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import
time
from
collections
import
defaultdict
from
inspect
import
getsource
import
ipywidgets
as
widgets
import
matplotlib
.
pyplot
as
plt
import
networkx
as
nx
import
numpy
as
np
from
IPython
.
display
import
HTML
from
IPython
.
display
import
display
from
PIL
import
Image
from
matplotlib
import
lines
from
games
import
TicTacToe
,
alpha_beta_player
,
random_player
,
Fig52Extended
from
learning
import
DataSet
from
logic
import
parse_definite_clause
,
standardize_variables
,
unify_mm
,
subst
from
search
import
GraphProblem
,
romania_map
# ______________________________________________________________________________
# Magic Words
def
pseudocode
(
algorithm
):
"""Print the pseudocode for the given algorithm."""
from
urllib
.
request
import
urlopen
from
IPython
.
display
import
Markdown
algorithm
=
algorithm
.
replace
(
' '
,
'-'
)
url
=
"https://raw.githubusercontent.com/aimacode/aima-pseudocode/master/md/{}.md"
.
format
(
algorithm
)
f
=
urlopen
(
url
)
md
=
f
.
read
().
decode
(
'utf-8'
)
md
=
md
.
split
(
'
\n
'
,
1
)[
-
1
].
strip
()
md
=
'#'
+
md
return
Markdown
(
md
)
def
psource
(
*
functions
):
"""Print the source code for the given function(s)."""
source_code
=
'
\n
\n
'
.
join
(
getsource
(
fn
)
for
fn
in
functions
)
try
:
from
pygments
.
formatters
import
HtmlFormatter
from
pygments
.
lexers
import
PythonLexer
from
pygments
import
highlight
display
(
HTML
(
highlight
(
source_code
,
PythonLexer
(),
HtmlFormatter
(
full
=
True
))))
except
ImportError
:
print
(
source_code
)
# ______________________________________________________________________________
# Iris Visualization
def
show_iris
(
i
=
0
,
j
=
1
,
k
=
2
):
"""Plots the iris dataset in a 3D plot.
The three axes are given by i, j and k,
which correspond to three of the four iris features."""
plt
.
rcParams
.
update
(
plt
.
rcParamsDefault
)
fig
=
plt
.
figure
()
ax
=
fig
.
add_subplot
(
111
,
projection
=
'3d'
)
iris
=
DataSet
(
name
=
"iris"
)
buckets
=
iris
.
split_values_by_classes
()
features
=
[
"Sepal Length"
,
"Sepal Width"
,
"Petal Length"
,
"Petal Width"
]
f1
,
f2
,
f3
=
features
[
i
],
features
[
j
],
features
[
k
]
a_setosa
=
[
v
[
i
]
for
v
in
buckets
[
"setosa"
]]
b_setosa
=
[
v
[
j
]
for
v
in
buckets
[
"setosa"
]]
c_setosa
=
[
v
[
k
]
for
v
in
buckets
[
"setosa"
]]
a_virginica
=
[
v
[
i
]
for
v
in
buckets
[
"virginica"
]]
b_virginica
=
[
v
[
j
]
for
v
in
buckets
[
"virginica"
]]
c_virginica
=
[
v
[
k
]
for
v
in
buckets
[
"virginica"
]]
a_versicolor
=
[
v
[
i
]
for
v
in
buckets
[
"versicolor"
]]
b_versicolor
=
[
v
[
j
]
for
v
in
buckets
[
"versicolor"
]]
c_versicolor
=
[
v
[
k
]
for
v
in
buckets
[
"versicolor"
]]
for
c
,
m
,
sl
,
sw
,
pl
in
[(
'b'
,
's'
,
a_setosa
,
b_setosa
,
c_setosa
),
(
'g'
,
'^'
,
a_virginica
,
b_virginica
,
c_virginica
),
(
'r'
,
'o'
,
a_versicolor
,
b_versicolor
,
c_versicolor
)]:
ax
.
scatter
(
sl
,
sw
,
pl
,
c
=
c
,
marker
=
m
)
ax
.
set_xlabel
(
f1
)
ax
.
set_ylabel
(
f2
)
ax
.
set_zlabel
(
f3
)
plt
.
show
()
# ______________________________________________________________________________
# MNIST
def
load_MNIST
(
path
=
"aima-data/MNIST/Digits"
,
fashion
=
False
):
import
os
,
struct
import
array
import
numpy
as
np
if
fashion
:
path
=
"aima-data/MNIST/Fashion"
plt
.
rcParams
.
update
(
plt
.
rcParamsDefault
)
plt
.
rcParams
[
'figure.figsize'
]
=
(
10.0
,
8.0
)
plt
.
rcParams
[
'image.interpolation'
]
=
'nearest'
plt
.
rcParams
[
'image.cmap'
]
=
'gray'
train_img_file
=
open
(
os
.
path
.
join
(
path
,
"train-images-idx3-ubyte"
),
"rb"
)
train_lbl_file
=
open
(
os
.
path
.
join
(
path
,
"train-labels-idx1-ubyte"
),
"rb"
)
test_img_file
=
open
(
os
.
path
.
join
(
path
,
"t10k-images-idx3-ubyte"
),
"rb"
)
test_lbl_file
=
open
(
os
.
path
.
join
(
path
,
't10k-labels-idx1-ubyte'
),
"rb"
)
magic_nr
,
tr_size
,
tr_rows
,
tr_cols
=
struct
.
unpack
(
">IIII"
,
train_img_file
.
read
(
16
))
tr_img
=
array
.
array
(
"B"
,
train_img_file
.
read
())
train_img_file
.
close
()
magic_nr
,
tr_size
=
struct
.
unpack
(
">II"
,
train_lbl_file
.
read
(
8
))
tr_lbl
=
array
.
array
(
"b"
,
train_lbl_file
.
read
())
train_lbl_file
.
close
()
magic_nr
,
te_size
,
te_rows
,
te_cols
=
struct
.
unpack
(
">IIII"
,
test_img_file
.
read
(
16
))
te_img
=
array
.
array
(
"B"
,
test_img_file
.
read
())
test_img_file
.
close
()
magic_nr
,
te_size
=
struct
.
unpack
(
">II"
,
test_lbl_file
.
read
(
8
))
te_lbl
=
array
.
array
(
"b"
,
test_lbl_file
.
read
())
test_lbl_file
.
close
()
# print(len(tr_img), len(tr_lbl), tr_size)
# print(len(te_img), len(te_lbl), te_size)
train_img
=
np
.
