f=2+2=4
1 2 3
4 6
7 5 8
f=3+3=6
1 2 3
4 6
7 5 8
f=1+3=4
1 2
4 6 3
7 5 8
f=2+4=6
4 1 2 3 f=3+1=4
4 5 6
7
8
1 2 3
4 5 6
7 8
f=4+2=6 5 1 2 3 f=4+0=4
4 5 6
7 8
Summary of Search Algorithms
type
ordering
optimal?
complete?
efficient?
depth-first
uninformed
LIFO
no
no
if lucky
breadth-first
uninformed
FIFO
yesa
yes
no
uniform cost
uninformed
g(n)
yesb
yesb
no
greedy
informed
h(n)
no
no
usually
A*
informed
g(n)+h(n)
yesc
yes
yes
a – optimal if step costs are identical
b – optimal and complete if step costs > 0
c – optimal if heuristic is admissible