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[
9
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T
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m
et
h
o
d
to
f
in
d
i
n
g
t
h
e
f
ir
s
t
s
o
lu
tio
n
a
n
d
f
i
n
d
in
g
s
o
m
e
s
o
l
u
tio
n
s
f
o
r
N
-
Qu
ee
n
s
p
r
o
b
lem
b
ased
o
n
g
e
n
etic
alg
o
r
ith
m
.
D
u
e
to
p
r
i
m
ar
y
s
tu
d
ies o
n
N
-
Q
u
ee
n
s
p
r
o
b
le
m
,
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
h
as e
x
ce
ed
ed
s
tan
d
ar
d
g
e
n
etic
alg
o
r
ith
m
.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
b
eg
in
s
w
it
h
p
air
o
f
in
d
i
v
id
u
al
s
as
i
n
itial
p
o
p
u
latio
n
o
b
tain
ed
f
r
o
m
t
w
o
s
u
b
p
r
o
p
le
m
s
,
w
h
ic
h
i
n
clu
d
es
p
o
ten
tial
s
o
l
u
tio
n
s
f
o
r
th
at
p
r
o
b
lem
.
E
v
er
y
in
d
i
v
id
u
al
o
f
p
o
p
u
latio
n
i
s
ca
lled
a
ch
r
o
m
o
s
o
m
e
,
ea
c
h
ch
r
o
m
o
s
o
m
e
m
a
tin
g
to
o
th
er
to
o
b
tain
f
ir
s
t
s
o
lu
t
io
n
,
ap
p
lied
s
ev
er
al
o
p
er
ato
r
s
f
o
r
g
en
eti
c
alg
o
r
ith
m
o
n
t
h
is
f
ir
s
t so
lu
t
io
n
to
o
b
tain
m
o
r
e
s
o
l
u
tio
n
s
.
Af
ter
i
n
tr
o
d
u
ctio
n
,
i
n
s
ec
o
n
d
p
ar
t o
f
th
i
s
p
ap
er
,
th
e
s
ta
n
d
ar
d
g
en
e
tic
al
g
o
r
ith
m
w
a
s
in
tr
o
d
u
ce
d
an
d
in
th
e
t
h
ir
d
p
ar
t,
t
h
e
m
o
d
if
ied
g
en
etic
a
lg
o
r
it
h
m
w
as
d
escr
ib
ed
.
I
n
t
h
e
f
o
u
r
t
h
p
ar
t,
t
h
e
p
r
o
p
o
s
ed
m
e
th
o
d
w
a
s
p
r
esen
ted
an
d
in
t
h
e
n
e
x
t
p
ar
t,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
w
a
s
ev
alu
ate
a
n
d
co
m
p
ar
e
it
w
i
t
h
s
ta
n
d
ar
d
g
en
etic
alg
o
r
ith
m
a
n
d
m
o
d
if
ied
g
e
n
eti
c
alg
o
r
ith
m
.
Fi
n
all
y
,
p
ar
t 6
,
co
n
tai
n
s
co
n
cl
u
d
i
n
g
r
e
m
ar
k
.
2.
ST
AND
ARD
G
E
N
E
T
I
C
A
L
G
O
RI
T
H
M
I
t
i
s
k
n
o
w
n
th
a
t
th
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
q
u
ee
n
s
th
at
ca
n
b
e
p
lace
d
o
n
an
n
x
n
ch
e
s
s
b
o
ar
d
,
s
o
th
at
n
o
t
w
o
attac
k
o
n
e
a
n
o
th
er
,
is
n
.
T
h
is
p
r
o
b
lem
co
n
ta
in
s
th
r
e
e
co
n
s
tr
ain
t
s
:
1
st
,
n
o
t
w
o
q
u
ee
n
s
ca
n
s
h
ar
e
a
s
a
m
e
co
lu
m
n
.
2
nd
,
n
o
t
w
o
q
u
ee
n
s
ca
n
s
h
ar
e
a
s
a
m
e
r
o
w
.
3
rd
,
n
o
t
w
o
q
u
ee
n
s
ca
n
s
h
ar
e
a
s
a
m
e
d
ia
g
o
n
al.
Dec
is
io
n
v
ar
iab
le
o
f
th
is
p
r
o
b
le
m
is
a
o
n
e
-
d
i
m
e
n
s
io
n
al
ar
r
ay
o
f
le
n
g
th
n
.
E
v
er
y
p
er
m
u
tatio
n
o
f
p
o
s
s
ib
le
v
alu
e
s
o
f
th
e
d
ec
is
i
o
n
v
ar
iab
les,
p
r
esen
ts
a
s
ta
te
o
f
s
ea
r
ch
-
s
p
ac
e
o
f
th
e
p
r
o
b
le
m
.
Def
in
i
tio
n
o
f
d
ec
is
io
n
v
ar
i
ab
le
s
at
is
f
ies t
h
e
f
ir
s
t c
o
n
s
tr
ai
n
t:
A
=
{(
Q
1
, Q
2
,
…,
Q
i
)
Q
i
(
1
,
2
,
…,
n
)
)
(
1
)
W
h
er
e
A
is
d
ec
is
io
n
v
ar
iab
le
an
d
Q
i
i
s
t
h
e
i
th
ce
ll
o
f
d
ec
is
i
o
n
v
ar
iab
le,
co
r
r
esp
o
n
d
in
g
i
th
co
lu
m
n
o
f
ch
es
s
b
o
ar
d
,
co
n
tain
i
n
g
th
e
r
o
w
o
f
q
u
ee
n
’
s
lo
ca
tio
n
,
th
e
co
m
p
lex
i
t
y
o
f
th
i
s
p
r
o
b
le
m
b
ec
o
m
e
s
O(
n
!
