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Phn tch thit k gii thutPh m Nguyn Khang, Thanh Ngh BM. Khoa h c my tnhKhoa CNTT i h c C n Th {pnkhang,dtnghi}cit.ctu.!du."n
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# Mc tiu# T bi ton n chng trnh# Cc k thut thit k gii thut
Chi ! tr" #u$ %ui
&'t c(n )hnh cn *u +n,Th- +n,Th- %-,. /0r112$3 #u$ ho(ch 4ng
# 5i t6
$
)4i 2ung
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Mc tiu# 5it cc k thut thit k gii thut7 t 8 t9ng
cho n gii thut chi tit:
# *i!u r; ngu$n %8 cth! 6 2ng ?c k thut n$:
%
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T bi ton n chng trnh
Bi tonthc t
Thit k @6 trnh
0ii thut
#include
Chng trnh
K thut thit k giithut:
Chia tr, quy hochng, hu n, nhnhcn, !
)gAn ngB %6 [email protected] C,CFFEG&E.
Hnh gi
I thut 6hn tchnh gi gii thut7H4 6hJc t(6 c
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I thut chi ! tr" /8 t9ng3#Lu cu7
Cn 6hi gii bi ton c> kch thNc n:
# Phng 6h67 T chi bi ton bn u thnh -4t OK bi ton con ng
2(ng QNi bi ton bn u c> kch thNc nhR hn n: 0ii cc bi ton con ?c cc %Si gii con Tng h?6 %Si gii con %Si gii c
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I thut chi ! tr" /6hn tch3
(
u ")o*n, m,
u +a*o
u ")o*n1, m2,
u +a*o1
u ")o*n2, m2,
u +a*o2
u ")o*nk, mk,
u +a*ok
T ng h p k t qu :
Tnh o t o, o$, -, ok
B)i ton an/ u
B)i ton con
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I thut chi ! tr" /gii thut3solve(n){
if(n nh c th gii c)gii bi ton KQreturnKQ;else{hi! bi ton thnh cc bi ton con
"ch th$c n%& n'&
KQ% solve(n1); gii bi ton con %KQ' solve(n2); gii bi ton con '
*+ng h, cc "-t .u KQ%& KQ'& KQreturnKQ;
/
0
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& 27 #uick Oort# 0ii thut #uick Dort
DY6 Z6 2[$ nOK th1o thJ t= t+ng 2n#\6 2ng k thut chi ! tr"7
Chi 2[$ nOK thnh ] 2[$ con TrNc khi chi 6hi 6hn ho(ch
0ii ] bi ton con DY6 Z6 2[$ bn tri DY6 Z6 2[$ bn 6hi
Tng h?6 kt ^u7
IhAng cn tng h?6
1
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& 27 #uick Oort2
8/13/2019 Thiet ke giai thuat
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H4 6hJc t(6 c
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& 27 M1rg1 Dort# 0ii thut M1rg1 Dort
DY6 Z6 2[$ nOK th1o thJ t= t+ng 2n#\6 2ng k thut chi ! tr"7
Chi 2[$ nOK thnh ] 2[$ con IhAng cn 6hn ho(chE cJ cYt 2[$ OK r %- ]
0ii ] bi ton con DY6 Z6 2[$ bn tri I# DY6 Z6 2[$ bn 6hi I#]
Tng h?6 kt ^u7
Tr4n kt ^u /th1o thJ t=3 c
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& 27 M1rg1 Dort$
8/13/2019 Thiet ke giai thuat
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H4 6hJc t(6 c
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5i t67 T- 6hn t tr4i# Cho -ng n6hn t# Phn t tr4i7 6hn t Zu`t hin nhiu hn n,]
%n# T- 6hn t tr4i c th! Oo Onh dd hojc d
# 0?i 87 Chi -ng thnh ] -ng con
&
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0i- ! tr"# TrSng h?6 jc bit c
8/13/2019 Thiet ke giai thuat
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& 2# T- ki- nh" 6hn trn -4t 2[$ [ OY6 Z6
T- 6hn t c> gi tr"trong -ng n6hn t: Phn t
u tin c> Q" tr -: Tr Q Q" tr t- th`$E nu khAng t-th`$ tr Q .# I thut gi- ! tr"
T- 6hn t giB
Do OnhQNi 6hn t giB )u bfng nhuTr Q Q" tr giB )unhR hn T- n tri )u%Nn hnT- n 6hi
Tr Q .
