cÁc ThuẬt GiẢi Ị tÔ mÀu ĐỒ

8/14/2019 cc Thut Gii t mu

1/18

T MU TH

ThS. Vnh By

Khoa Cn n h Thn tin

i hc K thut Cng ngh Tp. HCM

1


2/18

BI TON

Cho m t th m n nh. uan h ia nh i v nh

j, k hiu Qhij, l 1 nu nh i c ni vi nh j v 0 nungc li.

to n t ra m t n o t m u t sao c o

khng tn ti hai nh c quan h vi nhau c tchung mt mu vi s mu cn t l t nht?

Ths.V

nh

By

2


3/18

V D

a

a

d

b c

e

b c

de

Ths.V

p

h

p

h

nh

By

T 3 mu t nht cha?

3


4/18

THUT GII T MU TI UBc 1: [T mu] T mu i (i bt u xt t 1) cho nh c bc

ln nht.

Bc 2: [H bc & cm t]2.1. Bc ca nh c t mu i th bc:=0.

Ths.V

2.2. Bc ca n c quan v n c t mu t bc:= bc 1.

nh

By

. . .

Bc 3: Lp li bc 1 cho n khi tt c cc nh u c tmu.

4


5/18

MINH HAb c

e

a

h

b c

aa

b c

d

h

d

h

5

Ths. Vnh By


6/18

V D 2

Mt cng ty c 8 i pht thanh A, B, C, D, E, F, G, H c khongcch (km) c cho trong ma trn sau:

A B C D E F G H

A 0 100 50 30 200 150 40 120

B 0 30 80 120 50 200 150

Ths.V

C 0 120 100 30 80 50

D 0 50 120 150 30

nh

By

F 0 180 150

G 0 50

Do yu cu k thut nn cc i c khong cch 100km khng

H 0

.sng sao cho s trm cn lp lnh nht.

6


7/18

GII UYT

A B C D E F G H

A 0 100 50 30 200 150 40 120

B 0 30 80 120 50 200 150

D 0 50 120 150 30

E 0 200 120 120

F 0 180 150.

a) nh: gm cc i pht thanhb) Cung: ni gia 2 i c khong cch 100km.

G 0 50

H 0

Ta c ma trn quan h (hay th quan h nh sau):A B C D E F G H Bc

A 0 1 0 0 1 1 0 1 4

Ths.V

n

B 1 0 0 0 1 0 1 1 4

C 0 0 0 1 1 0 0 0 2

h

By

E 1 1 1 0 0 1 1 1 6

F 1 0 0 1 1 0 1 1 57G 0 1 0 1 1 1 0 0 4

H 1 1 0 0 1 1 0 0 4


8/18

GII QUYT

(TT

)

A B C D E F G H

A 0 1 0 0 1 1 0 1

B 1 0 0 0 1 0 1 1

2. p dng thut gii t mu

C 0 0 0 1 1 0 0 0

D 0 0 1 0 0 1 1 0

E 1 1 1 0 0 1 1 1

G 0 1 0 1 1 1 0 0H 1 1 0 0 1 1 0 0

A B C D E F G H

B c 4 4 2 3 6 5 4 4

Kt qu:

Mu 1: D, E.

3 3 1 3 0 4 3 3

2 3 1 2 - 0 2 2

, ,

Mu 3: A, G

Mu 4: H

1 0 1 2 - - 1 11 - 0 0 - - 0 1

0 - 0 - - - 0 08

Ths. Vnh By


9/18

V D 3

C 6 i bng A, B, C, D, E, F thi u vng trn (1lt bit rn cc trn u sau x ra:

- A u vi B, E.- B u vi A, F.- C u vi D, F.

Do yu cu th lc, mi i ch c thi u 1 trn

hs.V

nh

B

rong u n. y s p x p c c r n u v o c c u n saocho s tun din ra l t nht.

y

9


10/18

GII QUYT

1. Xc nh th:a) nh: cc trn u.b) Cung: ni gia hai trn u c cng mt i bng tham gia.

Ta c 10 nh: AC, AD, AF, BC, BD, BE, CE, DE, DF, EF.

Ths.V

AC AD AF BC BD BE CE DE DF EF Bc

AC 0 1 1 1 0 0 1 0 0 0 4

nh

By

AF 1 1 0 0 0 0 0 0 1 1 4

BC 1 0 0 0 1 1 1 0 0 0 4

0 1 0 1 0 1 0 1 1 0 5BE 0 0 0 1 1 0 1 1 0 1 5

CE 1 0 0 1 0 1 0 1 0 1 5

10DE 0 1 0 0 1 1 1 0 1 1 6

DF 0 1 1 0 1 0 0 1 0 1 5EF 0 0 1 0 0 1 1 1 1 0 5


11/18

GII QUYT (TT)

