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630
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co
n
ce
p
t
is
to
an
aly
ze
u
s
er
s
’
b
eh
av
io
r
s
f
r
o
m
s
elec
tin
g
o
r
s
co
r
in
g
an
d
to
s
ea
r
ch
f
o
r
s
im
ilar
u
s
er
s
’
f
av
o
r
ites
s
o
as
to
p
r
ed
ict
wh
ich
m
en
u
s
u
s
er
s
will
p
r
ef
er
[
9
]
,
[
1
0
]
.
Af
ter
th
at,
s
im
ilar
ity
am
o
n
g
u
s
er
s
is
m
ea
s
u
r
ed
[
1
1
]
.
Ho
wev
er
,
p
r
ev
io
u
s
s
tu
d
ies
wer
e
co
n
ce
r
n
ed
with
th
e
f
o
o
d
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
f
o
r
g
en
er
al
p
eo
p
le,
as
o
f
to
d
ay
ea
ch
co
n
s
u
m
er
r
eq
u
ir
es
d
if
f
er
en
t
m
en
u
s
in
ac
co
r
d
an
ce
with
th
eir
r
estrictio
n
s
s
u
ch
as
weig
h
t
an
d
u
n
d
er
ly
in
g
d
is
ea
s
es.
As
a
co
n
s
eq
u
en
ce
,
to
ac
h
iev
e
th
e
h
ig
h
est
ef
f
icien
cy
in
r
ec
o
m
m
en
d
atio
n
ac
co
r
d
in
g
to
r
eq
u
ir
em
en
ts
o
r
r
estrictio
n
s
o
f
ea
ch
u
s
er
,
o
th
er
tech
n
iq
u
es
m
u
s
t
b
e
tak
en
in
to
co
n
s
id
er
atio
n
.
I
n
th
is
r
eg
ar
d
,
it
is
co
n
s
is
ten
t
with
Gao
[
1
2
]
wh
o
co
n
d
u
cted
a
s
tu
d
y
o
n
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
an
d
f
o
u
n
d
th
at
k
n
ap
s
ac
k
tech
n
iq
u
e
was
s
u
itab
le
f
o
r
p
r
o
d
u
ct
r
ec
o
m
m
en
d
atio
n
u
n
d
er
o
r
g
an
izatio
n
al
r
estrictio
n
s
s
o
as
to
b
e
a
s
tr
ateg
y
f
o
r
g
en
er
atin
g
th
e
h
ig
h
est
r
ev
en
u
e.
T
h
e
k
n
ap
s
ac
k
tech
n
iq
u
e
is
ab
le
to
r
esp
o
n
d
to
o
r
g
an
izatio
n
al
r
eq
u
ir
em
en
ts
an
d
in
th
e
m
ea
n
tim
e
it
ca
n
m
ee
t
u
s
er
s
’
s
atis
f
ac
tio
n
.
T
h
er
ef
o
r
e,
th
is
r
esear
ch
s
tu
d
y
ap
p
lied
th
e
co
llab
o
r
ativ
e
f
ilter
in
g
tech
n
iq
u
e
f
o
r
ca
lcu
latin
g
n
e
w
u
s
er
s
’
f
av
o
r
ites
b
y
u
s
in
g
d
ata
o
f
th
e
o
ld
u
s
er
s
as
a
b
ase.
Me
an
wh
ile
k
n
ap
s
ac
k
m
eth
o
d
was
m
u
tu
ally
d
ev
elo
p
ed
f
o
r
f
o
o
d
r
ec
o
m
m
en
d
atio
n
in
ac
co
r
d
an
ce
with
r
estrictio
n
s
o
f
ea
ch
u
s
er
.
Deta
ils
o
f
ea
ch
tech
n
iq
u
e
ar
e
as f
o
llo
w:
−
C
o
llab
o
r
ativ
e
f
ilter
in
g
C
o
llab
o
r
at
iv
e
f
ilter
in
g
is
ca
lcu
latin
g
s
im
ilar
ity
am
o
n
g
u
s
er
s
b
y
u
s
in
g
b
eh
av
io
r
s
o
f
p
er
s
o
n
s
h
av
in
g
s
im
ilar
ities
wi
th
u
s
er
s
.
User
s
’
d
ata
ar
e
d
eter
m
in
ed
as
a
d
atab
ase
in
wo
r
k
in
g
o
n
p
r
e
d
ictio
n
a
n
d
r
ec
o
m
m
en
d
atio
n
o
f
lis
ts
to
u
s
er
s
ac
c
o
r
d
in
g
ly
i
n
u
s
in
g
t
h
e
f
o
o
d
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
o
n
t
h
e
b
asis
o
f
co
ll
ab
o
r
ativ
e
f
ilter
in
g
,
wh
ich
ca
n
b
e
d
iv
id
ed
in
t
o
2
s
tep
s
[
1
3
]
,
[
1
4
]
as
f
o
llo
ws:
i)
C
alcu
latin
g
to
f
ig
u
r
e
o
u
t
s
im
ilar
ity
o
f
u
s
er
s
:
T
h
is
m
eth
o
d
s
h
all
ca
lcu
late
Pear
s
o
n
’
s
co
r
r
elatio
n
c
o
ef
f
icien
t
b
et
wee
n
th
e
r
atin
g
g
iv
en
b
y
n
ew
u
s
er
s
an
d
o
l
d
u
s
er
s
to
ch
ec
k
s
im
ilar
ity
b
ased
o
n
th
e
co
r
r
elatio
n
(
1
)
[
1
5
]
,
[
1
6
]
:
(
,
)
=
∑
∈
∩
(
,
−
̅
)
(
,
−
̅
)
√
∑
∈
∩
(
,
−
̅
)
2
√
∑
∈
∩
(
,
−
̅
)
2
(
1
)
wh
er
e:
(
,
)
r
ef
er
s
to
s
im
ilar
ity
b
etwe
en
n
e
w
u
s
er
s
an
d
o
ld
u
s
er
s
.
