AI Informed Search Strategies by Examples

AI Informed Search Strategies by Examples

MENOUFIA UNIVERSITYFACULTY OF COMPUTERS AND INFORMATION

ALL DEPARTMENTSARTIFICIAL INTELLIGENCE

جامعة المنوفية

كلية الحاسبات والمعلومات

جميع األقسام

اإلصطناعيالذكاء

جامعة المنوفية

Ahmed Fawzy Gad

ahmed.fawzy@ci.menofia.edu.eg

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Heuristic Value

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Heuristic Value

Small Heuristic Value

Better Path

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Heuristic Value

Small Heuristic Value

Better Path

h(C)

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Heuristic Value

Small Heuristic Value

Better Path

h(C) h(B)

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Heuristic Value

Small Heuristic Value

Better Path

h(C) h(B)<

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Heuristic Value

Small Heuristic Value

Better Path

h(C) h(B)<C

Uninformed Search Vs. Informed Search ORHeuristically Informed Search

Heuristic Evaluation Function

Heuristic Value

Small Heuristic Value

Better Path

h(C) h(B)<C

Uninformed SearchNO INFORMATION

Direct SearchBEST PATH

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝟓

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝟓

𝒉𝟏

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝟓

𝒉𝟏 𝒉𝟐

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

𝑻𝒊𝒎𝒆

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝟓

𝒉𝟏 𝒉𝟐𝟔𝟎𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

𝑻𝒊𝒎𝒆

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝟓

𝒉𝟏 𝒉𝟐𝟔𝟎𝒔 𝟏𝟎𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

𝑻𝒊𝒎𝒆

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝟓

𝒉𝟏 𝒉𝟐𝟔𝟎𝒔 𝟏𝟎𝒔

𝒉𝟐

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

𝑻𝒊𝒎𝒆

Heuristic Evaluation Function

• Good heuristic evaluation function is what directs search to reachgoal with the smallest number of nodes.

• Good heuristic evaluation function is not time consuming in theheuristic value calculation.