zeros
((
tr_size
,
tr_rows
*
tr_cols
),
dtype
=
np
.
int16
)
train_lbl
=
np
.
zeros
((
tr_size
,),
dtype
=
np
.
int8
)
for
i
in
range
(
tr_size
):
train_img
[
i
]
=
np
.
array
(
tr_img
[
i
*
tr_rows
*
tr_cols
: (
i
+
1
)
*
tr_rows
*
tr_cols
]).
reshape
((
tr_rows
*
te_cols
))
train_lbl
[
i
]
=
tr_lbl
[
i
]
test_img
=
np
.
zeros
((
te_size
,
te_rows
*
te_cols
),
dtype
=
np
.
int16
)
test_lbl
=
np
.
zeros
((
te_size
,),
dtype
=
np
.
int8
)
for
i
in
range
(
te_size
):
test_img
[
i
]
=
np
.
array
(
te_img
[
i
*
te_rows
*
te_cols
: (
i
+
1
)
*
te_rows
*
te_cols
]).
reshape
((
te_rows
*
te_cols
))
test_lbl
[
i
]
=
te_lbl
[
i
]
return
(
train_img
,
train_lbl
,
test_img
,
test_lbl
)
digit_classes
=
[
str
(
i
)
for
i
in
range
(
10
)]
fashion_classes
=
[
"T-shirt/top"
,
"Trouser"
,
"Pullover"
,
"Dress"
,
"Coat"
,
"Sandal"
,
"Shirt"
,
"Sneaker"
,
"Bag"
,
"Ankle boot"
]
def
show_MNIST
(
labels
,
images
,
samples
=
8
,
fashion
=
False
):
if
not
fashion
:
classes
=
digit_classes
else
:
classes
=
fashion_classes
num_classes
=
len
(
classes
)
for
y
,
cls
in
enumerate
(
classes
):
idxs
=
np
.
nonzero
([
i
==
y
for
i
in
labels
])
idxs
=
np
.
random
.
choice
(
idxs
[
0
],
samples
,
replace
=
False
)
for
i
,
idx
in
enumerate
(
idxs
):
plt_idx
=
i
*
num_classes
+
y
+
1
plt
.
subplot
(
samples
,
num_classes
,
plt_idx
)
plt
.
imshow
(
images
[
idx
].
reshape
((
28
,
28
)))
plt
.
axis
(
"off"
)
if
i
==
0
:
plt
.
title
(
cls
)
plt
.
show
()
def
show_ave_MNIST
(
labels
,
images
,
fashion
=
False
):
if
not
fashion
:
item_type
=
"Digit"
classes
=
digit_classes
else
:
item_type
=
"Apparel"
classes
=
fashion_classes
num_classes
=
len
(
classes
)
for
y
,
cls
in
enumerate
(
classes
):
idxs
=
np
.
nonzero
([
i
==
y
for
i
in
labels
])
print
(
item_type
,
y
,
":"
,
len
(
idxs
[
0
]),
"images."
)
ave_img
=
np
.
mean
(
np
.
vstack
([
images
[
i
]
for
i
in
idxs
[
0
]]),
axis
=
0
)
# print(ave_img.shape)
plt
.
subplot
(
1
,
num_classes
,
y
+
1
)
plt
.
imshow
(
ave_img
.
reshape
((
28
,
28
)))
plt
.
axis
(
"off"
)
plt
.
title
(
cls
)
plt
.
show
()
# ______________________________________________________________________________
# MDP
def
make_plot_grid_step_function
(
columns
,
rows
,
U_over_time
):
"""ipywidgets interactive function supports single parameter as input.
This function creates and return such a function by taking as input
other parameters."""
def
plot_grid_step
(
iteration
):
data
=
U_over_time
[
iteration
]
data
=
defaultdict
(
lambda
:
0
,
data
)
grid
=
[]
for
row
in
range
(
rows
):
current_row
=
[]
for
column
in
range
(
columns
):
current_row
.
append
(
data
[(
column
,
row
)])
grid
.
append
(
current_row
)
grid
.
reverse
()
# output like book
fig
=
plt
.
imshow
(
grid
,
cmap
=
plt
.
cm
.
bwr
,
interpolation
=
'nearest'
)
plt
.
axis
(
'off'
)
fig
.
axes
.
get_xaxis
().
set_visible
(
False
)
fig
.
axes
.
get_yaxis
().
set_visible
(
False
)
for
col
in
range
(
len
(
grid
)):
for
row
in
range
(
len
(
grid
[
0
])):
magic
=
grid
[
col
][
row
]
fig
.
axes
.
text
(
row
,
col
,
"{0:.2f}"
.
format
(
magic
),
va
=
'center'
,
ha
=
'center'
)
plt
.
show
()
return
plot_grid_step
def
make_visualize
(
slider
):
"""Takes an input a sliderand returns callback function
for timer and animation."""
def
visualize_callback
(
Visualize
,
time_step
):
if
Visualize
is
True
:
for
i
in
range
(
slider
.
min
,
slider
.
max
+
1
):
slider
.
value
=
i
time
.
sleep
(
float
(
time_step
))
return
visualize_callback
# ______________________________________________________________________________
_canvas
=
"""
<script type="text/javascript" src="./js/canvas.js"></script>
<div>
<canvas id="{0}" width="{1}" height="{2}" style="background:rgba(158, 167, 184, 0.2);" onclick='click_callback(this, event, "{3}")'></canvas>
</div>
<script> var {0}_canvas_object = new Canvas("{0}");</script>
"""
# noqa
class
Canvas
:
"""Inherit from this class to manage the HTML canvas element in jupyter notebooks.
To create an object of this class any_name_xyz = Canvas("any_name_xyz")
The first argument given must be the name of the object being created.
IPython must be able to reference the variable name that is being passed."""
def
__init__
(
self
,
varname
,
width
=
800
,
height
=
600
,
cid
=
None
):
self
.
name
=
varname
self
.
cid
=
cid
or
varname
self
.
width
=
width
self
.
height
=
height
self
.
html
=
_canvas
.
format
(
self
.
cid
,
self
.
width
,
self
.
height
,
self
.
name
)
self
.
exec_list
=
[]
display_html
(
self
.
html
)
def
mouse_click
(
self
,
x
,
y
):
"""Override this method to handle mouse click at position (x, y)"""
raise
NotImplementedError
def
mouse_move
(
self
,
x
,
y
):
raise
NotImplementedError
def
execute
(
self
,
exec_str
):
"""Stores the command to be executed to a list which is used later during update()"""
if
not
isinstance
(
exec_str
,
str
):
print
(
"Invalid execution argument:"
,
exec_str
)
self
.
alert
(
"Received invalid execution command format"
)
prefix
=
"{0}_canvas_object."