∩
r
ef
er
s
to
s
im
ilar
ity
o
f
th
e
r
atin
g
g
iv
en
b
y
n
ew
u
s
er
s
an
d
o
ld
u
s
er
s
.
′
,
r
ef
er
s
to
th
e
r
atin
g
o
f
n
ew
u
s
er
s
to
th
e
lis
ts
.
̅
′
r
ef
er
s
to
th
e
a
v
er
ag
e
r
atin
g
g
i
v
en
b
y
n
ew
u
s
er
s
.
,
r
ef
er
s
to
th
e
r
atin
g
o
f
o
ld
u
s
er
s
to
th
e
lis
ts
.
̅
r
ef
er
s
to
th
e
a
v
er
ag
e
r
atin
g
g
i
v
en
b
y
o
ld
u
s
er
s
.
C
alcu
lated
v
alu
es
wer
e
u
s
ed
to
d
eter
m
in
e
s
tatis
tical
co
r
r
elatio
n
b
etwe
en
s
co
r
es
o
f
n
ew
an
d
o
ld
u
s
er
s
to
f
ig
u
r
e
o
u
t
p
r
ed
ictio
n
v
alu
e
;
an
d
ii)
C
alcu
latin
g
to
f
ig
u
r
e
o
u
t
p
r
ed
ictio
n
v
alu
e:
As
f
o
r
p
r
ed
ict
io
n
o
r
r
ec
o
m
m
en
d
atio
n
f
o
r
n
ew
u
s
er
s
b
ased
o
n
th
e
co
llab
o
r
ativ
e
f
ilter
in
g
b
etwe
en
n
ew
u
s
er
s
an
d
o
ld
u
s
er
s
,
ca
lcu
latio
n
is
m
ad
e
to
f
in
d
th
e
n
ea
r
est
v
alu
e
o
f
n
ew
u
s
er
s
g
iv
en
to
th
e
lis
ts
th
at
m
atch
th
o
s
e
o
f
o
ld
u
s
er
s
.
On
ce
th
e
ca
lcu
latio
n
is
m
ad
e,
th
e
s
y
s
tem
is
r
atin
g
u
s
er
s
co
r
es f
o
r
p
r
ed
ictin
g
n
ew
u
s
er
s
[
1
7
]
,
[
1
8
]
.
Gen
er
ally
,
ca
lcu
latio
n
is
b
ased
o
n
th
e
av
er
ag
e
r
atin
g
o
f
u
s
er
s
h
av
in
g
s
ev
er
al
s
im
ilar
ities
ac
co
r
d
in
g
b
y
(
2
)
.
,
=
̅
+
∑
(
,
′
)
(
′
,
−
̅
′
)
′
∈
∑
|
(
,
′
)
|
′
∈
(
2
)
wh
er
e:
,
r
ef
er
s
to
p
r
e
d
ictio
n
f
o
r
n
ew
u
s
er
s
to
th
e
ex
is
tin
g
lis
ts
.
̅
r
ef
er
s
to
th
e
a
v
er
ag
e
s
co
r
e
o
f
u
s
er
s
.
′
,
r
ef
er
s
to
s
co
r
es o
f
o
ld
u
s
er
s
to
th
e
lis
ts
.
̅
′
r
ef
er
s
to
th
e
a
v
er
ag
e
s
co
r
e
o
f
o
ld
u
s
er
s
.
(
,
′
)
r
ef
er
s
to
r
esu
lts
f
r
o
m
ca
lcu
latio
n
s
to
f
in
d
s
im
ilar
ity
b
etwe
en
u
s
er
s
.
T
h
e
lis
ts
ar
e
ar
r
an
g
ed
f
r
o
m
wh
at
u
s
er
s
lik
e
th
e
m
o
s
t to
wh
at
u
s
er
s
lik
e
th
e
least so
as to
r
ec
o
m
m
en
d
a
f
o
o
d
m
en
u
to
n
ew
u
s
er
s
.
I
n
ca
s
e
a
lo
t
o
f
m
en
u
s
ar
e
av
ailab
le
an
d
r
ec
o
m
m
en
d
ed
f
o
o
d
s
d
o
n
o
t
m
atch
u
s
er
s
’
r
eq
u
ir
em
en
ts
,
th
e
n
ex
t r
ec
o
m
m
en
d
ed
m
en
u
will b
e
s
h
o
wn
u
n
til u
s
er
s
’
r
eq
u
ir
em
en
ts
ar
e
m
et.