)
.
Seco
n
d
co
n
s
tr
ain
t is e
x
p
r
ess
ed
as f
o
llo
w
s
:
i,
j
{1
,
…,
n
},
Q
i
Q
j
(
2
)
T
h
ir
d
co
n
s
tr
ain
t is also
e
x
p
r
ess
ed
as f
o
llo
w
s
:
i,
j
{1
,
…,
n
},
|
−
|
|
i
−
j
|
(
3
)
A
f
it
n
es
s
f
u
n
c
tio
n
s
h
o
u
ld
r
et
u
r
n
h
i
g
h
er
v
al
u
es
f
o
r
b
etter
s
tates,
s
o
,
f
o
r
th
e
N
-
Q
u
ee
n
s
p
r
o
b
lem
w
e
u
s
e
th
e
n
u
m
b
er
o
f
n
o
n
a
tta
ck
in
g
p
air
s
o
f
q
u
ee
n
s
[((n
-
1)
x
n
)
/2
]
,
w
h
ic
h
h
as
a
v
al
u
e
o
f
4
5
f
o
r
a
s
o
lu
tio
n
1
0
-
q
u
ee
n
s
p
r
o
b
lem
.
T
h
is
ap
p
r
o
ac
h
lead
s
to
O(
n
)
c
o
m
p
le
x
it
y
o
f
th
e
f
i
tn
es
s
f
u
n
ct
io
n
.
Gen
etic
a
l
g
o
r
ith
m
i
s
m
e
m
b
er
o
f
co
m
p
u
tatio
n
al
m
et
h
o
d
’
s
f
a
m
il
y
w
h
ic
h
is
in
s
p
ir
ed
b
y
e
v
o
lu
ti
o
n
.
P
er
f
o
r
m
a
n
ce
o
f
g
en
et
ic
al
g
o
r
ith
m
i
s
f
lex
ib
le
en
o
u
g
h
to
m
a
k
e
it
ap
p
licab
le
t
o
a
w
id
e
r
an
g
e
o
f
p
r
o
b
le
m
s
,
s
u
ch
as
th
e
p
r
o
b
le
m
o
f
p
laci
n
g
n
q
u
ee
n
s
o
n
n
b
y
n
ch
es
s
b
o
ar
d
in
o
r
d
er
th
at
n
o
t
w
o
q
u
ee
n
s
ca
n
attac
k
ea
c
h
o
th
er
.
T
h
e
s
p
ac
e
s
o
lu
t
io
n
i
s
r
ep
r
esen
ted
as
t
h
e
p
o
p
u
latio
n
,
w
h
ic
h
co
n
s
is
ts
o
f
in
d
i
v
id
u
al
s
th
at
ar
e
ev
alu
a
ted
u
s
in
g
th
e
f
it
n
ess
f
u
n
ctio
n
r
ep
r
esen
tin
g
th
e
p
r
o
b
lem
b
ein
g
o
p
ti
m
ized
.
T
h
e
b
asic stru
ct
u
r
e
o
f
a
g
e
n
etic
al
g
o
r
ith
m
is
s
h
o
w
n
in
Fig
u
r
e
1.
I
n
ea
ch
iter
atio
n
(
g
en
er
at
io
n
)
o
f
alg
o
r
ith
m
,
a
ce
r
tain
n
u
m
b
er
o
f
b
est
-
r
an
k
i
n
g
i
n
d
iv
id
u
als
(
ch
r
o
m
o
s
o
m
e
s
)
is
s
elec
ted
in
th
e
m
a
n
n
er
to
cr
ea
te
n
e
w
b
ett
er
in
d
iv
id
u
als
(
ch
i
ld
r
en
)
.
Am
o
n
g
t
h
e
a
lg
o
r
it
h
m
s
th
at
ar
e
u
s
ed
f
o
r
s
elec
tio
n
o
p
e
r
atio
n
,
‘
r
o
u
let
te
w
h
ee
l’
a
n
d
‘
r
e
m
i
n
d
er
s
to
ch
as
tic
s
a
m
p
li
n
g
’
ar
e
m
o
r
e
s
ig
n
i
f
ica
n
t
[
1
2
]
.
I
n
th
is
p
ap
er
‘
r
o
u
lette
w
h
ee
l
’
tec
h
n
iq
u
e
is
u
s
ed
f
o
r
s
elec
tio
n
o
p
er
atio
n
,
w
h
er
e
ea
ch
i
n
d
iv
id
u
al
i
s
r
ep
r
esen
ted
b
y
a
s
p
ac
e
t
h
at
p
r
o
p
o
r
tio
n
ally
co
r
r
esp
o
n
d
s
to
its
f
it
n
ess
.
T
h
e
ch
ild
r
en
ar
e
cr
ea
ted
b
y
s
o
m
e
t
y
p
e
o
f
r
ec
o
m
b
in
atio
n
(
cr
o
s
s
o
v
er
)
an
d
th
e
y
r
ep
lace
th
e
w
o
r
s
t
-
r
an
k
ed
p
ar
t
o
f
th
e
p
o
p
u
latio
n
.
Af
ter
t
h
e
ch
ild
r
e
n
ar
e
o
b
tain
ed
,
a
m
u
tatio
n
o
p
er
ato
r
is
allo
w
ed
to
o
cc
u
r
an
d
t
h
e
n
ex
t
g
en
er
at
io
n
o
f
th
e
p
o
p
u
lat
io
n
is
cr
ea
ted
.