.
format
(
self
.
cid
)
self
.
exec_list
.
append
(
prefix
+
exec_str
+
';'
)
def
fill
(
self
,
r
,
g
,
b
):
"""Changes the fill color to a color in rgb format"""
self
.
execute
(
"fill({0}, {1}, {2})"
.
format
(
r
,
g
,
b
))
def
stroke
(
self
,
r
,
g
,
b
):
"""Changes the colors of line/strokes to rgb"""
self
.
execute
(
"stroke({0}, {1}, {2})"
.
format
(
r
,
g
,
b
))
def
strokeWidth
(
self
,
w
):
"""Changes the width of lines/strokes to 'w' pixels"""
self
.
execute
(
"strokeWidth({0})"
.
format
(
w
))
def
rect
(
self
,
x
,
y
,
w
,
h
):
"""Draw a rectangle with 'w' width, 'h' height and (x, y) as the top-left corner"""
self
.
execute
(
"rect({0}, {1}, {2}, {3})"
.
format
(
x
,
y
,
w
,
h
))
def
rect_n
(
self
,
xn
,
yn
,
wn
,
hn
):
"""Similar to rect(), but the dimensions are normalized to fall between 0 and 1"""
x
=
round
(
xn
*
self
.
width
)
y
=
round
(
yn
*
self
.
height
)
w
=
round
(
wn
*
self
.
width
)
h
=
round
(
hn
*
self
.
height
)
self
.
rect
(
x
,
y
,
w
,
h
)
def
line
(
self
,
x1
,
y1
,
x2
,
y2
):
"""Draw a line from (x1, y1) to (x2, y2)"""
self
.
execute
(
"line({0}, {1}, {2}, {3})"
.
format
(
x1
,
y1
,
x2
,
y2
))
def
line_n
(
self
,
x1n
,
y1n
,
x2n
,
y2n
):
"""Similar to line(), but the dimensions are normalized to fall between 0 and 1"""
x1
=
round
(
x1n
*
self
.
width
)
y1
=
round
(
y1n
*
self
.
height
)
x2
=
round
(
x2n
*
self
.
width
)
y2
=
round
(
y2n
*
self
.
height
)
self
.
line
(
x1
,
y1
,
x2
,
y2
)
def
arc
(
self
,
x
,
y
,
r
,
start
,
stop
):
"""Draw an arc with (x, y) as centre, 'r' as radius from angles 'start' to 'stop'"""
self
.
execute
(
"arc({0}, {1}, {2}, {3}, {4})"
.
format
(
x
,
y
,
r
,
start
,
stop
))
def
arc_n
(
self
,
xn
,
yn
,
rn
,
start
,
stop
):
"""Similar to arc(), but the dimensions are normalized to fall between 0 and 1
The normalizing factor for radius is selected between width and height by
seeing which is smaller."""
x
=
round
(
xn
*
self
.
width
)
y
=
round
(
yn
*
self
.
height
)
r
=
round
(
rn
*
min
(
self
.
width
,
self
.
height
))
self
.
arc
(
x
,
y
,
r
,
start
,
stop
)
def
clear
(
self
):
"""Clear the HTML canvas"""
self
.
execute
(
"clear()"
)
def
font
(
self
,
font
):
"""Changes the font of text"""
self
.
execute
(
'font("{0}")'
.
format
(
font
))
def
text
(
self
,
txt
,
x
,
y
,
fill
=
True
):
"""Display a text at (x, y)"""
if
fill
:
self
.
execute
(
'fill_text("{0}", {1}, {2})'
.
format
(
txt
,
x
,
y
))
else
:
self
.
execute
(
'stroke_text("{0}", {1}, {2})'
.
format
(
txt
,
x
,
y
))
def
text_n
(
self
,
txt
,
xn
,
yn
,
fill
=
True
):
"""Similar to text(), but with normalized coordinates"""
x
=
round
(
xn
*
self
.
width
)
y
=
round
(
yn
*
self
.
height
)
self
.
text
(
txt
,
x
,
y
,
fill
)
def
alert
(
self
,
message
):
"""Immediately display an alert"""
display_html
(
'<script>alert("{0}")</script>'
.
format
(
message
))
def
update
(
self
):
"""Execute the JS code to execute the commands queued by execute()"""
exec_code
=
"<script>
\n
"
+
'
\n
'
.
join
(
self
.
exec_list
)
+
"
\n
</script>"
self
.
exec_list
=
[]
display_html
(
exec_code
)
def
display_html
(
html_string
):
display
(
HTML
(
html_string
))
################################################################################
class
Canvas_TicTacToe
(
Canvas
):
"""Play a 3x3 TicTacToe game on HTML canvas"""
def
__init__
(
self
,
varname
,
player_1
=
'human'
,
player_2
=
'random'
,
width
=
300
,
height
=
350
,
cid
=
None
):
valid_players
=
(
'human'
,
'random'
,
'alpha_beta'
)
if
player_1
not
in
valid_players
or
player_2
not
in
valid_players
:
raise
TypeError
(
"Players must be one of {}"
.
format
(
valid_players
))
super
().