−
Kn
ap
s
ac
k
alg
o
r
ith
m
Kn
ap
s
ac
k
p
r
o
b
lem
m
ea
n
s
s
elec
tin
g
n
item
s
with
d
if
f
er
en
t
weig
h
ts
an
d
v
alu
es in
a
k
n
ap
s
ac
k
b
ased
o
n
th
e
co
n
d
itio
n
th
at
wh
en
all
v
alu
es
o
f
th
e
s
elec
ted
item
s
ar
e
ca
lcu
lated
m
u
s
t
h
av
e
th
e
h
ig
h
est
to
tal
v
alu
e
an
d
th
e
to
tal
weig
h
t
d
o
es
n
o
t
ex
ce
ed
th
e
m
ax
im
u
m
wei
g
h
t
th
at
th
e
k
n
ap
s
ac
k
ca
n
b
ea
r
[
1
9
]
,
[
2
0
]
.
Fo
r
ex
am
p
le,
if
a
th
ief
wo
u
ld
lik
e
to
s
teal
item
s
f
r
o
m
a
s
u
p
er
m
ar
k
et
b
y
s
elec
tin
g
item
s
in
th
e
s
h
elv
es
in
a
b
ac
k
p
ac
k
b
u
t th
e
b
ac
k
p
ac
k
h
as
lim
ited
ca
p
ac
ity
to
ca
r
r
y
weig
h
ts
.
T
h
u
s
,
wh
ich
item
s
th
e
th
ief
will
s
elec
t
in
th
e
b
ac
k
p
ac
k
to
g
ain
th
e
h
ig
h
est
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
6
3
0
-
638
632
to
tal
v
alu
e
o
f
th
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item
s
th
ey
wis
h
to
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as
s
h
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Fig
u
r
e
1
to
b
e
ca
lled
k
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ap
s
ac
k
p
r
o
b
lem
wh
ile
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e
to
tal
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m
u
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t
n
o
t
ex
ce
ed
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e
k
n
ap
s
ac
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p
ac
ity
;
0
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1
k
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r
o
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en
0
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1
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m
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tely
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leav
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letely
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0
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f
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ac
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n
o
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t
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e
tak
en
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Su
ch
p
r
o
b
lem
is
ca
lled
o
p
tim
izatio
n
p
r
o
b
lem
.
I
t
is
s
elec
tin
g
th
e
b
est
s
o
lu
tio
n
u
n
d
er
th
e
av
ailab
le
co
n
d
itio
n
.
0
-
1
Kn
ap
s
ac
k
p
r
o
b
lem
ca
n
n
o
t
b
e
s
o
lv
ed
b
y
g
r
ee
d
y
ap
p
r
o
ac
h
.
Fo
r
ex
am
p
le,
3
p
iece
s
o
f
item
s
to
b
e
s
elec
ted
in
a
b
ac
k
p
ac
k
h
av
e
weig
h
ts
an
d
v
alu
es
as
s
h
o
wn
in
th
e
T
ab
le
1
,
wh
ile
th
e
b
ac
k
p
ac
k
’
s
ca
p
ac
ity
d
o
es n
o
t e
x
ce
ed
6
k
g
[
2
1
]
.
Fig
u
r
e
1
.
Kn
a
p
s
ac
k
p
r
o
b
lem
Tab
le 1
.
E
x
am
p
le
o
f
p
r
o
d
u
ct
v
alu
e
p
er
k
ilo
g
r
am
I
t
e
m
A
B
C
P
r
i
c
e
10
28
12
W
e
i
g
h
t
1
4
2
R
a
t
i
o
=
(
P
r
i
c
e
/
W
e
i
g
h
t
)
10
7
6
I
f
g
r
ee
d
y
ap
p
r
o
ac
h
is
u
s
ed
,
th
e
f
ir
s
t
item
to
b
e
s
elec
ted
is
A
s
i
n
ce
it
h
as
th
e
h
ig
h
est
v
alu
e
p
er
k
ilo
g
r
am
,
f
o
llo
wed
b
y
B
,
m
ak
in
g
th
e
to
t
al
v
alu
e
o
f
A
an
d
B
is
1
0
+2
8
=
3
8
an
d
th
e
t
o
tal
weig
h
t o
f
A
an
d
B
is
5
k
ilo
g
r
am
wh
ich
d
o
es
n
o
t
ex
ce
ed
th
e
b
a
ck
p
ac
k
’
s
ca
p
ac
ity
.
Ho
wev
e
r
,
i
t
is
n
o
t
th
e
b
est
s
o
lu
tio
n
.
T
h
e
item
s
th
at
g
iv
e
th
e
h
ig
h
est
v
alu
e
in
th
e
b
ac
k
p
ac
k
ar
e
B
an
d
C
as
th
e
to
tal
v
alu
e
o
f
B
a
n
d
C
is
2
8
+1
2
=4
0
.
I
t
ca
n
b
e
co
n
clu
d
ed
th
at
th
e
g
r
ee
d
y
ap
p
r
o
ac
h
is
u
n
ab
le
to
g
iv
e
th
e
b
est
v
alu
e
in
th
is
ex
am
p
le.
T
h
er
e
f
o
r
e,
th
e
m
et
h
o
d
u
s
ed
to
s
o
lv
e
th
e
p
r
o
b
lem
i
n
th
is
s
tu
d
y
is
d
y
n
a
m
ic
p
r
o
g
r
am
m
in
g
ap
p
r
o
ac
h
[
2
2
]
-
[
2
4
]
Dy
n
am
ic
p
r
o
g
r
am
m
in
g
ap
p
r
o
ac
h
is
p
r
o
b
lem
-
s
o
lv
in
g
to
g
et
th
e
b
est
s
o
lu
tio
n
.