T
h
e
p
r
o
c
ess
is
iter
ated
u
n
til
t
h
e
ev
o
l
u
tio
n
co
n
d
itio
n
ter
m
in
ate
s
.
Gen
etic
al
g
o
r
ith
m
l
ik
e
m
a
n
y
o
f
h
e
u
r
is
tic
al
g
o
r
ith
m
s
,
d
o
es
n
o
t
g
u
ar
an
tee
o
f
f
i
n
d
i
n
g
s
o
lu
t
io
n
b
ec
au
s
e
ch
o
o
s
i
n
g
s
tar
tin
g
p
o
in
t
o
f
s
ea
r
ch
a
n
d
ta
k
in
g
s
tep
s
to
w
ar
d
s
o
l
u
tio
n
h
a
v
e
b
ee
n
ca
r
r
ied
o
u
t
r
an
d
o
m
l
y
.
I
n
p
r
o
b
le
m
s
l
ik
e
N
-
Qu
ee
n
s
t
h
at
its
s
tate
s
p
ac
e
g
r
o
w
s
ex
p
o
n
e
n
tiall
y
,
s
tar
tin
g
p
o
in
t
o
f
s
ea
r
c
h
is
d
ir
ec
tl
y
r
ela
te
d
to
th
e
p
r
o
b
ab
ilit
y
o
f
f
i
n
d
in
g
s
o
l
u
tio
n
[
3
]
[
1
0
]
[
1
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
AI
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
201
8
:
1
2
7
-
1
3
4
132
G
e
n
e
t
i
c
A
l
g
o
r
i
t
h
m
g
e
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e
r
a
t
e
r
a
n
d
o
m
i
n
i
t
i
a
l
p
o
p
u
l
a
t
i
o
n
e
v
a
l
u
a
t
e
t
h
e
f
i
t
n
e
ss o
f
e
a
c
h
i
n
d
i
v
i
d
u
a
l
i
n
t
h
e
p
o
p
u
l
a
t
i
o
n
r
e
p
e
a
t
se
l
e
c
t
b
e
st
-
r
a
n
k
i
n
g
i
n
d
i
v
i
d
u
a
l
s t
o
r
e
p
r
o
d
u
c
e
c
r
e
a
t
e
n
e
w
g
e
n
e
r
a
t
i
o
n
t
h
r
o
u
g
h
c
r
o
s
so
v
e
r
a
n
d
m
u
t
a
t
i
o
n
e
v
a
l
u
a
t
e
t
h
e
i
n
d
i
v
i
d
u
a
l
f
i
t
n
e
sse
s
u
n
t
i
l
(
t
e
r
mi
n
a
t
i
n
g
c
o
n
d
i
t
i
o
n
)
r
e
t
u
r
n
b
e
st
c
h
r
o
mo
so
me
Fig
u
r
e
1
.
Stru
ct
u
r
e
o
f
Ge
n
etic
A
l
g
o
r
ith
m
[
3
]
3.
M
O
DIFIE
D
G
E
NE
T
I
C
A
L
G
O
RI
T
H
M
Mo
d
if
ied
g
en
et
ic
alg
o
r
it
h
m
[
1
1
]
,
is
th
e
r
esu
l
t
o
f
co
llab
o
r
atio
n
b
et
w
ee
n
g
e
n
etic
alg
o
r
ith
m
a
n
d
m
i
n
i
m
al
co
n
f
licts
al
g
o
r
ith
m
.
Min
i
m
al
co
n
f
lict
s
alg
o
r
it
h
m
i
s
lo
o
k
in
g
at
ad
j
ac
en
t
s
p
ac
e
o
f
ea
ch
ca
n
d
id
ate
to
p
r
o
b
le
m
’
s
s
o
l
u
tio
n
an
d
tr
y
in
g
to
r
ep
lace
cu
r
r
en
t
ca
n
d
id
ate
b
y
o
n
e
o
f
its
n
ei
g
h
b
o
r
s
w
h
ic
h
h
as
a
b
etter
f
it
n
ess
-
v
alu
e.
I
n
F
i
g
u
r
e
2
,
g
r
a
y
ar
ea
s
r
ep
r
esen
t
m
o
d
if
ied
s
ec
tio
n
s
o
f
s
ta
n
d
ar
d
g
en
etic
al
g
o
r
it
h
m
.
Min
i
m
al
co
n
f
lict
s
o
p
er
ato
r
ap
p
lied
t
o
ea
ch
ca
n
d
id
ates a
f
ter
cr
o
s
s
o
v
er
an
d
m
u
ta
tio
n
.
Fig
u
r
e
2
.
Flo
w
c
h
ar
t
o
f
Mo
d
if
i
ed
Gen
etic
A
lg
o
r
it
h
m
4.
T
H
E
P
RO
P
O
SE
D
AL
G
O
RI
T
H
M
As
it
is
m
en
t
io
n
ed
b
ef
o
r
e,
in
N
-
Q
u
ee
n
s
p
r
o
b
lem
ea
c
h
p
er
m
u
tatio
n
o
f
p
o
s
s
ib
le
v
al
u
es
o
f
th
e
d
ec
is
io
n
v
ar
iab
le
ca
n
b
e
a
ca
n
d
id
ate
to
p
r
o
b
lem
’
s
s
o
l
u
tio
n
.