𝒉𝟏 𝒉𝟐𝟓 𝟕

𝒉𝟏𝟓

𝒉𝟏 𝒉𝟐𝟔𝟎𝒔 𝟏𝟎𝒔

𝒉𝟐

𝟏𝟎𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

# 𝒐𝒇 𝑵𝒐𝒅𝒆𝒔

𝑯𝒆𝒖𝒓𝒊𝒔𝒕𝒊𝒄 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏

𝑻𝒊𝒎𝒆

Hill ClimbingGoal – Node G

S ---

Current Children

Hill ClimbingGoal – Node G

S ---

Current Children

S

Hill ClimbingGoal – Node G

S ---

Current Children

S

S

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

S

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D

S

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

S

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

S

D

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D

S

D

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

S

D

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E

S

D

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

S

D

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

S

D

E

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E

S

D

E

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

S

D

E

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F

S

D

E

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

S

D

E

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

S

D

E

F

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

F

S

D

E

F

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

F G

S

D

E

F

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

F G

S

D

E

F

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

F G

S

D

E

F

G

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

F G

S

D

E

F

G ---

Hill ClimbingGoal – Node G

S ---

Current Children

S 𝑫𝟖.𝟗, 𝑨𝟏𝟎.𝟒

D ---

D 𝑬𝟔.𝟗, 𝑨𝟏𝟎.𝟒

E ---

E 𝑭𝟑.𝟎, 𝑩𝟔.𝟕

F ---

F G

S

D

E

F

GG ---

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a

a

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

a

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f

a

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

a

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

a

f

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f

a

f

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

g

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

g ---

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

g ---g

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

g ---

g

g

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

g ---

g ---

g

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

g ---

g ---

g

Search FinishedNo GOAL

Hill ClimbingGoal – Node KLocal Maxima a ---

Current Children

a 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

f ---

f 𝒈𝟑, 𝒆𝟓

a

f

g ---

g ---

g

Search FinishedNo GOAL

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎

𝒂𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕

𝒂𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕

𝒂𝟏𝟎

𝒇𝟕

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓

𝒈𝟑

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎𝒈𝟑

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓

𝒈𝟑

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5 2

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5 2

Cost

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5 2

Cost 3

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5 2

Cost 3 9

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5 2

Cost 3 9

Total

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5 2

Cost 3 9

Total 8

Cost: Node to NodeHeuristic: Node to Goal

Greedy Best-First SearchGoal – Node K

𝒂𝟏𝟎 ---

Current Children

𝒂𝟏𝟎 𝒇𝟕, 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒋𝟖,𝒃𝟏𝟎

𝒇𝟕 𝒈𝟑,𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒂𝟏𝟎

𝒇𝟕

𝒈𝟑 𝒆𝟓, 𝒋𝟖,𝒃𝟏𝟎

𝒆𝟓 𝒋𝟖,𝒃𝟏𝟎

𝒈𝟑

𝒆𝟓

𝒆𝟓 𝒊𝟔,𝒋𝟖,𝒃𝟏𝟎

𝒊𝟔 𝒋𝟖,𝒃𝟏𝟎𝒊𝟔

𝒊𝟔 𝒌𝟎,𝒋𝟖,𝒃𝟏𝟎

𝒌𝟎 𝒋𝟖,𝒃𝟏𝟎𝒌𝟎

Similar to Uniform CostJust use Heuristic

& Avoids Cost

Heuristic 5 2

Cost 3 9

Total 8 11

Cost: Node to NodeHeuristic: Node to Goal

A* Search – Combines Heuristic & CostGoal - Bucharest

A* Search – ContinueGoal -Bucharest

Arad

AradArad

AradArad

Arad Children

Sibiu

AradArad

Arad Children

Sibiu

Timisoara

AradArad

Arad Children

Sibiu

Timisoara

Zerind

AradArad

Arad Children

Sibiu

Timisoara

Zerind

AradArad

Arad Children

Calculate Total Cost

Sibiu

Timisoara

Zerind

AradArad

Arad Children

Calculate Total Cost

Order Asc.

Sibiu

Timisoara

Zerind

AradArad

Arad Children

Calculate Total Cost

Order Asc.