C
o
m
p
o
n
en
ts
o
f
co
n
s
id
er
ed
item
s
ar
e
d
iv
id
ed
in
to
s
u
b
-
co
m
p
o
n
en
ts
an
d
r
esu
lts
f
r
o
m
th
e
p
r
ev
io
u
s
ca
lcu
latio
n
ar
e
k
ep
t
in
th
e
f
o
r
m
o
f
tab
les
f
o
r
b
ein
g
co
n
s
id
er
ed
in
th
e
n
ex
t tim
e.
I
t
is
ca
lled
a
r
ec
u
r
s
iv
e
p
r
o
ce
s
s
o
r
ca
llin
g
a
f
u
n
ctio
n
f
r
o
m
its
elf
u
n
til
th
e
f
in
al
s
o
lu
tio
n
is
o
b
tain
ed
.
So
lv
in
g
k
n
ap
s
ac
k
p
r
o
b
lem
u
s
in
g
th
e
d
y
n
am
ic
p
r
o
g
r
am
m
in
g
ap
p
r
o
ac
h
d
eter
m
in
es
th
er
e
ar
e
n
item
s
wh
er
e
ea
ch
item
I
(
I
=1
…
n
)
h
as
a
weig
h
t
wi
an
d
an
in
teg
er
v
alu
e
v
i.
T
h
e
m
ax
im
u
m
weig
h
t
a
b
ac
k
p
ac
k
ca
n
ca
r
r
y
is
W
,
th
e
p
r
o
b
lem
ca
n
b
e
wr
itten
in
th
e
f
o
r
m
o
f
o
p
tim
izatio
n
p
r
o
b
lem
[
2
5
]
as
f
o
llo
w:
wh
er
e
n
is
th
e
n
u
m
b
er
o
f
all
i
tem
s
,
w
=
{w
1
, w
2
,
...,
w
n
}
r
ef
er
s
to
a
weig
h
t o
f
ea
ch
item
i.
v
=
{v
1
, v
2
,
…,
v
n
}
r
ef
er
s
to
th
e
v
alu
e
o
f
ea
ch
item
i.
T
h
u
s
,
th
e
s
tep
s
to
s
o
lv
e
p
r
o
b
lem
h
o
w
to
s
elec
t
item
s
to
g
ain
th
e
o
p
tim
u
m
v
alu
e
an
d
th
e
to
tal
weig
h
t
d
o
es
n
o
t
ex
ce
ed
th
e
b
ac
k
p
ac
k
’
s
ca
p
ac
ity
ar
e
s
h
o
wn
as f
o
llo
w:
Ma
x
im
ize
∑
=
1
Su
b
ject
to
∑
≤
=
1
W
h
en
0
≤
≤
1
r
ef
er
s
to
ea
c
h
item
I
,
th
e
v
alu
e
o
f
h
as
2
v
alu
es;
1
=
tak
e
an
item
co
m
p
letely
an
d
0
=
leav
e
an
item
co
m
p
letely
.
T
h
e
ab
o
v
e
ex
am
p
le
ca
n
u
s
e
Kn
ap
Sack
(
v
,
w,
n
W
)
wh
en
n
=3
an
d
W
=6
0
,
i=1
.
.
6
w=
{1
,
4
,
2
}
v
={
1
0
,
2
8
,
1
2
}.
T
h
e
ca
lcu
latio
n
o
f
V
[
i,
w]
as
s
h
o
wn
in
th
e
T
ab
le
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
I
mp
leme
n
ta
tio
n
o
f
a
p
ers
o
n
a
li
z
ed
fo
o
d
r
ec
o
mme
n
d
a
tio
n
s
ystem
…
(
N
a
tta
p
o
r
n
Th
o
n
g
s
r
i
)
633
T
ab
le
2
.
C
alcu
latio
n
o
f
V
[
i,
w]
i
t
e
m
0
1
2
3
4
5
6
i
=
1
,
w
1
=
1
,
v
1
=
1
0
0
10
10
10
10
10
10
i
=
2
,
w
2
=
4
,
v
2
=
2
8
0
10
10
10
max
(
2
8
+
0
,
10)
28
max
(
2
8
+
1
0
,
1
0
)
38
max
(
2
8
+
1
0
,
1
0
)
38
i
=
3
,
w
3
=
2
,
v
3
=
1
2
0
0
max
(
1
2
+
0
,
10)
12
max
(
1
2
+
1
0
)
22
max
(
1
2
+
1
0
,
2
8
)
28
max
(
1
2
+
1
0
,
3
8
)
38
max
(
1
2
+
2
8
,
3
8
)
40
I
t
ca
n
b
e
ex
p
lain
ed
b
y
co
n
s
id
er
in
g
th
e
f
ir
s
t
item
i=1
h
av
in
g
a
weig
h
t
o
f
1
th
at
ca
n
b
e
s
elec
ted
in
a
b
ac
k
p
ac
k
h
av
in
g
a
weig
h
t
f
r
o
m
1
to
6
.
T
h
e
v
alu
e
s
h
o
wn
in
th
e
tab
le
is
th
e
to
tal
v
alu
e
o
f
item
s
p
u
t
in
th
e
b
ac
k
p
ac
k
at
th
e
weig
h
t o
f
w
i
,
i=2
at
w
2
=4
an
d
v
2
=2
8
.
T
h
e
f
ir
s
t
b
ac
k
p
ac
k
ca
n
ca
r
r
y
w=
1
an
d
it
is
f
o
u
n
d
th
at
it
ca
n
ca
r
r
y
th
e
2
nd
item
.