__init__
(
varname
,
width
,
height
,
cid
)
self
.
ttt
=
TicTacToe
()
self
.
state
=
self
.
ttt
.
initial
self
.
turn
=
0
self
.
strokeWidth
(
5
)
self
.
players
=
(
player_1
,
player_2
)
self
.
font
(
"20px Arial"
)
self
.
draw_board
()
def
mouse_click
(
self
,
x
,
y
):
player
=
self
.
players
[
self
.
turn
]
if
self
.
ttt
.
terminal_test
(
self
.
state
):
if
0.55
<=
x
/
self
.
width
<=
0.95
and
6
/
7
<=
y
/
self
.
height
<=
6
/
7
+
1
/
8
:
self
.
state
=
self
.
ttt
.
initial
self
.
turn
=
0
self
.
draw_board
()
return
if
player
==
'human'
:
x
,
y
=
int
(
3
*
x
/
self
.
width
)
+
1
,
int
(
3
*
y
/
(
self
.
height
*
6
/
7
))
+
1
if
(
x
,
y
)
not
in
self
.
ttt
.
actions
(
self
.
state
):
# Invalid move
return
move
=
(
x
,
y
)
elif
player
==
'alpha_beta'
:
move
=
alpha_beta_player
(
self
.
ttt
,
self
.
state
)
else
:
move
=
random_player
(
self
.
ttt
,
self
.
state
)
self
.
state
=
self
.
ttt
.
result
(
self
.
state
,
move
)
self
.
turn
^=
1
self
.
draw_board
()
def
draw_board
(
self
):
self
.
clear
()
self
.
stroke
(
0
,
0
,
0
)
offset
=
1
/
20
self
.
line_n
(
0
+
offset
, (
1
/
3
)
*
6
/
7
,
1
-
offset
, (
1
/
3
)
*
6
/
7
)
self
.
line_n
(
0
+
offset
, (
2
/
3
)
*
6
/
7
,
1
-
offset
, (
2
/
3
)
*
6
/
7
)
self
.
line_n
(
1
/
3
, (
0
+
offset
)
*
6
/
7
,
1
/
3
, (
1
-
offset
)
*
6
/
7
)
self
.
line_n
(
2
/
3
, (
0
+
offset
)
*
6
/
7
,
2
/
3
, (
1
-
offset
)
*
6
/
7
)
board
=
self
.
state
.
board
for
mark
in
board
:
if
board
[
mark
]
==
'X'
:
self
.
draw_x
(
mark
)
elif
board
[
mark
]
==
'O'
:
self
.
draw_o
(
mark
)
if
self
.
ttt
.
terminal_test
(
self
.
state
):
# End game message
utility
=
self
.
ttt
.
utility
(
self
.
state
,
self
.
ttt
.
to_move
(
self
.
ttt
.
initial
))
if
utility
==
0
:
self
.
text_n
(
'Game Draw!'
,
offset
,
6
/
7
+
offset
)
else
:
self
.
text_n
(
'Player {} wins!'
.
format
(
"XO"
[
utility
<
0
]),
offset
,
6
/
7
+
offset
)
# Find the 3 and draw a line
self
.
stroke
([
255
,
0
][
self
.
turn
], [
0
,
255
][
self
.
turn
],
0
)
for
i
in
range
(
3
):
if
all
([(
i
+
1
,
j
+
1
)
in
self
.
state
.
board
for
j
in
range
(
3
)])
and
\
len
({
self
.
state
.
board
[(
i
+
1
,
j
+
1
)]
for
j
in
range
(
3
)})
==
1
:
self
.
line_n
(
i
/
3
+
1
/
6
,
offset
*
6
/
7
,
i
/
3
+
1
/
6
, (
1
-
offset
)
*
6
/
7
)
if
all
([(
j
+
1
,
i
+
1
)
in
self
.
state
.
board
for
j
in
range
(
3
)])
and
\
len
({
self
.
state
.
board
[(
j
+
1
,
i
+
1
)]
for
j
in
range
(
3
)})
==
1
:
self
.
line_n
(
offset
, (
i
/
3
+
1
/
6
)
*
6
/
7
,
1
-
offset
, (
i
/
3
+
1
/
6
)
*
6
/
7
)
if
all
([(
i
+
1
,
i
+
1
)
in
self
.
state
.
board
for
i
in
range
(
3
)])
and
\
len
({
self
.
state
.
board
[(
i
+
1
,
i
+
1
)]
for
i
in
range
(
3
)})
==
1
:
self
.
line_n
(
offset
,
offset
*
6
/
7
,
1
-
offset
, (
1
-
offset
)
*
6
/
7
)
if
all
([(
i
+
1
,
3
-
i
)
in
self
.
state
.
board
for
i
in
range
(
3
)])
and
\
len
({
self
.
state
.
board
[(
i
+
1
,
3
-
i
)]
for
i
in
range
(
3
)})
==
1
:
self
.
line_n
(
offset
, (
1
-
offset
)
*
6
/
7
,
1
-
offset
,
offset
*
6
/
7
)
# restart button
self
.
fill
(
0
,
0
,
255
)
self
.
rect_n
(
0.5
+
offset
,
6
/
7
,
0.4
,
1
/
8
)
self
.
fill
(
0
,
0
,
0
)
self
.
text_n
(
'Restart'
,
0.5
+
2
*
offset
,
13
/
14
)
else
:
# Print which player's turn it is
self
.
text_n
(
"Player {}'s move({})"
.
format
(
"XO"
[
self
.
turn
],
self
.
players
[
self
.
turn
]),
offset
,
6
/
7
+
offset
)
self
.
update
()
def
draw_x
(
self
,
position
):
self
.
stroke
(
0
,
255
,
0
)
x
,
y
=
[
i
-
1
for
i
in
position
]
offset
=
1
/
15
self
.
line_n
(
x
/
3
+
offset
, (
y
/
3
+
offset
)
*
6
/
7
,
x
/
3
+
1
/
3
-
offset
, (
y
/
3
+
1
/
3
-
offset
)
*
6
/
7
)
self
.
line_n
(
x
/
3
+
1
/
3
-
offset
, (
y
/
3
+
offset
)
*
6
/
7
,
x
/
3
+
offset
, (
y
/
3
+
1
/
3
-
offset
)
*
6
/
7
)
def
draw_o
(
self
,
position
):
self
.
stroke
(
255
,
0
,
0
)
x
,
y
=
[
i
-
1
for
i
in
position
]
self
.
arc_n
(
x
/
3
+
1
/
6
, (
y
/
3
+
1
/
6
)
*
6
/
7
,
1
/
9
,
0
,
360
)
class
Canvas_min_max
(
Canvas
):
"""MinMax for Fig52Extended on HTML canvas"""
def
__init__
(
self
,
varname
,
util_list
,
width
=
800
,
height
=
600
,
cid
=
None
):
super
.