T
h
es
e
ca
n
d
id
ates
ar
e
also
ca
lled
"c
h
r
o
m
o
s
o
m
e
s
"
.
A
co
llectio
n
o
f
ca
n
d
id
ates a
r
e
ca
lled
"
p
o
p
u
latio
n
"
.
Gen
etic
al
g
o
r
ith
m
is
co
n
s
is
ted
o
f
s
e
v
er
al
o
p
er
ato
r
s
to
m
o
d
if
y
p
o
p
u
latio
n
in
s
e
v
er
al
iter
atio
n
s
an
d
d
u
r
in
g
th
e
s
e
iter
atio
n
s
n
e
w
c
h
r
o
m
o
s
o
m
e
s
m
a
y
b
e
s
o
lu
t
io
n
s
ar
e
c
r
ea
ted
.
I
n
th
is
p
ar
t,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
b
ased
o
n
g
en
etic
al
g
o
r
ith
m
is
in
tr
o
d
u
ce
d
to
tr
y
i
n
g
in
cr
ea
s
e
alg
o
r
ith
m
’
s
s
p
ee
d
o
f
r
ea
ch
i
n
g
to
f
ir
s
t
s
o
lu
t
io
n
with
s
i
m
p
lest
s
i
n
g
le
i
ter
atio
n
;
a
ls
o
it
ca
n
o
b
tain
m
o
r
e
s
o
lu
tio
n
s
ap
p
l
y
i
n
g
s
e
v
er
al
o
p
er
ato
r
s
f
o
r
g
en
etic
a
lg
o
r
it
h
m
o
n
t
h
e
f
ir
s
t so
lu
tio
n
as
s
h
o
wn
in
t
h
e
f
o
llo
w
in
g
s
tate
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
S
o
lvin
g
N
-
Qu
ee
n
s
P
r
o
b
lem
U
s
in
g
S
u
b
p
r
o
b
lems b
a
s
ed
o
n
G
en
etic
A
lg
o
r
ith
m
(
I
s
ma
il A
.
Hu
meid
)
133
4
.
1
.
F
irst
S
o
lutio
n o
f
N
-
Q
ueens
P
ro
ble
m
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
b
tain
s
th
e
f
ir
s
t so
l
u
tio
n
o
f
N
-
Qu
ee
n
s
p
r
o
b
lem
u
s
in
g
t
h
e
f
o
llo
w
i
n
g
s
t
ep
s
.
4
.
1
.
1
.
G
ener
a
t
ing
S
ub
pro
ble
m
s
o
f
N
-
Q
ueen
s
T
h
e
s
u
b
p
r
o
b
lem
s
i
n
N
-
Q
u
ee
n
s
o
b
tain
b
y
c
h
o
ices
t
w
o
s
u
b
s
e
ts
o
f
d
ec
is
io
n
v
ar
iab
le
"
A
"
in
E
q
u
atio
n
(
1
)
.
First
s
u
b
s
et
s
tar
t
f
r
o
m
Q
1
to
Q
Cbest
,
w
h
er
e
C
b
es
t
=
f
lo
o
r
(
n
/2
)
ca
lled
"
lo
ca
l
b
est
cr
o
s
s
o
v
er
"
w
h
ic
h
h
a
s
b
ee
n
f
o
u
n
d
to
y
ield
s
at
is
f
ac
to
r
y
r
es
u
lts
in
a
n
u
m
b
er
o
f
e
x
p
er
i
m
e
n
ts
a
n
d
co
m
p
u
tatio
n
al
e
x
p
en
s
es
s
i
g
n
if
ica
n
tl
y
,
t
h
e
o
th
er
s
u
b
s
et
s
tar
t f
r
o
m
[
Q
C
best+
1
]
to
Q
n
,
as sh
o
w
n
i
n
F
i
g
u
r
e
3
(
a)
.
Fig
u
r
e
3
(
b
)
s
h
o
w
s
t
w
o
s
u
b
p
r
o
b
le
m
s
o
f
t
h
e
1
0
-
q
u
ee
n
s
.
T
h
e
C
b
est
=
5
s
o
th
e
f
ir
s
t
s
u
b
p
r
o
b
lem
in
v
o
lv
e
s
g
etti
n
g
p
o
s
itio
n
o
f
f
i
v
e
q
u
ee
n
s
Q
1
,
Q
2
,
Q
3
,
Q
4
a
n
d
Q
5
i
n
t
o
th
eir
co
r
r
ec
t
p
o
s
itio
n
s
.
T
h
e
o
th
er
s
u
b
p
r
o
b
le
m
in
v
o
l
v
es
g
et
tin
g
p
o
s
it
io
n
o
f
f
i
v
e
q
u
ee
n
s
Q
6
,
Q
7
,
Q
8
,
Q
9
a
n
d
Q
10
i
n
to
t
h
eir
co
r
r
ec
t
p
o
s
itio
n
s
.
(
No
tice
th
at
th
e
lo
ca
tio
n
s
o
f
th
e
o
t
h
er
q
u
ee
n
s
in
t
w
o
s
u
b
p
r
o
p
b
lem
s
w
h
ich
s
y
m
b
o
lic
*
ar
e
ir
r
ele
v
an
t
f
o
r
th
e
p
u
r
p
o
s
es
o
f
s
o
lv
i
n
g
p
r
o
b
le
m
a
n
d
m
o
v
e
s
o
f
th
o
s
e
q
u
ee
n
s
d
o
n
'
t
co
u
n
t
to
w
ar
d
s
th
e
co
s
t.)
.