T
h
u
s
,
th
e
v
alu
e
V[
2
,
1
]
=V
[
1
,
1
]
is
th
e
v
alu
e
o
f
th
e
item
s
elec
ted
p
r
ev
io
u
s
ly
.
T
h
e
b
ac
k
p
ac
k
w=
2
an
d
3
–
th
e
weig
h
ts
o
f
th
e
b
ac
k
p
ac
k
s
ar
e
less
th
an
th
e
item
s
p
u
t
in
th
e
b
ac
k
p
ac
k
s
,
th
e
item
s
ar
e
n
o
t
p
u
t in
th
e
b
ac
k
p
ac
k
s
b
u
t th
e
p
r
ev
io
u
s
item
is
m
ain
tain
ed
.
T
h
e
b
ac
k
p
ac
k
th
at
ca
n
ca
r
r
y
w=
4
is
f
o
u
n
d
th
at
it
ca
n
ca
r
r
y
th
e
2
nd
item
.
T
h
er
ef
o
r
e,
th
e
v
alu
e
V[
1
,
4
]
=m
ax
{V[
1
,
4
]
,
v
[
2
]
+V
[
1
,
0
]
}=
m
ax
{2
8
+0
,
1
0
}=
2
8
.
T
h
e
wh
o
le
tab
le
is
ca
lcu
lated
in
th
e
s
am
e
way
in
all
b
o
x
es.
T
h
e
o
p
tim
u
m
v
alu
e
in
th
e
last
b
o
x
is
4
0
wh
ich
is
o
b
tain
e
d
f
r
o
m
th
e
3
rd
item
h
av
in
g
th
e
v
alu
e
o
f
1
2
in
co
m
b
in
atio
n
with
th
e
2
nd
item
h
av
in
g
th
e
v
alu
e
o
f
2
8
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
d
ev
elo
p
m
en
t
o
f
a
p
er
s
o
n
alize
d
f
o
o
d
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
b
ased
o
n
co
llab
o
r
ativ
e
f
ilter
in
g
an
d
k
n
ap
s
ac
k
p
r
o
b
lem
alg
o
r
ith
m
in
ter
m
s
o
f
s
y
s
tem
ar
ch
itectu
r
e
an
d
d
esig
n
is
s
h
o
wn
in
Fig
u
r
e
2
.
As illu
s
tr
ated
in
Fig
u
r
e
2
,
u
s
er
s
f
ill
th
eir
p
er
s
o
n
al
d
ata
co
m
p
r
is
in
g
s
ex
,
weig
h
t,
h
eig
h
t,
f
av
o
r
ite
f
o
o
d
r
atin
g
.
Nex
t,
th
e
s
y
s
tem
s
h
all
b
r
in
g
p
er
s
o
n
al
d
ata
v
ar
iab
le
o
f
u
s
er
s
in
co
n
ju
n
ctio
n
with
k
n
ap
s
ac
k
m
eth
o
d
to
r
ec
o
m
m
en
d
th
em
m
en
u
s
th
at
m
atch
th
eir
p
r
ef
er
en
ce
s
an
d
r
estrictio
n
s
s
u
ch
as
u
n
d
er
ly
in
g
d
is
ea
s
es
o
f
ea
ch
u
s
er
u
n
d
er
th
e
n
u
m
b
er
o
f
ca
lo
r
ies
th
ey
n
ee
d
ea
ch
d
ay
.
T
h
e
f
o
o
d
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
b
ased
o
n
co
llab
o
r
ativ
e
f
ilter
in
g
is
d
iv
id
ed
in
to
2
s
tep
s
as f
o
llo
ws:
Fig
u
r
e
2
.
I
ll
u
s
tr
atio
n
o
f
p
r
o
p
o
s
ed
s
y
s
tem
ar
ch
itectu
r
e
2
.
1
.
Ca
lcula
t
ing
t
o
f
ind
s
im
ila
rit
y
o
f
us
er
s
by
s
e
a
rc
hin
g
f
o
r
s
im
ila
rit
y
bet
wee
n
o
ld
us
er
s
a
nd
new
us
er
s
us
ing
B
y
s
ea
r
ch
in
g
f
o
r
s
im
ilar
ity
b
etwe
en
o
ld
u
s
er
s
an
d
n
ew
u
s
er
s
u
s
in
g
,
th
e
b
elo
w
f
o
r
m
u
la
is
u
s
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
6
3
0
-
638
634
(
,
)
=
∑
∈
∩
(
,
−
̅
)
(
,
−
̅
)
√
∑
∈
∩
(
,
−
̅
)
2
√
∑
∈
∩
(
,
−
̅
)
2
2
.
2
.
Ca
lcula
t
ing
t
o
f
ig
ure
o
ut
predict
io
n v
a
lue
T
h
e
ca
lcu
latio
n
to
d
eter
m
in
e
th
e
s
im
ilar
ity
o
f
u
s
er
s
as sh
o
wn
in
th
e
Fig
u
r
e
3
.
,
=
̅
+
∑
(
,
′
)
(
u
,
−
̅
)
′
∈
∑
|
(
,
′
)
|
′
∈
Fig
u
r
e
3
.
T
h
e
ca
lcu
latio
n
t
o
d
e
ter
m
in
e
th
e
s
im
ilar
ity
o
f
u
s
er
s
Pu
,
R
ice
p
o
r
r
id
g
e
with
s
h
r
im
p
=
3
.
5
+
(
−
0
.
0625
)
(
5
−
3
.