__init__
(
varname
,
width
,
height
,
cid
)
self
.
utils
=
{
node
:
util
for
node
,
util
in
zip
(
range
(
13
,
40
),
util_list
)}
self
.
game
=
Fig52Extended
()
self
.
game
.
utils
=
self
.
utils
self
.
nodes
=
list
(
range
(
40
))
self
.
l
=
1
/
40
self
.
node_pos
=
{}
for
i
in
range
(
4
):
base
=
len
(
self
.
node_pos
)
row_size
=
3
**
i
for
node
in
[
base
+
j
for
j
in
range
(
row_size
)]:
self
.
node_pos
[
node
]
=
((
node
-
base
)
/
row_size
+
1
/
(
2
*
row_size
)
-
self
.
l
/
2
,
self
.
l
/
2
+
(
self
.
l
+
(
1
-
5
*
self
.
l
)
/
3
)
*
i
)
self
.
font
(
"12px Arial"
)
self
.
node_stack
=
[]
self
.
explored
=
{
node
for
node
in
self
.
utils
}
self
.
thick_lines
=
set
()
self
.
change_list
=
[]
self
.
draw_graph
()
self
.
stack_manager
=
self
.
stack_manager_gen
()
def
min_max
(
self
,
node
):
game
=
self
.
game
player
=
game
.
to_move
(
node
)
def
max_value
(
node
):
if
game
.
terminal_test
(
node
):
return
game
.
utility
(
node
,
player
)
self
.
change_list
.
append
((
'a'
,
node
))
self
.
change_list
.
append
((
'h'
,))
max_a
=
max
(
game
.
actions
(
node
),
key
=
lambda
x
:
min_value
(
game
.
result
(
node
,
x
)))
max_node
=
game
.
result
(
node
,
max_a
)
self
.
utils
[
node
]
=
self
.
utils
[
max_node
]
x1
,
y1
=
self
.
node_pos
[
node
]
x2
,
y2
=
self
.
node_pos
[
max_node
]
self
.
change_list
.
append
((
'l'
, (
node
,
max_node
-
3
*
node
-
1
)))
self
.
change_list
.
append
((
'e'
,
node
))
self
.
change_list
.
append
((
'p'
,))
self
.
change_list
.
append
((
'h'
,))
return
self
.
utils
[
node
]
def
min_value
(
node
):
if
game
.
terminal_test
(
node
):
return
game
.
utility
(
node
,
player
)
self
.
change_list
.
append
((
'a'
,
node
))
self
.
change_list
.
append
((
'h'
,))
min_a
=
min
(
game
.
actions
(
node
),
key
=
lambda
x
:
max_value
(
game
.
result
(
node
,
x
)))
min_node
=
game
.
result
(
node
,
min_a
)
self
.
utils
[
node
]
=
self
.
utils
[
min_node
]
x1
,
y1
=
self
.
node_pos
[
node
]
x2
,
y2
=
self
.
node_pos
[
min_node
]
self
.
change_list
.
append
((
'l'
, (
node
,
min_node
-
3
*
node
-
1
)))
self
.
change_list
.
append
((
'e'
,
node
))
self
.
change_list
.
append
((
'p'
,))
self
.
change_list
.
append
((
'h'
,))
return
self
.
utils
[
node
]
return
max_value
(
node
)
def
stack_manager_gen
(
self
):
self
.
min_max
(
0
)
for
change
in
self
.
change_list
:
if
change
[
0
]
==
'a'
:
self
.
node_stack
.
append
(
change
[
1
])
elif
change
[
0
]
==
'e'
:
self
.
explored
.
add
(
change
[
1
])
elif
change
[
0
]
==
'h'
:
yield
elif
change
[
0
]
==
'l'
:
self
.
thick_lines
.
add
(
change
[
1
])
elif
change
[
0
]
==
'p'
:
self
.
node_stack
.
pop
()
def
mouse_click
(
self
,
x
,
y
):
try
:
self
.
stack_manager
.
send
(
None
)
except
StopIteration
:
pass
self
.
draw_graph
()
def
draw_graph
(
self
):
self
.
clear
()
# draw nodes
self
.
stroke
(
0
,
0
,
0
)
self
.
strokeWidth
(
1
)
# highlight for nodes in stack
for
node
in
self
.
node_stack
:
x
,
y
=
self
.
node_pos
[
node
]
self
.
fill
(
200
,
200
,
0
)
self
.
rect_n
(
x
-
self
.
l
/
5
,
y
-
self
.
l
/
5
,
self
.
l
*
7
/
5
,
self
.
l
*
7
/
5
)
for
node
in
self
.
nodes
:
x
,
y
=
self
.
node_pos
[
node
]
if
node
in
self
.
explored
:
self
.
fill
(
255
,
255
,
255
)
else
:
self
.
fill
(
200
,
200
,
200
)
self
.
rect_n
(
x
,
y
,
self
.
l
,
self
.
l
)
self
.
line_n
(
x
,
y
,
x
+
self
.
l
,
y
)
self
.
line_n
(
x
,
y
,
x
,
y
+
self
.
l
)
self
.
line_n
(
x
+
self
.
l
,
y
+
self
.
l
,
x
+
self
.
l
,
y
)
self
.
line_n
(
x
+
self
.
l
,
y
+
self
.
l
,
x
,
y
+
self
.
l
)
self
.
fill
(
0
,
0
,
0
)
if
node
in
self
.
explored
:
self
.
text_n
(
self
.
utils
[
node
],
x
+
self
.
l
/
10
,
y
+
self
.
l
*
9
/
10
)
# draw edges
for
i
in
range
(
13
):
x1
,
y1
=
self
.
node_pos
[
i
][
0
]
+
self
.
l
/
2
,
self
.
node_pos
[
i
][
1
]
+
self
.
l
for
j
in
range
(
3
):
x2
,
y2
=
self
.
node_pos
[
i
*
3
+
j
+
1
][
0
]
+
self
.
l
/
2
,
self
.
node_pos
[
i
*
3
+
j
+
1
][
1
]
if
i
in
[
1
,
2
,
3
]:
self
.
stroke
(
200
,
0
,
0
)
else
:
self
.
stroke
(
0
,
200
,
0
)
if
(
i
,
j
)
in
self
.
thick_lines
:
self
.
strokeWidth
(
3
)
else
:
self
.
strokeWidth
(
1
)
self
.
line_n
(
x1
,
y1
,
x2
,
y2
)
self
.
update
()
class
Canvas_alpha_beta
(
Canvas
):
"""Alpha-beta pruning for Fig52Extended on HTML canvas"""
def
__init__
(
self
,
varname
,
util_list
,
width
=
800
,
height
=
600
,
cid
=
None
):
super
().