(
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I thut ^u$ %ui /8 t9ng3# 0ii bi ton tKi u
T- -4t +/i gii t0i 1utrong OK cc %Si gii Mi +/i giig- thnh nthnh 2h3n: #u trnh Z$ 2=ng -4t %Si gii ?c Z1- nh
^u trnh t- nthnh 6hn: Mi thnh 6hn?c t- ki- trong bNc:
Cc 415c6hi c> 6ng gi0ng nhau: p -i bNcE t c> th! 2W 2ng chXn %= -4t
thnh 6hn: Du khi th=c hin < nbNc t ?c %Si gii
0
1
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I thut ^u$ %ui /6hng 6h63# Phng 6h6
&'t c(n /brut1 qorc13 T- ht t`t c cc %Si gii H4 6hJc t(6 thSi gin %$ th
)hnh cn /brnch n2 boun23 Ch t- nhBng %Si gii c> %?i Ci tin thSi gin th=c hin
1
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&'t c(n /8 t9ng3#s t9ng7
0n giKng chi ! tr" nhng Z$ 2=ng %Si gii t 2Ni %n trongkhi chi ! tr" % 6hn tch t trn ZuKng
# M4t 6hng n,%Si gii C7 0- nthnh 6hn CE C]E .E Cn
# p -i bNc iE c> -4t OK %= chXn cho thnh 6hn i: ChXn -4t gi tr" no > cho thnh 6hn i 0Xi ^u$ ! t- thnh 6hn i F
*
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$3
B c i*
B c i4
C5i6 7 B c i4
C5i6 7 $ B c i4
C5i6 7 k
B c i t8m th)nh ph n th i c a 9 i gi i C
: a ch n
: a ch n $ : a ch n k
&'t c(n /6hn tch3
$
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&'t c(n /gii thut3search(int i){
if(i 0 n)
Kie1 t2!& 3o 3nh l4i gii 5$i ccl4i gii hi6n c 74i gii t8i u
else{
9o2 (: l! ch :; 7! ch
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& 27 bi ton v hu#&`n 7
5n cS Qu c> kch thNc vZv Hjt v con hu Oo cho chUng khAng +n nhu
$$
$%
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& 27 bi ton v hu
$%
$&
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& 27 bi ton v hu
$&
$'
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&'t c(n /gii thut3
try(int i){ for"%B1 {
cu2C,o3 " if(3!9e(cu2C,o3)) {
3!5e(cu2C,o3)if(i D n)
[email protected](iE%)
else,2int(3olution) c!ncel(cu2C,o3)
/ /
/
$'
$(
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)hnh cn# Ci tin gii thut ^u$ %ui Q't c(n
T(i -i bNcE t OV Z1- Z't Z1- c> nn i bNc
k ti6 nB h$ khAng &ic Z1- Z't 2= trn khi ni78 cn c
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&'t c(n QO )hnh cnVt c n Nhnh c n
else{
for(: 7 c! i){=i> :;
3e!2ch(i E %);
=i> null;
/
/
else{
for(: 7 c! i) tnh cFn cho 7 :
GH I-, cc 7 theo cFn
for(: 7 c! i) {
if(cn ca j cn tt){
c=i> :;3e!2ch (i E %);
=i> null;
/
/
/
$0
$1
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I thut hu +n /gr112$3# Mc ch7
T- -4t %Si gii tKt trong thSi gin ch`6 nhn ?c /4
6hJc t(6 thJc th$ Q %$ th3#s t9ng Chi ^u trnh t- %Si gii thnh nhiu bNc nh k thut
^u$ %ui#&Ni -i bNc