5
)
+
(
0
.
3214
)
(
5
−
3
.
5
)
|
−
0
.
0625
|
+
|
0
.
3214
|
=
4
.
5
W
h
en
m
en
u
p
r
ef
er
en
ce
s
u
s
in
g
th
e
co
llab
o
r
ativ
e
f
ilter
in
g
m
eth
o
d
ar
e
ca
lcu
lated
,
th
e
m
en
u
s
with
th
e
h
ig
h
est
p
r
ef
er
en
ce
s
co
r
e
ar
e
s
elec
ted
b
u
t
th
ey
m
u
s
t
n
o
t
ex
ce
ed
th
e
n
u
m
b
er
o
f
ca
lo
r
ies
ea
ch
u
s
er
n
ee
d
s
ea
ch
d
ay
.
T
h
is
s
tu
d
y
ap
p
lied
th
e
k
n
ap
s
ac
k
alg
o
r
ith
m
to
s
elec
t
th
e
r
ec
o
m
m
en
d
ed
m
en
u
s
b
y
u
s
in
g
u
s
er
s
’
p
r
ef
er
en
c
e
s
co
r
es g
iv
en
to
th
e
m
en
u
s
.
P(u
,
i)
r
ef
er
s
to
th
e
v
a
lu
e
o
f
item
s
.
T
h
e
n
u
m
b
er
o
f
ca
lo
r
ies o
f
ea
ch
m
en
u
r
ep
r
esen
ts
th
e
weig
h
ts
o
f
item
s
.
T
h
e
n
u
m
b
er
o
f
ca
lo
r
ies
ea
ch
u
s
er
n
ee
d
s
ea
ch
d
ay
,
r
estrictio
n
s
,
r
ep
r
esen
ts
th
e
ca
p
ac
ity
o
f
a
b
ac
k
p
ac
k
.
T
h
e
n
u
m
b
er
o
f
ca
lo
r
ies
ea
ch
u
s
er
n
ee
d
s
p
er
d
ay
is
ca
lcu
lated
f
r
o
m
b
asal
m
etab
o
lic
r
ate
(
B
MR)
b
ased
o
n
s
ex
,
ag
e,
weig
h
t,
an
d
h
eig
h
t
.
Fo
r
m
ale:
B
MR =
6
6
.
5
+
(
1
3
.
7
5
×
weig
h
t i
n
k
g
)
+
(
5
.
0
0
3
×
h
eig
h
t in
cm
)
–
(
6
.
7
5
5
×
a
g
e
i
n
y
ea
r
s
)
Fo
r
f
em
ale:
B
MR =
6
5
5
+
(
9
.
5
6
3
×
weig
h
t in
k
g
)
+
(
1
.
8
5
0
×
h
eig
h
t in
c
m
)
–
(
4
.
6
7
6
×
ag
e
in
y
ea
r
s
)
T
h
e
ap
p
licatio
n
o
f
k
n
ap
s
ac
k
u
s
in
g
d
y
n
a
m
ic
p
r
o
g
r
am
m
in
g
ap
p
r
o
ac
h
f
o
r
s
elec
tin
g
r
ec
o
m
m
en
d
ed
m
en
u
s
d
eter
m
in
es
th
er
e
ar
e
n
item
s
wh
er
e
ea
ch
item
i(
i=1
…
n
)
co
n
tain
s
ci
ca
lo
r
ies
an
d
u
s
er
s
’
p
r
ef
er
en
ce
o
f
m
e
n
u
s
is
.
T
h
e
n
u
m
b
er
o
f
ca
lo
r
ies th
ey
n
ee
d
ea
ch
d
ay
=
B
M
R
wh
ich
ca
n
b
e
r
e
p
r
esen
ted
b
y
th
e
f
o
ll
o
win
g
s
y
m
b
o
ls
:
W
h
en
n
is
all
f
o
o
d
m
en
u
s
.
c=
{c
1
, c
2
,
…
,
c
n
}
r
e
p
r
esen
ts
th
e
n
u
m
b
er
o
f
ca
lo
r
ies o
f
f
o
o
d
m
en
u
i
p
=
{p
1
,
p
2
,
…
,
p
n
}
r
ep
r
esen
ts
p
r
ef
er
e
n
ce
o
f
f
o
o
d
m
en
u
i
Selectin
g
wh
ich
f
o
o
d
m
en
u
s
to
g
ain
th
e
h
ig
h
est
p
r
ef
e
r
en
ce
v
alu
e
th
at
d
o
es
n
o
t
ex
ce
ed
th
e
n
u
m
b
er
o
f
ca
lo
r
ies
th
ey
n
ee
d
ea
ch
d
a
y
.
Ma
x
im
ize
∑
=
1
Su
b
ject
to
∑
≤
=
1
W
h
en
0
≤
≤
1
r
ep
r
esen
ts
f
o
o
d
m
en
u
i
,
th
e
v
alu
e
o
f
.