__init__
(
varname
,
width
,
height
,
cid
)
self
.
utils
=
{
node
:
util
for
node
,
util
in
zip
(
range
(
13
,
40
),
util_list
)}
self
.
game
=
Fig52Extended
()
self
.
game
.
utils
=
self
.
utils
self
.
nodes
=
list
(
range
(
40
))
self
.
l
=
1
/
40
self
.
node_pos
=
{}
for
i
in
range
(
4
):
base
=
len
(
self
.
node_pos
)
row_size
=
3
**
i
for
node
in
[
base
+
j
for
j
in
range
(
row_size
)]:
self
.
node_pos
[
node
]
=
((
node
-
base
)
/
row_size
+
1
/
(
2
*
row_size
)
-
self
.
l
/
2
,
3
*
self
.
l
/
2
+
(
self
.
l
+
(
1
-
6
*
self
.
l
)
/
3
)
*
i
)
self
.
font
(
"12px Arial"
)
self
.
node_stack
=
[]
self
.
explored
=
{
node
for
node
in
self
.
utils
}
self
.
pruned
=
set
()
self
.
ab
=
{}
self
.
thick_lines
=
set
()
self
.
change_list
=
[]
self
.
draw_graph
()
self
.
stack_manager
=
self
.
stack_manager_gen
()
def
alpha_beta_search
(
self
,
node
):
game
=
self
.
game
player
=
game
.
to_move
(
node
)
# Functions used by alpha_beta
def
max_value
(
node
,
alpha
,
beta
):
if
game
.
terminal_test
(
node
):
self
.
change_list
.
append
((
'a'
,
node
))
self
.
change_list
.
append
((
'h'
,))
self
.
change_list
.
append
((
'p'
,))
return
game
.
utility
(
node
,
player
)
v
=
-
np
.
inf
self
.
change_list
.
append
((
'a'
,
node
))
self
.
change_list
.
append
((
'ab'
,
node
,
v
,
beta
))
self
.
change_list
.
append
((
'h'
,))
for
a
in
game
.
actions
(
node
):
min_val
=
min_value
(
game
.
result
(
node
,
a
),
alpha
,
beta
)
if
v
<
min_val
:
v
=
min_val
max_node
=
game
.
result
(
node
,
a
)
self
.
change_list
.
append
((
'ab'
,
node
,
v
,
beta
))
if
v
>=
beta
:
self
.
change_list
.
append
((
'h'
,))
self
.
pruned
.
add
(
node
)
break
alpha
=
max
(
alpha
,
v
)
self
.
utils
[
node
]
=
v
if
node
not
in
self
.
pruned
:
self
.
change_list
.
append
((
'l'
, (
node
,
max_node
-
3
*
node
-
1
)))
self
.
change_list
.
append
((
'e'
,
node
))
self
.
change_list
.
append
((
'p'
,))
self
.
change_list
.
append
((
'h'
,))
return
v
def
min_value
(
node
,
alpha
,
beta
):
if
game
.
terminal_test
(
node
):
self
.
change_list
.
append
((
'a'
,
node
))
self
.
change_list
.
append
((
'h'
,))
self
.
change_list
.
append
((
'p'
,))
return
game
.
utility
(
node
,
player
)
v
=
np
.
inf
self
.
change_list
.
append
((
'a'
,
node
))
self
.
change_list
.
append
((
'ab'
,
node
,
alpha
,
v
))
self
.
change_list
.
append
((
'h'
,))
for
a
in
game
.
actions
(
node
):
max_val
=
max_value
(
game
.
result
(
node
,
a
),
alpha
,
beta
)
if
v
>
max_val
:
v
=
max_val
min_node
=
game
.
result
(
node
,
a
)
self
.
change_list
.
append
((
'ab'
,
node
,
alpha
,
v
))
if
v
<=
alpha
:
self
.
change_list
.
append
((
'h'
,))
self
.
pruned
.
add
(
node
)
break
beta
=
min
(
beta
,
v
)
self
.
utils
[
node
]
=
v
if
node
not
in
self
.
pruned
:
self
.
change_list
.
append
((
'l'
, (
node
,
min_node
-
3
*
node
-
1
)))
self
.
change_list
.
append
((
'e'
,
node
))
self
.
change_list
.
append
((
'p'
,))
self
.
change_list
.
append
((
'h'
,))
return
v
return
max_value
(
node
,
-
np
.
inf
,
np
.
inf
)
def
stack_manager_gen
(
self
):
self
.
alpha_beta_search
(
0
)
for
change
in
self
.
change_list
:
if
change
[
0
]
==
'a'
:
self
.
node_stack
.
append
(
change
[
1
])
elif
change
[
0
]
==
'ab'
:
self
.
ab
[
change
[
1
]]
=
change
[
2
:]
elif
change
[
0
]
==
'e'
:
self
.
explored
.
add
(
change
[
1
])
elif
change
[
0
]
==
'h'
:
yield
elif
change
[
0
]
==
'l'
:
self
.
thick_lines
.
add
(
change
[
1
])
elif
change
[
0
]
==
'p'
:
self
.
node_stack
.
pop
()
def
mouse_click
(
self
,
x
,
y
):
try
:
self
.
stack_manager
.
send
(
None
)
except
StopIteration
:
pass
self
.
draw_graph
()
def
draw_graph
(
self
):
self
.
clear
()
# draw nodes
self
.
stroke
(
0
,
0
,
0
)
self
.
strokeWidth
(
1
)
# highlight for nodes in stack
for
node
in
self
.
node_stack
:
x
,
y
=
self
.
node_pos
[
node
]
# alpha > beta
if
node
not
in
self
.
explored
and
self
.
ab
[
node
][
0
]
>
self
.
ab
[
node
][
1
]:
self
.
fill
(
200
,
100
,
100
)
else
:
self
.
fill
(
200
,
200
,
0
)
self
.
rect_n
(
x
-
self
.
l
/
5
,
y
-
self
.
l
/
5
,
self
.
l
*
7
/
5
,
self
.
l
*
7
/
5
)
for
node
in
self
.
nodes
:
x
,
y
=
self
.
node_pos
[
node
]
if
node
in
self
.
explored
:
if
node
in
self
.
pruned
:
self
.
fill
(
50
,
50
,
50
)
else
:
self
.
fill
(
255
,
255
,
255
)
else
:
self
.
fill
(
200
,
200
,
200
)
self
.
rect_n
(
x
,
y
,
self
.
l
,
self
.
l
)
self
.
line_n
(
x
,
y
,
x
+
self
.
l
,
y
)
self
.
line_n
(
x
,
y
,
x
,
y
+
self
.
l
)
self
.