Select Min. Cost

Sibiu

Timisoara

Zerind

Sibiu

Arad Children

Heuristic

Sibiu

Timisoara

Zerind

Sibiu

Arad Children

Heuristic Cost

Sibiu

Timisoara

Zerind

Sibiu

+

Arad Children

Heuristic Cost Total

Sibiu

Timisoara

Zerind

Sibiu

+

Arad Children

=

Heuristic Cost

253

Total

Sibiu

Timisoara

Zerind

Sibiu

+

Arad Children

=

Heuristic Cost

253 140

Total

Sibiu

Timisoara

Zerind

Sibiu

+ =

Arad Children

+

Heuristic Cost

253 140

Total

393+

Sibiu

Timisoara

Zerind

Sibiu

+ =

Arad Children

=

Heuristic Cost

253 140

Total

393+ =

Sibiu

Timisoara

Zerind

Sibiu

+ =

Arad Children

Heuristic Cost

253 140

Total

393+ =

Sibiu

Timisoara

Zerind

Sibiu

+ =

Arad Children

393

Heuristic Cost Total

Sibiu

Timisoara

Zerind

Timisoara

+ =

Arad Children

393

Heuristic Cost

329

Total

Sibiu

Timisoara

Zerind

Timisoara

+ =

Arad Children

393

Heuristic Cost

329 118

Total

+

Sibiu

Timisoara

Zerind

Timisoara

+ =

Arad Children

393

Heuristic Cost

329 118

Total

447+ =

Sibiu

Timisoara

Zerind

Timisoara

+ =

Arad Children

393

Heuristic Cost

329 118

Total

447+ =

Sibiu

Timisoara

Zerind

Timisoara

+ =

Arad Children

393

447

Heuristic Cost Total

Sibiu

Timisoara

Zerind

Zerind

+ =

Arad Children

393

447

Heuristic Cost

374

Total

Sibiu

Timisoara

Zerind

Zerind

+ =

Arad Children

393

447

Heuristic Cost

374 75

Total

+

Sibiu

Timisoara

Zerind

Zerind

+ =

Arad Children

393

447

Heuristic Cost

374 75

Total

449+ =

Sibiu

Timisoara

Zerind

Zerind

+ =

Arad Children

393

447

Heuristic Cost

374 75

Total

449+ =

Sibiu

Timisoara

Zerind

Zerind

+ =

Arad Children

393

447

449

Current Queue

Sibiu

393

Current Queue

Sibiu

393

Timisoara

447

Current Queue

Sibiu

393

Timisoara

447

Zerind

449

Current Queue

Sibiu

393

Timisoara

447

Zerind

449

Sibiu

393

Sibiu

SibiuSibiu

Arad

SibiuSibiu

Sibiu Children

Arad

Fagaras

SibiuSibiu

Sibiu Children

Arad

Fagaras

Orades

SibiuSibiu

Sibiu Children

Arad

Fagaras

Orades

SibiuSibiu

Sibiu Children

Ramnicu

Arad

Fagaras

Orades

SibiuSibiu

Sibiu Children

Calculate Total Cost

Ramnicu

Arad

Fagaras

Orades

SibiuSibiu

Sibiu Children

Calculate Total Cost

Order Asc.

Ramnicu

Arad

Fagaras

Orades

SibiuSibiu

Sibiu Children

Calculate Total Cost

Order Asc.

Select Min. Cost

Ramnicu

Arad

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

Heuristic

Arad

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

Heuristic Cost

Arad

+

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

Heuristic Cost Total

Arad

+

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

=

Heuristic Cost

366

Total

Arad

+

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

=

Heuristic Cost

366 280

Total

+

Arad

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

Heuristic Cost

366 280

Total

646+ =

Arad

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

Heuristic Cost

366 280

Total

646+ =

Arad

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

Heuristic Cost Total

Fagaras

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

Heuristic Cost

176

Total

Fagaras

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

Heuristic Cost

176 239

Total

+

Fagaras

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

Heuristic Cost

176 239

Total

415+ =

Fagaras

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

Heuristic Cost

176 239

Total

415+ =

Fagaras

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

Heuristic Cost Total

Orades

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

Heuristic Cost

380

Total

Orades

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

Heuristic Cost

380 291

Total

+

Orades

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

Heuristic Cost

380 291

Total

671+ =

Orades

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

Heuristic Cost

380 291

Total

671+ =

Orades

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

671

Heuristic Cost Total

Ramnicu

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

671

Heuristic Cost

193

Total+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

671

Ramnicu

Heuristic Cost

193 220

Total

+

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

671

Ramnicu

Heuristic Cost

193 220

Total

413+ =

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

671

Ramnicu

Heuristic Cost

193 220

Total

413+ =

+ =

Sibiu Children

Arad

Fagaras

Orades

Ramnicu

646

415

671

413

Ramnicu

Current Queue

Timisoara

447

Zerind

449

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Ramnicu

413

Fagaras

415

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Ramnicu

413

Fagaras

415

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Ramnicu

413

Fagaras

415

Ramnicu

413

Ramnicu

RamnicuRamnicu

Craiova

RamnicuRamnicu

RamnicuChildren

Craiova

Pitesti

RamnicuRamnicu

RamnicuChildren

Craiova

Pitesti

Sibiu

RamnicuRamnicu

RamnicuChildren

Craiova

Pitesti

Sibiu

RamnicuRamnicu

RamnicuChildren

Calculate Total Cost

Craiova

Pitesti

Sibiu

RamnicuRamnicu

RamnicuChildren

Calculate Total Cost

Order Asc.