DY6 Z6 cc %= chXn cho bNc > th1o thJ t= no > wc>%?ix /t+ng 2n hojc gi- 2n tl$ th1o cch %6 %un3
ChXn %= chXn tKt nh`t ri i ti6 bNc k /kh9ng quay+ui3
$1
$2
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& 2# M$ rUt tin TM7
@o(i gi`$7 yy:yyy QnE zy:yyy QnE ]y:yyy QnQ y:yyy Qn:
Mi %o(i tin u c> OK %?ng khAng h(n ch: Ihch hng cn rUt -4t OK tin nQn /tnh ch{nn y:yyy QnE h$ nchi ht cho y:yyy3:
Phng n tr tin Oo cho tr < nQn Q OK tS
gi`$ b(c 6hi tr % t nh`t:
$2
%3
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& 2 -$ rUt tin TM /tt3# M$ rUt tin TM7
0Xi _ d /_E _]E _|E _}3 % -4t 6hng n tr tin: _ % OK tS gi`$ b(c yy:yyy QnE _] % OK tS gi`$ b(c
zy:yyy QnE _| % OK tS gi`$ b(c ]y:yyy Qn Q _} %OK tS gi`$ b(c y:yyy Qn: Mc tiu % _ F _] F _| F _} (t nhR nh`t QNi rng
bu4c %7
_~yy:yyyF_]~zy:yyyF_|~]y:yyyF_}~y:yyy d n
%3
#s t9ng7 H! /_ F _] F _| F _}3 nhR nh`t th cc tS gi`$ b(c
-nh gi %Nn 6hi ?c chXn nhiu nh`t 733
%
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& 2 -$ rUt tin TM /tt3
%
#s t9ng7 H! /_ F _] F _| F _}3 nhR nh`t th cc tS gi`$ b(c
-nh gi %Nn 6hi ?c chXn nhiu nh`t 733 TrNc ht t chXn tKi cc tS gi`$ b(c yy:yyy QnE
_ % OK ngu$n %Nn nh`t Oo cho _ ~ yy:yyy n: DK tin cn rUt cn %(i % n _ ~ yyyyy Chu$!n Ong chXn %o(i gi`$ b(c zy:yyy ngE Q cJ
ti6 tc nh th cho cc %o(i -nh gi khcE Q:Q:
%$
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#u$ ho(ch 4ng# Mc ch7
Ci tin thut ton chi ! tr" hojc ^u$ %ui Q't c(n !gi- thSi gin th=c hin
#s t9ng7 @u trB cc kt ^u c K= c"a cc
4i ton con %c9ng th?c truy [email protected]' @6 bng ^u$ ho(ch
%$
%%
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#u$ ho(ch 4ng# @6 bng ^u$ ho(ch
DK chiu d OK bin trong cAng thJc tru$ hi Thit %6 ^u$ tYc in kt ^u Qo bng ^u$ ho(ch
Hin cc A khAng 6h thu4c trNc Hin cc A 6h thu4c Ou
Tr bng t- kt ^u /thSng ch t- ?c gi tr"3 @n Qt trn bng ! t- %Si gii tKi u
%%
%&
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& 27 tnh t h?6# T h?67
C/nEk3 d nu /ndk3 hojc kdy C/nEk3 d C/nE k3 F C/nE k3
%&
C(4,2)
C(3,1) C(3,2)
C(2,0) C(2,1) C(2,1) C(2,2)
%'
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& 27 tnh t h?6# H4 6hJc t(6 gii thut ^u$7
T/n3 % thSi gin ! tnh OK t h?6 ch6 k c 6hng trnh ^u$7T/3 d CT/n3 d ]T/n3 F C]de &$ 4 6hJc t(6 ^u %Nn7 T/n3 d /]n3
%'
%(
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& 27 tnh t h?6# #u$ ho(ch 4ng7 T/n3 d /n]3
%
C 0 1 2 3 4
0 1
1 1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
k
n
%0
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Chi ! tr" QO ^u$ ho(ch 4ngChia tr Quy ho ch ng
# ; t ng
Phu