C
lear
l
y
,
t
h
e
co
s
t
o
f
t
h
e
s
o
l
u
tio
n
o
f
ea
ch
s
u
b
p
r
o
b
lem
is
a
lo
w
er
b
o
u
n
d
o
n
th
e
co
s
t
o
f
t
h
e
co
m
p
lete
p
r
o
b
le
m
.
T
h
e
s
o
l
u
tio
n
ca
n
f
i
n
d
f
o
r
e
v
e
r
y
p
o
s
s
ib
le
s
u
b
p
r
o
b
le
m
i
n
s
ta
n
ce
-
in
t
h
e
e
x
a
m
p
le,
e
v
er
y
p
o
s
s
ib
l
e
co
n
f
i
g
u
r
atio
n
o
f
t
h
e
f
iv
e
q
u
ee
n
s
,
a
s
d
escr
ib
e
in
th
e
f
o
llo
w
i
n
g
s
tep
.
(
a)
(
b
)
Fig
u
r
e
3
.
T
h
e
T
w
o
S
u
b
s
ets o
f
Dec
is
io
n
Var
iab
le
o
f
t
h
e
(
A
)
N
-
Q
u
ee
n
s
an
d
(
B
)
1
0
-
Qu
ee
n
s
4
.
1
.
2
.
Co
nfig
ura
t
io
n n
Q
ueens
O
nto
S
ub
pro
b
le
m
s
Af
ter
g
en
er
ated
t
w
o
s
u
b
p
r
o
b
le
m
s
o
f
N
-
Q
u
ee
n
s
,
t
h
e
s
o
l
u
tio
n
ca
n
f
in
d
f
o
r
ev
er
y
p
o
s
s
ib
le
s
u
b
p
r
o
b
le
m
in
s
ta
n
ce
.
T
h
e
co
n
f
i
g
u
r
atio
n
n
q
u
ee
n
s
o
n
to
t
w
o
s
u
b
p
r
o
b
lem
s
ca
n
cr
ea
te
a
p
air
o
f
c
h
r
o
m
o
s
o
m
e
s
t
h
at
ca
n
m
ate
to
o
b
tain
th
e
f
ir
s
t so
lu
tio
n
as
d
escr
ib
e
in
th
e
f
o
llo
w
i
n
g
t
w
o
c
ases
:
Ca
s
e
1
:
T
h
e
p
air
o
f
th
e
ch
r
o
m
o
s
o
m
e
s
t
h
at
co
n
f
ig
u
r
ed
in
t
h
e
m
a
n
n
er
as
F
i
g
u
r
e
4
w
h
er
e
n
u
m
b
er
o
f
q
u
ee
n
s
(
n
)
=
k
x
6
+
L
;
f
o
r
k
=
0
,
1
,
2
,
3
,
…
;
Fig
u
r
e
4
(
a)
s
h
o
w
s
t
h
e
t
w
o
c
h
r
o
m
o
s
o
m
es
w
h
er
e
L
=
8
,
in
th
e
f
ir
s
t
c
h
r
o
m
o
s
o
m
e
:
Q
1
=
C
b
est
,
Q
2
=
C
b
est
+2
,
Q
3
=
C
b
est+4
,
Q
4
=
C
b
est+6
,
…;
an
d
in
t
h
e
o
th
er
ch
r
o
m
o
s
o
m
e
:
Q
n
=
C
b
est+1
,
Q
n
-
1
=
C
b
est
-
1
,
Q
n
-
2
=
C
b
est
-
3
,
Q
n
-
3
=
C
b
est
-
5
,
…
;
f
ig
u
r
e
4
(
b
)
s
h
o
w
s
th
e
t
w
o
ch
r
o
m
o
s
o
m
e
s
w
h
er
e
L
=
9
,
i
n
t
h
e
f
ir
s
t
c
h
r
o
m
o
s
o
m
e:
Q
1
=
C
b
es
t+1
,
Q
2
=
C
b
es
t+3
,
Q
3
=
C
b
est+5
,
Q
4
=
C
b
est+7
,
…;
a
n
d
in
t
h
e
o
th
er
ch
r
o
m
o
s
o
m
e
Q
n
=
1
,
Q
n
-
1
=
C
b
est+2
,
Q
n
-
2
=
C
b
es
t,
Q
n
-
3
=
C
b
est
-
2
,
Q
n
-
4
=
C
b
est
-
4
,
…
C
b
e
st
C
b
e
st
+2
C
b
e
st
+4
C
b
e
st
+6
…
*
*
*
*
…
…
*
*
*
*
…
C
be
s
t
-
5
C
b
e
st
-
3
C
b
e
st
-
1
C
b
e
st
+1
C
b
e
st
+1
C
b
e
st
+3
C
b
e
st
+5
C
b
e
st
+7
…
*
*
*
*
*
…
…
*
*
*
*
…
C
b
e
st
-
4
C
b
e
st
-
2
C
b
e
st
C
b
e
st
+2
1
Fig
u
r
e
4
.
1
-
P
o
in
t Cro
s
s
o
v
er
(
C
b
est)
C
u
ts
P
air
o
f
t
h
e
C
h
r
o
m
o
s
o
m
es
f
r
o
m
‘
B
r
ea
k
P
o
in
t
’
,
W
h
en
N
=
K
X
6
+
L
; Fo
r
K
=
0
,
1
,
2
,
3
,
…; A
)
L
=
8
.
