This contains the information about the searching algorithms for the input and then solve it.

1. Informed Search

2. Outline
• Best-first search
• Greedy best-first search
• A* search

3. Search Heuristics
 A heuristic is:
 A function that estimates how close a state is to a goal
 Designed for a particular search problem
 Examples: Manhattan distance, Euclidean distance for
pathing
10
5
11.2

4. Example: Heuristic Function

5. Best-first search
• Idea: use an evaluation function f(n) for each node
• estimate of "desirability"
Expand most desirable unexpanded node
• Implementation:
Order the nodes in fringe in decreasing order of desirability

6. Best-first search
A
T S Z
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140 75

7. Best-first search
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T S Z
O
118
140 75
71

8. Best-first search
A
T S Z
S
O
118
140 75
71
151

9. Best-first search
A
T S Z
S
R F
O
118
140 75
71
151
90
80

10. Best-first search
A
T S Z
C
S
R F
O
P
118
140 75
71
151
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97
146

11. Best-first search
A
T S Z
C
S
R F
O
P
C B
118
140 75
71
151
90
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146
138 101

12. Best-first search
A
T S Z
C
S
R F
O
P
C B
118
140 75
71
151
90
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146
138 101

13. Best-first search (DIY)

14. Properties of Best First Search
• Complete? No – can get stuck in loops
• Optimal? No

15. Difference between Uniform Cost Search and
Best First Search
• Uniform-cost search is uninformed search
• It doesn't use any domain knowledge.
• It expands the least cost node, and it does so in every direction because no information
about the goal is provided.
• Best-first search is informed search
• It uses a heuristic function to estimate how close the current state is to the goal.

16. Greedy best-first search
• Evaluation function f(n) = h(n) (heuristic)
= estimate of cost from n to goal
• e.g., hSLD(n) = straight-line distance from n to Bucharest
• Greedy best-first search expands the node that appears to be closest to goal

17. Greedy best-first search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

18. Greedy best-first search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

19. Greedy best-first search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

20. Greedy best-first search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

21. Greedy best-first search (DIY)

22. Properties of greedy best-first search
• Complete? No – can get stuck in loops
• Optimal? No

23. A* search
• Idea: avoid expanding paths that are already expensive
• Evaluation function f(n) = g(n) + h(n)
• g(n) = cost so far to reach n
• h(n) = estimated cost from n to goal
• f(n) = estimated total cost of path through n to goal

24. A* search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

25. A* search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

26. A* search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

27. A* search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

28. A* search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

29. A* search example
A 366
B 0
C 160
D 242
E 161
F 176
G 77
H 151
I 226
L 244
M 241
N 234
O 380
P 100
R 193
S 253
T 329
U 80
V 199
Z 374

30. Admissible heuristics
• A heuristic h(n) is admissible if for every node n,
h(n) ≤ h*(n), where h*(n) is the true cost to reach the goal state from n.
• An admissible heuristic never overestimates the cost to reach the goal, i.e., it
is optimistic
• Example: hSLD(n) (never overestimates the actual road distance)
• Theorem: If h(n) is admissible, A* using TREE-SEARCH is optimal

31. Properties of A*
• Complete? Yes (unless there are infinitely many nodes with f ≤ f(G) )
• Space? Keeps all nodes in memory
• Optimal? Yes

32. A* search (DIY)

33. Video of Demo Contours UCS Empty

34. Video of Demo Contours (Empty) -- Greedy

35. Video of Demo Contours (Empty) – A*

36. Video of Demo Contours UCS Pacman Small Maze

37. Video of Demo Contours Greedy (Pacman Small
Maze)

38. Video of Demo Contours (Pacman Small
Maze) – A*

39. Comparison
Greedy Uniform Cost A*