line_n
(
x
+
self
.
l
,
y
+
self
.
l
,
x
+
self
.
l
,
y
)
self
.
line_n
(
x
+
self
.
l
,
y
+
self
.
l
,
x
,
y
+
self
.
l
)
self
.
fill
(
0
,
0
,
0
)
if
node
in
self
.
explored
and
node
not
in
self
.
pruned
:
self
.
text_n
(
self
.
utils
[
node
],
x
+
self
.
l
/
10
,
y
+
self
.
l
*
9
/
10
)
# draw edges
for
i
in
range
(
13
):
x1
,
y1
=
self
.
node_pos
[
i
][
0
]
+
self
.
l
/
2
,
self
.
node_pos
[
i
][
1
]
+
self
.
l
for
j
in
range
(
3
):
x2
,
y2
=
self
.
node_pos
[
i
*
3
+
j
+
1
][
0
]
+
self
.
l
/
2
,
self
.
node_pos
[
i
*
3
+
j
+
1
][
1
]
if
i
in
[
1
,
2
,
3
]:
self
.
stroke
(
200
,
0
,
0
)
else
:
self
.
stroke
(
0
,
200
,
0
)
if
(
i
,
j
)
in
self
.
thick_lines
:
self
.
strokeWidth
(
3
)
else
:
self
.
strokeWidth
(
1
)
self
.
line_n
(
x1
,
y1
,
x2
,
y2
)
# display alpha and beta
for
node
in
self
.
node_stack
:
if
node
not
in
self
.
explored
:
x
,
y
=
self
.
node_pos
[
node
]
alpha
,
beta
=
self
.
ab
[
node
]
self
.
text_n
(
alpha
,
x
-
self
.
l
/
2
,
y
-
self
.
l
/
10
)
self
.
text_n
(
beta
,
x
+
self
.
l
,
y
-
self
.
l
/
10
)
self
.
update
()
class
Canvas_fol_bc_ask
(
Canvas
):
"""fol_bc_ask() on HTML canvas"""
def
__init__
(
self
,
varname
,
kb
,
query
,
width
=
800
,
height
=
600
,
cid
=
None
):
super
().
__init__
(
varname
,
width
,
height
,
cid
)
self
.
kb
=
kb
self
.
query
=
query
self
.
l
=
1
/
20
self
.
b
=
3
*
self
.
l
bc_out
=
list
(
self
.
fol_bc_ask
())
if
len
(
bc_out
)
is
0
:
self
.
valid
=
False
else
:
self
.
valid
=
True
graph
=
bc_out
[
0
][
0
][
0
]
s
=
bc_out
[
0
][
1
]
while
True
:
new_graph
=
subst
(
s
,
graph
)
if
graph
==
new_graph
:
break
graph
=
new_graph
self
.
make_table
(
graph
)
self
.
context
=
None
self
.
draw_table
()
def
fol_bc_ask
(
self
):
KB
=
self
.
kb
query
=
self
.
query
def
fol_bc_or
(
KB
,
goal
,
theta
):
for
rule
in
KB
.
fetch_rules_for_goal
(
goal
):
lhs
,
rhs
=
parse_definite_clause
(
standardize_variables
(
rule
))
for
theta1
in
fol_bc_and
(
KB
,
lhs
,
unify_mm
(
rhs
,
goal
,
theta
)):
yield
([(
goal
,
theta1
[
0
])],
theta1
[
1
])
def
fol_bc_and
(
KB
,
goals
,
theta
):
if
theta
is
None
:
pass
elif
not
goals
:
yield
([],
theta
)
else
:
first
,
rest
=
goals
[
0
],
goals
[
1
:]
for
theta1
in
fol_bc_or
(
KB
,
subst
(
theta
,
first
),
theta
):
for
theta2
in
fol_bc_and
(
KB
,
rest
,
theta1
[
1
]):
yield
(
theta1
[
0
]
+
theta2
[
0
],
theta2
[
1
])
return
fol_bc_or
(
KB
,
query
, {})
def
make_table
(
self
,
graph
):
table
=
[]
pos
=
{}
links
=
set
()
edges
=
set
()
def
dfs
(
node
,
depth
):
if
len
(
table
)
<=
depth
:
table
.
append
([])
pos
=
len
(
table
[
depth
])
table
[
depth
].
append
(
node
[
0
])
for
child
in
node
[
1
]:
child_id
=
dfs
(
child
,
depth
+
1
)
links
.
add
(((
depth
,
pos
),
child_id
))
return
(
depth
,
pos
)
dfs
(
graph
,
0
)
y_off
=
0.85
/
len
(
table
)
for
i
,
row
in
enumerate
(
table
):
x_off
=
0.95
/
len
(
row
)
for
j
,
node
in
enumerate
(
row
):
pos
[(
i
,
j
)]
=
(
0.025
+
j
*
x_off
+
(
x_off
-
self
.
b
)
/
2
,
0.025
+
i
*
y_off
+
(
y_off
-
self
.
l
)
/
2
)
for
p
,
c
in
links
:
x1
,
y1
=
pos
[
p
]
x2
,
y2
=
pos
[
c
]
edges
.
add
((
x1
+
self
.
b
/
2
,
y1
+
self
.
l
,
x2
+
self
.
b
/
2
,
y2
))
self
.
table
=
table
self
.
pos
=
pos
self
.
edges
=
edges
def
mouse_click
(
self
,
x
,
y
):
x
,
y
=
x
/
self
.
width
,
y
/
self
.
height
for
node
in
self
.
pos
:
xs
,
ys
=
self
.
pos
[
node
]
xe
,
ye
=
xs
+
self
.
b
,
ys
+
self
.
l
if
xs
<=
x
<=
xe
and
ys
<=
y
<=
ye
:
self
.
context
=
node
break
self
.
draw_table
()
def
draw_table
(
self
):
self
.
clear
()
self
.
strokeWidth
(
3
)
self
.
stroke
(
0
,
0
,
0
)
self
.
font
(
"12px Arial"
)
if
self
.
valid
:
# draw nodes
for
i
,
j
in
self
.
pos
:
x
,
y
=
self
.
pos
[(
i
,
j
)]
self
.
fill
(
200
,
200
,
200
)
self
.
rect_n
(
x
,
y
,
self
.
b
,
self
.
l
)
self
.
line_n
(
x
,
y
,
x
+
self
.
b
,
y
)
self
.
line_n
(
x
,
y
,
x
,
y
+
self
.