B
)
L
=
9
Ca
s
e
2
:
T
h
e
p
air
o
f
th
e
c
h
r
o
m
o
s
o
m
es
t
h
at
co
n
f
ig
u
r
ed
in
th
e
m
an
n
er
a
s
F
i
g
u
r
e
5
w
h
er
e
n
u
m
b
er
o
f
q
u
ee
n
s
(
n
)
k
x
6
+
L
;
f
o
r
k
=
0
,
1
,
2
,
3
,
…
.
Fig
u
r
e
5
s
h
o
w
s
t
h
e
t
w
o
ch
r
o
m
o
s
o
m
e
s
,
in
th
e
f
ir
s
t
c
h
r
o
m
o
s
o
m
e:
Q
1
=
n
-
1
,
Q
2
=
n
-
3
,
Q
3
=
n
-
5
,
Q
4
=
n
-
7
,
…;
an
d
in
th
e
o
t
h
er
ch
r
o
m
o
s
o
m
e
Q
Cbe
st+
1
=
n
,
Q
C
best+
2
=
n
-
2
,
Q
Cbest+
3
=
n
-
4
,
Q
Cbest+
4
=
n
-
6
,
…
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
AI
Vo
l.
7
,
No
.
3
,
Sep
tem
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ize
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le
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e
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ed
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et
h
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i
n
4
.
1
r
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ch
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to
f
ir
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t
s
o
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tio
n
u
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i
n
g
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ati
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t
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e
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u
t
a
n
y
iter
atio
n
a
n
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th
e
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r
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ed
m
et
h
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d
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in
4
.
2
r
ea
ch
e
s
to
s
o
l
u
tio
n
s
u
s
i
n
g
s
i
m
p
le
i
ter
atio
n
s
(
m
u
tatio
n
o
p
er
atio
n
)
,
f
in
all
y
i
n
4
.
3
r
ea
ch
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to
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o
l
u
tio
n
s
u
s
i
n
g
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a
ve
r
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mb
er
o
f
iter
a
tio
n
s
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e
s
a
m
e
as
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th
e
g
en
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ith
m
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it
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a
m
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ato
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e
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eth
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d
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in
4
.
3
u
s
e
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tate
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ac
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less
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h
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g
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o
r
it
h
m
,
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o
t
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e
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ed
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et
h
o
d
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in
4
.
3
h
as less
s
p
ac
e
co
m
p
le
x
it
y
.
I
n
[
1
1
]
,
h
er
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d
h
is
co
lleag
u
e
r
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l
ts
w
it
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m
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ar
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et
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ied
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ith
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ith
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ith
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ith
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ith
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ize
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ess
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ith
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e
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ve
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e
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r
ith
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s
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m
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les
2
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n
d
3
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o
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at
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e
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t
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ed
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eth
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in
4
.
3
b
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e
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icien
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et
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.
2
.
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ize
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ail
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4
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3
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Fro
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ased
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in
i
m
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l c
o
n
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licts
o
p
er
ato
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
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AI
Vo
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7
,
No
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3
,
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b
er
201
8
:
1
2
7
-
1
3
4
136
T
ab
le
1
.
First
So
lu
ti
o
n
A
cc
o
r
d
in
g
to
4
.
1
in
th
e
"
P
r
o
p
o
s
ed
Me
th
o
d
"
n
f
i
r
st
so
l
u
t
i
o
n
o
f
N
-
Q
u
e
e
n
s
p
r
o
b
l
e
m
n
=
4
3
1
4
2
n
=
5
4
2
5
3
1
n
=
6
5
3
1
6
4
2
n
=
7
6
4
2
7
5
3
1
n
=
8
4
6
8
2
7
1
3
5
n
=
9
5
7
9
3
8
2
4
6
1
n
=
10
9
7
5
3
1
1
0
8
6
4
2
n
=
11
1
0
8
6
4
2
1
1
9
7
5
3
1
n
=
12
1
1
9
7
5
3
1
1
2
1
0
8
6
4
2
n
=
13
1
2
1
0
8
6
4
2
1
3
1
1
9
7
5
3
1
n
=
14
7
9
1
1
1
3
1
3
5
1
0
1
2
1
4
2
4
6
8
n
=
15
8
1
0
1
2
1
4
2
4
6
1
1
1
3
1
5
3
5
7
9
1
n
=
16
1
5
1
3
1
1
9
7
5
3
1
1
6
1
4
1
2
1
0
8
6
4
2
T
ab
le
2
.
C
o
m
p
ar
in
g
t
h
e
"
av
er
ag
e
n
u
m
b
er
o
f
s
o
lu
tio
n
s
"
in
2
0
r
u
n
s
ac
co
r
d
in
g
to
4
.
1
.
2
(
ca
s
e
1
)
o
f
th
e
"
s
tan
d
ar
d
g
en
et
ic
alg
o
r
it
h
m
"
an
d
"
p
r
o
p
o
s
ed
m
et
h
o
d
"
4
.
2
,
4
.
3
n
A
v
e
r
a
g
e
N
o
.
o
f
S
o
l
u
t
i
o
n
s i
n
(GA)
A
v
e
r
a
g
e
N
o
.
o
f
S
o
l
u
t
i
o
n
s i
n
P
r
o
p
o
se
d
me
t
h
o
d
(
4
.
3
)
N
o
.
o
f
S
o
l
u
t
i
o
n
s
i
n
P
r
o
p
o
se
d
me
t
h
o
d
(
4
.
2
)
n
=
8
5
7
.
7
1
3
.
1
1
n
=
9
6
7
.
3
1
3
.
6
1
n
=
14
0
.