Craiova

Pitesti

Sibiu

RamnicuRamnicu

RamnicuChildren

Calculate Total Cost

Order Asc.

Select Min. Cost

Craiova

RamnicuChildren

Craiova

Pitesti

Sibiu

Heuristic

Craiova

RamnicuChildren

Craiova

Pitesti

Sibiu

Heuristic Cost

Craiova

+

RamnicuChildren

Craiova

Pitesti

Sibiu

Heuristic Cost Total

Craiova

+

RamnicuChildren

Craiova

Pitesti

Sibiu

=

Heuristic Cost

160

Total

Craiova

+

RamnicuChildren

Craiova

Pitesti

Sibiu

=

Heuristic Cost

160 366

Total

+

Craiova

+ =

RamnicuChildren

Craiova

Pitesti

Sibiu

Heuristic Cost

160 366

Total

526+ =

Craiova

+ =

RamnicuChildren

Craiova

Pitesti

Sibiu

Heuristic Cost

160 366

Total

526+ =

Craiova

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

Heuristic Cost Total

Pitesti

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

Heuristic Cost

100

Total

Pitesti

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

Heuristic Cost

100 317

Total

+

Pitesti

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

Heuristic Cost

100 317

Total

417+ =

Pitesti

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

Heuristic Cost

100 317

Total

417+ =

Pitesti

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

417

Heuristic Cost Total

Sibiu

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

417

Heuristic Cost

253

Total

Sibiu

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

417

Heuristic Cost

253 300

Total

+

Sibiu

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

417

Heuristic Cost

253 300

Total

553+ =

Sibiu

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

417

Heuristic Cost

253 300

Total

553+ =

Sibiu

+ =

RamnicuChildren

526Craiova

Pitesti

Sibiu

417

553

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Fagaras

415

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Fagaras

415

Pitesti

417

Craiova

526

Sibiu

553

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Fagaras

415Pitesti

417

Craiova

526

Sibiu

553

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Fagaras

415Pitesti

417

Craiova

526

Sibiu

553

Fagaras

415

Fagaras

FagarasFagaras

Sibiu

FagarasFagaras

FagarasChildren

Sibiu

Bucharest

FagarasFagaras

FagarasChildren

Sibiu

Bucharest

FagarasFagaras

FagarasChildren

Calculate Total Cost

Sibiu

Bucharest

FagarasFagaras

FagarasChildren

Calculate Total Cost

Order Asc.

Sibiu

Bucharest

FagarasFagaras

FagarasChildren

Calculate Total Cost

Order Asc.