W
h
er
e
h
as
2
v
alu
es;
tak
in
g
an
item
co
m
p
letel
y
=
1
an
d
lea
v
in
g
a
n
item
co
m
p
l
etely
=
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
I
mp
leme
n
ta
tio
n
o
f
a
p
ers
o
n
a
li
z
ed
fo
o
d
r
ec
o
mme
n
d
a
tio
n
s
ystem
…
(
N
a
tta
p
o
r
n
Th
o
n
g
s
r
i
)
635
Kn
ap
Sack
alg
o
r
ith
m
f
o
r
f
o
o
d
r
ec
o
m
m
en
d
atio
n
s
u
p
d
ate
f
r
o
m
[
2
6
]
as f
o
llo
ws:
KnapSack(c,p,n,BMR)
for
c
=
0
to
C
do
P[0,
c]
=
0
for
i
=
1
to
n
do
P[i,
0]
=
0
for
c
=
0
to
BMR
do
if
c[i]
≤
w
and
(p[i]+
P[i
-
1,c
-
c[i]]
>
P[i
-
1,c]))
then
P[i,
c]
=
p[i]+
P[i
-
1,c
-
c[i]]
keep[i,c]
=
1
else
P[i,
c]
=
V[i
-
1,
c]
keep[i,c]
=
0
K
=
BMR
for
i
=
n
downto
1
if
(keep[i,K]
==
1)
output
i
K
=
K
-
c[i]
return
V[n,BMR]
3.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
I
n
th
is
o
f
co
llab
o
r
ativ
e
f
ilter
in
g
an
d
Kn
ap
s
ac
k
m
eth
o
d
.
T
h
e
r
esu
lts
in
d
icate
d
th
at
s
o
m
e
p
r
o
b
lem
s
in
th
e
d
ev
elo
p
m
en
t
o
f
th
e
s
y
s
tem
wer
e
d
is
co
v
er
ed
wh
ich
co
u
ld
b
e
co
n
s
id
er
ed
as
th
e
r
ef
er
en
ce
g
u
id
elin
es
f
o
r
f
u
r
th
er
d
ev
elo
p
m
en
t.
First
o
f
r
esear
ch
,
d
ata
m
in
in
g
th
eo
r
y
was
ap
p
lied
to
cr
ea
te
a
p
er
s
o
n
alize
d
f
o
o
d
r
ec
o
m
m
en
d
atio
n
with
th
e
in
teg
r
ated
tech
n
iq
u
e
all,
s
in
ce
co
llab
o
r
ativ
e
f
ilter
in
g
tech
n
iq
u
e
r
eq
u
ir
es
in
itial
d
ata
f
r
o
m
p
r
ev
io
u
s
u
s
er
p
r
ef
er
en
ce
s
as
in
f
o
r
m
atio
n
f
o
r
p
o
ten
tial
u
s
er
r
ec
o
m
m
en
d
atio
n
.
Du
r
in
g
in
itial
p
h
ase
o
f
th
e
s
y
s
tem
,
a
co
ld
-
s
tar
t
p
r
o
b
lem
was
f
o
u
n
d
as
th
e
ac
q
u
is
itio
n
o
f
u
s
er
p
r
ef
er
en
ce
in
f
o
r
m
atio
n
h
ad
s
till
v
er
y
litt
le
in
ter
ac
tio
n
s
[
7
]
,
[
2
7
]
.
T
h
er
ef
o
r
e,
a
ce
r
tain
am
o
u
n
t
o
f
tim
e
is
r
eq
u
ir
ed
f
o
r
d
ata
ac
q
u
is
itio
n
in
o
r
d
er
to
o
b
tain
s
u
f
f
icien
t
d
ata
f
o
r
p
r
o
ce
s
s
in
g
.
I
n
th
is
p
ap
er
,
th
e
in
itial
d
ata
ac
q
u
is
itio
n
p
r
o
b
lem
f
o
r
u
s
e
in
m
o
d
el
lear
n
in
g
was
r
eso
lv
ed
b
y
q
u
esti
o
n
n
air
es.
User
p
r
ef
er
en
ce
s
f
o
r
f
o
o
d
item
s
wer
e
r
an
d
o
m
ly
co
llected
,
wh
ich
wer
e
u
s
ed
as
e
d
ef
au
lt
in
f
o
r
m
atio
n
f
o
r
th
e
s
y
s
tem
.
L
ater
,
th
e
s
y
s
tem
will
co
llect
f
o
o
d
p
r
ef
er
en
ce
s
f
r
o
m
u
s
er
s
wh
o
lo
g
in
to
u
s
e
th
e
s
y
s
tem
th
r
o
u
g
h
th
e
web
p
ag
e
in
d
ef
in
itely
.
An
o
th
er
p
r
o
b
lem
f
o
u
n
d
was
if
th
er
e
wer
e
u
n
av
ailab
ilit
y
o
f
in
itial
d
ata
o
f
a
u
s
er
'
s
f
av
o
r
ite
f
o
o
d
lis
t
f
o
r
u
s
in
g
to
tr
ain
in
th
e
m
o
d
el,
th
e
s
y
s
tem
ca
n
n
o
t
r
ec
o
m
m
en
d
f
o
o
d
item
s
th
at
ar
e
clo
s
e
to
th
e
u
s
er
'
s
p
r
ef
er
en
ce
s
.
Simp
ly
p
u
t,
a
s
o
lu
tio
n
to
th
is
p
r
o
b
lem
r
eq
u
ir
es
en
o
u
g
h
in
f
o
r
m
atio
n
.