5
3
.
7
2
n
=
15
0
.
3
5
3
n
=
20
-
6
5
n
=
21
-
6
4
n
=
26
-
6
4
n
=
27
-
4
3
n
=
32
-
11
11
n
=
33
-
8
10
n
=
38
-
12
12
n
=
39
-
10
12
n
=
44
-
10
11
n
=
45
-
13
13
T
ab
le
3
.
C
o
m
p
ar
in
g
t
h
e
"
A
v
er
ag
e
Nu
m
b
er
o
f
So
l
u
tio
n
s
"
in
2
0
R
u
n
s
A
cc
o
r
d
in
g
T
o
4
.
1
.
2
(
C
ase
2
)
o
f
th
e
"
Stan
d
ar
d
Gen
etic
A
l
g
o
r
ith
m
"
an
d
"P
r
o
p
o
s
ed
Me
th
o
d
"
4
.
2
,
4
.
3
n
A
v
e
r
a
g
e
N
o
.
o
f
S
o
l
u
t
i
o
n
s i
n
(GA)
A
v
e
r
a
g
e
N
o
.
o
f
S
o
l
u
t
i
o
n
s i
n
P
r
o
p
o
se
d
me
t
h
o
d
(
4
.
3
)
N
o
.
o
f
S
o
l
u
t
i
o
n
s
i
n
P
r
o
p
o
se
d
me
t
h
o
d
(
4
.
2
)
n
=
4
2
2
1
n
=
5
9
.
4
2
.
9
1
n
=
6
4
2
.
1
1
n
=
7
38
5
.
3
1
n
=
10
2
0
.
1
1
1
.
3
3
n
=
11
6
.
5
8
.
8
3
n
=
12
1
.
3
6
.
5
3
n
=
13
1
.
5
7
4
n
=
16
-
4
.
8
3
n
=
17
-
5
.
6
4
n
=
1
8
-
6
4
n
=
34
-
17
16
n
=
36
-
1
9
.
3
16
n
=
40
-
21
17
n
=
42
-
24
21
n
=
46
-
31
23
n
=
48
-
32
29
n
=
50
-
13
13
6.
CO
NCLU
SI
O
N
C
o
n
s
id
er
in
g
th
a
t
s
ta
n
d
ar
d
g
en
etic
alg
o
r
it
h
m
an
d
m
o
d
if
ied
g
en
etic
al
g
o
r
ith
m
ar
e
n
o
t
ef
f
ic
i
en
t
e
n
o
u
g
h
in
s
o
l
v
in
g
lar
g
e
s
tate
s
p
ac
es
o
f
N
-
Qu
ee
n
s
p
r
o
b
lem
as
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
T
h
is
p
ap
er
,
p
r
esen
ted
a
p
r
o
p
o
s
ed
m
et
h
o
d
to
atte
m
p
t
r
eso
lv
e
w
e
ak
n
e
s
s
o
f
th
e
s
e
al
g
o
r
ith
m
s
u
s
in
g
s
u
b
p
r
o
b
lem
s
o
f
N
-
Q
u
ee
n
s
,
w
h
ic
h
o
b
tain
t
h
e
in
itial
p
o
p
u
latio
n
o
f
g
e
n
etic
a
lg
o
r
ith
m
.
T
h
is
ca
n
ac
ce
ler
ate
g
en
et
ic
alg
o
r
it
h
m
i
n
o
r
d
er
to
f
i
n
d
th
e
p
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o
b
lem
’
s
s
o
lu
tio
n
,
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u
ick
er
.
Als
o
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
ca
n
h
elp
g
en
eti
c
alg
o
r
ith
m
to
av
o
id
co
m
p
lex
i
t
y
o
f
iter
atio
n
s
a
n
d
r
ed
u
cin
g
it.
A
cc
o
r
d
in
g
to
t
h
e
r
esu
lts
w
h
ic
h
ar
e
d
ec
lar
ed
in
s
ec
tio
n
5
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
all
s
tates
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
S
o
lvin
g
N
-
Qu
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n
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G
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A
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r
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(
I
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Hu
meid
)
137
i
m
p
r
o
v
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e
f
f
ic
ien
c
y
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f
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t
an
d
ar
d
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r
ith
m
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m
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ied
g
en
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tic
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r
ith
m
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u
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p
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.
RE
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NC
E
S
[1
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Hu
,
R.
C.
Eb
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rh
a
rt,
Y.
S
h
i,
“
S
wa
rm
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telli
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in
g
s o
f
th
e
IEE
E
S
w
a
r
m
In
telli
g
e
n
c
e
S
y
m
p
o
siu
m
(S
IS
'
0
3
),
p
p
.
2
4
3
-
2
4
6
,
In
d
ian
a
p
o
li
s,
I
n
d
,
USA
,
A
p
ril
2
0
0
3
.
[2
]
S
tu
a
rt
j.
Ru
ss
e
ll
,
P
e
ter No
rv
ig
,
“
Arti
fi
c
ia
l
I
n
telli
g
e
n
c
e
A
M
o
d
e
rn
Ap
p
ro
a
c
h
”,
(
3
rd
E
d
it
io
n
),
P
re
n
ti
c
e
H
a
ll
,
2
0
1
0
.
[3
]
I.
M
a
rti
n
jak
,
M
.
G
o
lu
b
,
“
Co
mp
a
riso
n
o
f
He
u
ristic
Al
g
o
ri
th
ms
fo
r
th
e
N
-
Qu
e
e
n
Pro
b
lem
”
,
P
r
o
c
e
e
d
in
g
s
o
f
th
e
2
9
th
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
I
n
f
o
rm
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
In
terfa
c
e
s
,
IT
I
2
0
0
7
,
p
p
.