AC AD AF BC BD BE CE DE D

F

EF Bc

AC 0 1 1 1 0 0 1 0 0 0 4

AD 1 0 1 0 1 0 0 1 1 0 5

2. p dng thut gii

AF 1 1 0 0 0 0 0 0 1 1 4

BC 1 0 0 0 1 1 1 0 0 0 4

BD 0 1 0 1 0 1 0 1 1 0 5

BE 0 0 0 1 1 0 1 1 0 1 5

t m u CE 1 0 0 1 0 1 0 1 0 1 5DE 0 1 0 0 1 1 1 0 1 1 6

DF 0 1 1 0 1 0 0 1 0 1 5

EF 0 0 1 0 0 1 1 1 1 0 5

Bc 4 5 4 4 5 5 5 6 5 5

4 4 4 4 4 4 4 0 4 4

0 3 3 3 4 4 3 - 4 4

- 2 3 2 0 3 3 - 3 4

11

Ths. Vnh By


12/18

THUT GII THAM LAM (GREEDY)

Bc 1:=

Bc 2:i := i+1

Ths.V

T mu i cho tt c cc nh c th t c.

Bc 3:

nh

By

.

12


13/18

V D

AC AD AF BC BD BE CE DE D

F

EF

AC 0 1 1 1 0 0 1 0 0 0

AD 1 0 1 0 1 0 0 1 1 0

Cho ma trn bn

AF 1 1 0 0 0 0 0 0 1 1

BC 1 0 0 0 1 1 1 0 0 0

BD 0 1 0 1 0 1 0 1 1 0

BE 0 0 0 1 1 0 1 1 0 1

CE 1 0 0 1 0 1 0 1 0 1

DE 0 1 0 0 1 1 1 0 1 1

DF 0 1 1 0 1 0 0 1 0 1Ths

AC AD AF BC BD BE CE DE DF EF

i=1 1 i=1 1 1 i=1 1 1 1

.V

nh

By

AD AF BC BE CE DE DF

i=2 2 i=2 2 2

AF BE CE DE DF

i=3 3 i=3 3 3

13

CE DE DF

i=4 4 i=4 4 4

DE

i=5 5


14/18

THUT GII SP TH T+ THAM LAM

Bc 1:.

i := 0Bc 2:

Ths.V

i := i+1

T mu i cho tt c cc nh c th t c (xt t tri sang).

nh

By

Lp li bc 2 cho n khi tt c cc nh u c t mu.

14


15/18

V D 1

AC AD AF BC BD BE CE DE DF EF Bc

AC 0 1 1 1 0 0 1 0 0 0 4

AD 1 0 1 0 1 0 0 1 1 0 5

AF 1 1 0 0 0 0 0 0 1 1 4

Cho ma trn bn

BC 1 0 0 0 1 1 1 0 0 0 4

BD 0 1 0 1 0 1 0 1 1 0 5

BE 0 0 0 1 1 0 1 1 0 1 5

CE 1 0 0 1 0 1 0 1 0 1 5

DE 0 1 0 0 1 1 1 0 1 1 6

DF 0 1 1 0 1 0 0 1 0 1 5

EF 0 0 1 0 0 1 1 1 1 0 5Ths

DE AD BD BE CE DF EF AC AF BC

i=1 1 i=1 1 1

.V

nh

By

AD BD BE CE DF EF AF BC

i=2 2 i=2 2 2

BD CE DF EF AF BC

i=3 3 i=3 3 3 i=3 3 3 3

15

DF EF BC

i=4 4 i=4 4 4

EF

i=5 5


16/18

V D 2

Mt cuc hi tho c 9 ch a, b, c, d, e, f, g, h, i bit rng ccch sau khn c h din ra tron cn mt bui: ac,

bde, adg, cdf, dfg, egh, ghi.Hy sp xp cc ch vo cc bui sao cho s bui din ra l tT

. hs.V

n

hB

y

16


17/18

GII QUYT

1. Xc nh th:a) nh: cc ch .

bui.

Ta c 9 nh: a, b, c, d, e, f, g, h, i.Ma trn quan h (hay th quan h nh sau):

Ths.

a b c d e f g h i Bc

a 0 1 1 1


a 0 0 1 1 0 0 1 0 0


a 0 0 1 1 0 0 1 0 0 3

nh

By

b 0 1 1

c 0 1 1

d 0 1 1 1

b 0 0 1 1 0 0 0 0

c 0 1 0 1 0 0 0

d 0 1 1 1 0 0

b 0 0 0 1 1 0 0 0 0 2

c 1 0 0 1 0 1 0 0 0 3

d 1 1 1 0 1 1 1 0 0 6

e 0 1 1f 0 1

0 1 1

e 0 0 1 1 0f 0 1 0 0

0 1 1

e 0 1 0 1 0 0 1 1 0 4f 0 0 1 1 0 0 1 0 0 3

1 0 0 1 1 1 0 1 1 617

h 0 1

i 0

h 0 1

i 0

h 0 0 0 0 1 0 1 0 1 3

i 0 0 0 0 0 0 1 1 0 2


18/18

V D 3

Cho ng nm giao thng nh sau trong BE l ng 1 chiu:

AE Yu cu:

1. Xc nh th.

D

2. T mu th.Sao cho ti mi thi im, cc

tuyn lu thng khng giao

B

.

C

18

Ths. Vnh By

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