Select Min. Cost

Heuristic Cost Total

Sibiu

+ =

Sibiu

Bucharest

FagarasChildren

Heuristic Cost

253

Total

Sibiu

+ =

Sibiu

Bucharest

FagarasChildren

Heuristic Cost

253 338

Total

+

Sibiu

+ =

Sibiu

Bucharest

FagarasChildren

Heuristic Cost

253 338

Total

591+ =

Sibiu

+ =

Sibiu

Bucharest

FagarasChildren

Heuristic Cost

253 338

Total

591+ =

Sibiu

+ =

591Sibiu

Bucharest

FagarasChildren

Heuristic Cost Total

Bucharest

+ =

591Sibiu

Bucharest

FagarasChildren

Heuristic Cost

0

Total

Bucharest

+ =

591Sibiu

Bucharest

FagarasChildren

Heuristic Cost

0 450

Total

+

Bucharest

+ =

591Sibiu

Bucharest

FagarasChildren

Heuristic Cost

0 450

Total

450+ =

Bucharest

+ =

591Sibiu

Bucharest

FagarasChildren

Heuristic Cost

0 450

Total

450+ =

Bucharest

+ =

591

450

Sibiu

Bucharest

FagarasChildren

Current Queue

Arad

646

Timisoara

447

Zerind

449Orades

671

Pitesti

417

Craiova

526

Sibiu

553

Current Queue

Arad

646

Timisoara

447

Zerind

449Orades

671

Pitesti

417

Craiova

526

Sibiu

591

Bucharest

450

Sibiu

553

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Pitesti

417

Craiova

526

Sibiu

591

Bucharest

450

Sibiu

553

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Pitesti

417

Craiova

526

Sibiu

591

Pitesti

417Bucharest

450

Sibiu

553

Pitesti

PitestiPetisti

Bucharest

PitestiPetisti

PetistiChildren

Bucharest

Craiova

PitestiPetisti

PetistiChildren

Bucharest

Craiova

Ramnicu

PitestiPetisti

PetistiChildren

Bucharest

Craiova

Ramnicu

PitestiPetisti

PetistiChildren

Calculate Total Cost

Bucharest

Craiova

Ramnicu

PitestiPetisti

PetistiChildren

Calculate Total Cost

Order Asc.

Bucharest

Craiova

Ramnicu

PitestiPetisti

PetistiChildren

Calculate Total Cost

Order Asc.

Select Min. Cost

Heuristic Cost Total

Bucharest

+ =

RamnicuChildren

Bucharest

Craiova

Ramnicu

Heuristic Cost

0

Total

Bucharest

+ =

RamnicuChildren

Bucharest

Craiova

Ramnicu

Heuristic Cost

0 418

Total

+

Bucharest

+ =

RamnicuChildren

Bucharest

Craiova

Ramnicu

Heuristic Cost

0 418

Total

418+ =

Bucharest

+ =

RamnicuChildren

Bucharest

Craiova

Ramnicu

Heuristic Cost

0 418

Total

418+ =

Bucharest

+ =

RamnicuChildren

418Bucharest

Craiova

Ramnicu

Heuristic Cost Total

Craiova

+ =

RamnicuChildren

418Bucharest

Craiova

Ramnicu

Heuristic Cost

160

Total

Craiova

+ =

RamnicuChildren

418Bucharest

Craiova

Ramnicu

Heuristic Cost

160 455

Total

+

Craiova

+ =

RamnicuChildren

418Bucharest

Craiova

Ramnicu

Heuristic Cost

160 455

Total

615+ =

Craiova

+ =

RamnicuChildren

418Bucharest

Craiova

Ramnicu

Heuristic Cost

160 455

Total

615+ =

Craiova

+ =

RamnicuChildren

418

615

Bucharest

Craiova

Ramnicu

Heuristic Cost Total

Ramnicu

+ =

RamnicuChildren

418

615

Bucharest

Craiova

Ramnicu

Heuristic Cost

193

Total

Ramnicu

+ =

RamnicuChildren

418

615

Bucharest

Craiova

Ramnicu

Heuristic Cost

193 414

Total

+

Ramnicu

+ =

RamnicuChildren

418

615

Bucharest

Craiova

Ramnicu

Heuristic Cost

193 414

Total

607+ =

Ramnicu

+ =

RamnicuChildren

418

615

Bucharest

Craiova

Ramnicu

Heuristic Cost

193 414

Total

607+ =

Ramnicu

+ =

RamnicuChildren

418

615

607

Bucharest

Craiova

Ramnicu

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Craiova

615

Sibiu

591

Bucharest

450

Sibiu

553

Bucharest

418

Craiova

526

Ramnicu

607

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Craiova

615

Sibiu

591

Bucharest

450

Sibiu

553

Bucharest

418

Craiova

526

Ramnicu

607

Current Queue

Arad

646

Timisoara

447

Zerind

449

Orades

671

Craiova

615

Sibiu

591

Bucharest

450

Sibiu

553

Bucharest

418

Craiova

526

Ramnicu

607

Bucharest

418

Bucharest

BucharestBucharest

BucharestBucharest

GOAL

Path to Goal