7
5
9
-
7
6
4
,
Ca
v
tat,
C
ro
a
ti
a
,
Ju
n
e
2
5
-
2
8
,
2
0
0
7
.
[4
]
K.
D.
Cra
wf
o
rd
,
“
S
o
lvin
g
th
e
N
-
Qu
e
e
n
s
Pro
b
lem
Us
in
g
Ge
n
e
ti
c
Al
g
o
rit
h
ms
”
,
In
P
ro
c
e
e
d
in
g
s
A
CM
/S
I
GA
P
P
S
y
m
p
o
siu
m
o
n
A
p
p
li
e
d
Co
m
p
u
ti
n
g
,
Ka
n
sa
s
Cit
y
,
p
p
.
1
0
3
9
-
1
0
4
7
,
1
9
9
2
.
[5
]
S
.
Kh
a
n
,
M
.
Bi
lal,
M
.
S
h
a
rif
,
M
.
S
a
ji
d
,
R.
Ba
ig
,
“
S
o
lu
t
io
n
o
f
n
-
Qu
e
e
n
Pro
b
lem
Us
in
g
A
CO
”
M
u
lt
it
o
p
ic
Co
n
f
e
re
n
c
e
,
2
0
0
9
.
INM
IC
2
0
0
9
.
I
EE
E
1
3
th
In
tern
a
ti
o
n
a
l,
Isla
m
a
b
a
d
,
p
p
.
1
-
5
,
1
4
-
1
5
De
c
.
2
0
0
9
.
[6
]
J.
T
u
rn
e
r,
A
.
Ho
m
a
i
f
a
r,
S
.
A
li
,
“
Th
e
n
-
q
u
e
e
n
s p
r
o
b
lem
a
n
d
g
e
n
e
ti
c
a
lg
o
rit
h
m
s”
,
in
IEE
E
,
p
p
.
2
6
2
-
2
6
7
,
1
9
9
2
.
[7
]
M
.
Bo
ii
k
o
v
ic,
M
.
G
o
lu
b
,
L
.
Bu
d
in
,
“
S
o
lv
i
n
g
n
-
Qu
e
e
n
p
r
o
b
lem
u
sin
g
g
lo
b
a
l
p
a
ra
ll
e
l
g
e
n
e
ti
c
a
lg
o
rit
h
m
”
,
in
IEE
E
,
p
p
.
1
0
4
-
1
0
7
,
v
o
l.
2
,
2
0
0
3
.
[8
]
A
.
M
.
T
u
rk
y
,
M
.
S
.
A
h
m
a
d
“
Us
in
g
G
e
n
e
ti
c
A
lg
o
rit
h
m
f
o
r
S
o
lv
in
g
N
-
Qu
e
e
n
s
P
r
o
b
lem
”
,
in
IEE
E
,
p
p
.
745
-
7
4
7
,
2
0
1
0
.
[9
]
A
.
Am
o
o
sh
a
h
i,
M
.
J
o
u
d
a
k
i,
M
.
I
m
a
n
i,
N.
M
a
z
h
a
ri,
“
P
re
se
n
ti
n
g
a
n
e
w
m
e
th
o
d
b
a
se
d
o
n
c
o
o
p
e
ra
ti
v
e
P
S
O
to
so
lv
e
p
e
rm
u
tatio
n
p
r
o
b
lem
s: A
c
a
se
stu
d
y
o
f
n
-
q
u
e
e
n
p
r
o
b
lem
”
,
in
IEE
E
,
p
p
.
2
1
8
-
2
2
2
,
2
0
1
1
.
[1
0
]
R.
G
.
S
h
a
rm
a
,
B.
Ke
sw
a
n
i,
“
i
m
p
lem
e
n
tatio
n
o
f
n
-
q
u
e
e
n
s
p
u
z
z
le
u
sin
g
m
e
ta
-
h
e
u
risti
c
a
lg
o
rit
h
m
(c
u
c
k
o
o
se
a
rc
h
)”
,
in
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
L
a
tes
t
T
re
n
d
s i
n
En
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
y
,
p
p
.
3
4
3
-
3
4
7
,
v
o
l
.
2
,
2
0
1
3
.
[1
1
]
J.
E.
A
.
h
e
ris,
M
.
A
.
Os
k
o
e
i,
“
M
o
d
if
ied
G
e
n
e
ti
c
A
lg
o
rit
h
m
f
o
r
S
o
lv
in
g
n
-
Qu
e
e
n
s
P
ro
b
lem
”
,
in
IEE
E
,
2
0
1
4
.
[1
2
]
“
D.
W
h
it
le
y
,
“
a
g
e
n
e
ti
c
a
lg
o
rit
h
m
tu
t
o
rial”
,
sta
t
isti
c
s a
n
d
c
o
m
p
u
t
in
g
,
p
p
.
6
5
-
8
5
,
1
9
9
4
”
.
[1
3
]
J.
Be
ll
,
B.
S
tev
e
n
s,
“
A
su
rv
e
y
o
f
k
n
o
w
n
re
su
lt
s
a
n
d
re
se
a
rc
h
a
re
a
s
f
o
r
n
-
q
u
e
e
n
s”
,
Disc
re
te
M
a
th
e
ma
ti
c
s
3
0
9
,
p
p
.
1
-
3
1
,
2
0
0
9
.
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