Fin
ally
,
th
e
c
o
m
p
o
n
en
ts
o
f
th
e
d
ev
elo
p
ed
s
y
s
tem
as
ass
is
tiv
e
to
o
l
f
o
r
u
s
er
s
in
m
ak
in
g
d
ec
is
io
n
s
ab
o
u
t
th
eir
m
en
u
ch
o
ices
co
m
p
r
is
e
f
illi
n
g
o
u
t
a
u
s
er
p
r
o
f
ile,
u
s
er
r
atin
g
to
war
d
s
th
e
m
en
u
in
th
e
s
y
s
tem
,
r
atin
g
s
im
ilar
ities
b
etwe
en
n
ew
an
d
o
ld
u
s
er
s
to
o
b
tain
p
r
ed
icto
r
f
o
r
th
e
r
ec
o
m
m
en
d
ed
m
en
u
s
u
itab
le
f
o
r
ea
ch
u
s
er
ac
co
r
d
in
g
to
n
u
tr
itio
n
in
f
o
r
m
atio
n
.
Mo
r
e
im
p
o
r
tan
tly
,
th
e
r
esu
lts
o
f
th
is
em
p
ir
ical
s
tu
d
y
im
p
lied
th
at
f
o
r
f
u
r
th
er
s
tu
d
y
,
in
g
r
ed
ien
ts
co
n
tain
ed
in
th
e
s
y
s
tem
s
h
o
u
ld
b
e
u
s
ed
as
p
ar
t
o
f
th
e
u
s
er
ch
o
ice,
esp
ec
iall
y
f
o
o
d
aller
g
ic
u
s
er
s
wh
en
item
r
ec
o
m
m
en
d
atio
n
.
I
n
ad
d
itio
n
,
an
y
in
g
r
ed
ien
ts
u
s
er
s
ar
e
aller
g
ic
to
s
h
o
u
ld
d
elete
d
f
r
o
m
th
e
r
ec
o
m
m
en
d
er
s
y
s
tem
.
Af
ter
th
e
m
eth
o
d
d
ev
elo
p
m
en
t
was
f
in
is
h
ed
,
th
e
r
esear
ch
er
d
ev
elo
p
ed
th
e
s
y
s
tem
.
T
h
e
Fig
u
r
e
4
(
a)
-
(
e)
s
h
o
ws th
e
ex
am
p
le
o
f
th
e
s
cr
ee
n
o
f
th
e
d
ev
elo
p
ed
s
y
s
tem
(
s
ee
in
ap
p
en
d
ix
)
.
As
s
o
o
n
as
th
e
s
y
s
tem
was
co
m
p
letely
f
in
is
h
ed
,
th
e
r
esear
ch
er
b
r
o
u
g
h
t
th
e
s
y
s
tem
to
u
s
er
s
co
m
p
r
is
in
g
9
0
p
u
b
lic
h
ea
lth
wo
r
k
o
p
er
ato
r
s
to
test
an
d
r
ate
s
atis
f
ac
tio
n
s
s
co
r
es
to
war
d
s
th
e
s
y
s
tem
.
T
h
e
h
ig
h
est s
co
r
e
=
5
p
o
in
ts
m
ea
n
in
g
ex
tr
em
ely
s
atis
f
ied
,
1
p
o
in
t =
ab
s
o
lu
tely
d
is
s
atis
f
ied
.
T
h
e
m
ea
n
s
co
r
e
o
f
ass
ess
m
en
t
r
esu
lts
o
f
s
atis
f
ac
tio
n
to
war
d
s
th
e
o
p
er
atin
g
s
y
s
tem
,
s
cr
ee
n
d
esig
n
,
ef
f
icien
cy
o
f
th
e
o
p
er
atin
g
s
y
s
tem
was
4
.
2
0
,
co
n
s
id
er
ed
u
s
er
s
wer
e
s
atis
f
ied
with
th
e
s
y
s
tem
at
a
h
ig
h
lev
el.
T
h
e
s
tu
d
y
r
esu
lts
an
d
b
o
d
y
o
f
k
n
o
wled
g
e
in
d
if
f
er
en
t
asp
ec
ts
u
s
ed
to
d
ev
elo
p
th
e
f
o
o
d
r
ec
o
m
m
en
d
atio
n
b
ased
o
n
co
llab
o
r
ativ
e
f
ilter
in
g
an
d
k
n
ap
s
ac
k
p
r
o
b
lem
alg
o
r
ith
m
en
ab
le
th
e
f
o
o
d
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
to
b
e
co
m
p
lete
an
d
ac
tu
ally
f
u
n
ctio
n
al.
T
h
e
s
y
s
tem
ca
n
b
e
u
s
ed
to
b
e
a
p
ar
t
o
f
elim
in
atin
g
th
e
p
r
o
b
lem
s
r
elate
d
to
n
o
n
-
co
m
m
u
n
icab
le
d
is
ea
s
es,
a
h
ar
m
f
u
l
th
r
ea
t
in
d
ev
elo
p
in
g
co
u
n
tr
ies.
B
esid
es,
th
e
s
y
s
tem
ca
n
g
iv
e
a
g
u
id
elin
e
to
r
elev
an
t
p
er
s
o
n
s
s
u
ch
as
g
o
v
er
n
m
e
n
t
ag
en
cies,
Min
is
tr
y
o
f
Pu
b
lic
Hea
lth
in
clu
d
in
g
s
o
f
twar
e
d
ev
elo
p
er
s
to
s
tu
d
y
an
d
f
u
r
th
er
d
ev
elo
p
th
e
s
y
s
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I
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I
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g
,
Vo
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12
,
No
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1
,
Feb
r
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20
22
:
6
3
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638
636
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Vo
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12
,
No
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1
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Feb
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20
22
:
6
3
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638
638
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Evaluation Warning : The document was created with Spire.PDF for Python.