l
)
self
.
line_n
(
x
+
self
.
b
,
y
,
x
+
self
.
b
,
y
+
self
.
l
)
self
.
line_n
(
x
,
y
+
self
.
l
,
x
+
self
.
b
,
y
+
self
.
l
)
self
.
fill
(
0
,
0
,
0
)
self
.
text_n
(
self
.
table
[
i
][
j
],
x
+
0.01
,
y
+
self
.
l
-
0.01
)
# draw edges
for
x1
,
y1
,
x2
,
y2
in
self
.
edges
:
self
.
line_n
(
x1
,
y1
,
x2
,
y2
)
else
:
self
.
fill
(
255
,
0
,
0
)
self
.
rect_n
(
0
,
0
,
1
,
1
)
# text area
self
.
fill
(
255
,
255
,
255
)
self
.
rect_n
(
0
,
0.9
,
1
,
0.1
)
self
.
strokeWidth
(
5
)
self
.
stroke
(
0
,
0
,
0
)
self
.
line_n
(
0
,
0.9
,
1
,
0.9
)
self
.
font
(
"22px Arial"
)
self
.
fill
(
0
,
0
,
0
)
self
.
text_n
(
self
.
table
[
self
.
context
[
0
]][
self
.
context
[
1
]]
if
self
.
context
else
"Click for text"
,
0.025
,
0.975
)
self
.
update
()
############################################################################################################
##################### Functions to assist plotting in search.ipynb ####################
############################################################################################################
def
show_map
(
graph_data
,
node_colors
=
None
):
G
=
nx
.
Graph
(
graph_data
[
'graph_dict'
])
node_colors
=
node_colors
or
graph_data
[
'node_colors'
]
node_positions
=
graph_data
[
'node_positions'
]
node_label_pos
=
graph_data
[
'node_label_positions'
]
edge_weights
=
graph_data
[
'edge_weights'
]
# set the size of the plot
plt
.
figure
(
figsize
=
(
18
,
13
))
# draw the graph (both nodes and edges) with locations from romania_locations
nx
.
draw
(
G
,
pos
=
{
k
:
node_positions
[
k
]
for
k
in
G
.
nodes
()},
node_color
=
[
node_colors
[
node
]
for
node
in
G
.
nodes
()],
linewidths
=
0.3
,
edgecolors
=
'k'
)
# draw labels for nodes
node_label_handles
=
nx
.
draw_networkx_labels
(
G
,
pos
=
node_label_pos
,
font_size
=
14
)
# add a white bounding box behind the node labels
[
label
.
set_bbox
(
dict
(
facecolor
=
'white'
,
edgecolor
=
'none'
))
for
label
in
node_label_handles
.
values
()]
# add edge lables to the graph
nx
.
draw_networkx_edge_labels
(
G
,
pos
=
node_positions
,
edge_labels
=
edge_weights
,
font_size
=
14
)
# add a legend
white_circle
=
lines
.
Line2D
([], [],
color
=
"white"
,
marker
=
'o'
,
markersize
=
15
,
markerfacecolor
=
"white"
)
orange_circle
=
lines
.
Line2D
([], [],
color
=
"orange"
,
marker
=
'o'
,
markersize
=
15
,
markerfacecolor
=
"orange"
)
red_circle
=
lines
.
Line2D
([], [],
color
=
"red"
,
marker
=
'o'
,
markersize
=
15
,
markerfacecolor
=
"red"
)
gray_circle
=
lines
.
Line2D
([], [],
color
=
"gray"
,
marker
=
'o'
,
markersize
=
15
,
markerfacecolor
=
"gray"
)
green_circle
=
lines
.
Line2D
([], [],
color
=
"green"
,
marker
=
'o'
,
markersize
=
15
,
markerfacecolor
=
"green"
)
plt
.
legend
((
white_circle
,
orange_circle
,
red_circle
,
gray_circle
,
green_circle
),
(
'Un-explored'
,
'Frontier'
,
'Currently Exploring'
,
'Explored'
,
'Final Solution'
),
numpoints
=
1
,
prop
=
{
'size'
:
16
},
loc
=
(
.8
,
.75
))
# show the plot. No need to use in notebooks. nx.draw will show the graph itself.
plt
.
show
()
# helper functions for visualisations
def
final_path_colors
(
initial_node_colors
,
problem
,
solution
):
"Return a node_colors dict of the final path provided the problem and solution."
# get initial node colors
final_colors
=
dict
(
initial_node_colors
)
# color all the nodes in solution and starting node to green
final_colors
[
problem
.
initial
]
=
"green"
for
node
in
solution
:
final_colors
[
node
]
=
"green"
return
final_colors
def
display_visual
(
graph_data
,
user_input
,
algorithm
=
None
,
problem
=
None
):
initial_node_colors
=
graph_data
[
'node_colors'
]
if
user_input
==
False
:
def
slider_callback
(
iteration
):
# don't show graph for the first time running the cell calling this function
try
:
show_map
(
graph_data
,
node_colors
=
all_node_colors
[
iteration
])
except
:
pass
def
visualize_callback
(
Visualize
):
if
Visualize
is
True
:
button
.
value
=
False
global
all_node_colors
iterations
,
all_node_colors
,
node
=
algorithm
(
problem
)
solution
=
node
.
solution
()
all_node_colors
.
append
(
final_path_colors
(
all_node_colors
[
0
],
problem
,
solution
))
slider
.
max
=
len
(
all_node_colors
)
-
1
for
i
in
range
(
slider
.
max
+
1
):
slider
.
value
=
i
# time.sleep(.5)
slider
=
widgets
.
IntSlider
(
min
=
0
,
max
=
1
,
step
=
1
,
value
=
0
)
slider_visual
=
widgets
.
interactive
(
slider_callback
,
iteration
=
slider
)
display
(
slider_visual
)
button
=
widgets
.
ToggleButton
(
value
=
False
)
button_visual
=
widgets
.
interactive
(
visualize_callback
,
Visualize
=
button
)
display
(
button_visual
)
if
user_input
==
True
:
node_colors
=
dict
(
initial_node_colors
)
if
isinstance
(
algorithm
,
dict
):
assert
set
(
algorithm
.
keys
()).
issubset
({
"Breadth First Tree Search"
,
"Depth First Tree Search"
,
"Breadth First Search"
,
"Depth First Graph Search"
,
"Best First Graph Search"
,
"Uniform Cost Search"
,
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