NHDT_TRR2

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BI TP N THI MN TON RI RC

Cu hi 1 Cho n th v hng G = gm 10 nh c biu din di dng danh sch k nh sau: Ke(1) = 2, 9, 10 Ke(6) = 4, 5, 7 Ke(2) = 1, 3, 4, 8, 9, 10 Ke (7) = 4, 6, 8 Ke(3) = 2, 4, 5, 10 Ke (8) = 2, 4, 7, 9 Ke(4) = 2, 3, 5, 6, 7, 8 Ke (9) = 1, 2, 8, 10 Ke (5) = 3, 4, 6 Ke (10)= 1, 2, 3, 9

Hy thc hin: a) Tm deg(u) vi mi uV? b) Hy biu din th G = di dng ma trn k? c) Hy biu din th G = di dng danh sch cnh?

Cu hi 2 Cho n th v hng G = gm 10 nh v 20 cnh c biu din di dng danh sch cnh nh sau:

nh u nh cui nh u nh cui 1 2 5 7 1 5 5 9 1 8 5 10 1 10 6 7 2 3 6 10 2 4 7 8 2 6 7 9 4 6 7 10 4 8 8 9 5 6 9 10

Hy thc hin:

a) Tm deg(u) vi mi uV? b) Hy biu din th G = di dng ma trn k? c) Hy biu din th G = di dng danh sch k?

Cu hi 3 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 1 0 1 1 0 0 2 0 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 1 1 1 0 0 4 1 1 1 0 1 1 1 1 0 0 5 1 0 0 1 0 1 1 1 0 0 6 0 1 1 1 1 0 0 1 0 0 7 1 0 1 1 1 0 0 1 0 0 8 1 0 1 1 1 1 0 0 0 0 9 0 0 0 0 0 0 0 0 0 1


0 0 0 0 0 0 0 0 0 1 0 Hy thc hin:

a) Tm deg(u) vi mi uV? (Khng LT) b) Hy biu din th G = di dng danh sch cnh? c) Hy biu din th G = di dng danh sch k?

Cu hi 4 Cho a th v hng G = gm 10 nh v 20 cnh c biu din di dng danh sch cnh nh sau:


Hy thc hin:

a) Tm deg(u) vi mi uV? b) Hy biu din th G = di dng ma trn k? c) Tm s ng i di 2 trn th G t nh 1 n cc nh 3, 7 v 10?

Cu hi 5 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 2 0 2 0 0 0 0 0 0 2 2 0 1 1 1 0 0 0 0 0 3 0 1 0 1 1 0 0 0 0 0 4 2 1 1 0 2 0 0 0 0 0 5 0 1 1 2 0 2 1 0 0 0 6 0 0 0 0 2 0 0 2 0 0 7 0 0 0 0 1 0 0 1 0 0 8 0 0 0 0 0 2 1 0 1 2 9 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 0

Hy thc hin: a) Tm deg(u) vi mi uV? (Khng LT) b) Hy biu din th G = di dng danh sch cnh? c) Tm s ng i t nh 4 n cc nh 1, 5 v 9?

Cu hi 6 Cho n th c hng G = gm 10 nh c biu din di dng danh sch k nh sau:

Ke(1) = 4, 10 Ke (6) = 1, 4, 7 Ke(2) = 4, 5, 6 Ke (7) = 3, 9 Ke(3) = 8 Ke (8)= 7, 9 Ke(4) = 2, 10 Ke(9) = 8


Ke (5) = 7, 8 Ke(10) = 1, 2

Hy thc hin: a) Tm deg+(u), deg-(u) vi mi uV? b) Hy biu din th G = di dng ma trn k? c) Hy biu din th G = di dng danh sch cnh?

Cu hi 7 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 1 1 0 0 0 5 0 0 0 0 0 1 0 0 0 0 6 0 0 0 0 0 0 1 1 0 0 7 0 0 0 1 0 0 0 1 0 0 8 1 1 0 0 0 0 0 0 0 0 9 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0

Hy thc hin: a) Tm deg+(u), deg-(u) vi mi uV? b) Hy biu din th G = di dng danh sch k? c) Hy biu din th G = di dng danh sch cnh?

Cu hi 8 Cho n th c hng G = gm 10 nh v 20 cnh c biu din di dng danh sch cnh nh sau:


Hy thc hin: a) Tm deg+(u), deg-(u) vi mi uV? b) Hy biu din th G = di dng danh sch k? c) Hy biu din th G = di dng ma trn k?



1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 1 1 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 0 0 1 1 0 0 0 4 1 1 0 0 1 0 0 0 0 0 5 0 1 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 1 0 0 0 7 0 0 1 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm s thnh phn lin thng ca th G,

ch r kt qu ti mi bc thc hin theo thut ton?



1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 1 1 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 0 0 1 1 0 0 0 4 1 1 0 0 1 0 0 0 0 0 5 0 1 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 1 0 0 0 7 0 0 1 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm s thnh phn lin thng ca th G,

ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 11 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0 5 0 1 1 1 0 0 0 0 0 0 6 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm s thnh phn lin thng ca th G,


1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0 5 0 1 1 1 0 0 0 0 0 0 6 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0

Hy thc hin:


a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm s thnh phn lin thng ca th G,


1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 1 1 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 4 1 1 0 0 1 0 0 0 0 0 5 0 1 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm tt c cc cnh cu ca th G, ch

r kt qu ti mi bc thc hin theo thut ton? Cu hi 14 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 1 1 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 4 1 1 0 0 1 0 0 0 0 0 5 0 1 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm tt c cc cnh cu ca th G, ch r

kt qu ti mi bc thc hin theo thut ton?



1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0 5 0 1 1 1 0 0 0 0 0 0 6 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm tt c cc nh tr ca th G, ch r

kt qu ti mi bc thc hin theo thut ton? Cu hi 16 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0 5 0 1 1 1 0 0 0 0 0 0 6 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm tt c cc nh tr ca th G, ch r

kt qu ti mi bc thc hin theo thut ton? Cu hi 17 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 0 0 0 0 1 1 2 1 0 1 1 0 0 0 1 1 1 3 0 1 0 1 1 0 0 0 0 1 4 0 1 1 0 1 1 1 1 0 0 5 0 0 1 1 0 1 0 0 0 0 6 0 0 0 1 1 0 1 0 0 0 7 0 0 0 1 0 1 0 1 0 0 8 0 0 0 1 0 0 1 0 1 0 9 1 1 0 0 0 0 0 1 0 1


0 1 1 1 0 0 0 0 0 1 0 Hy thc hin:

a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm mt ng i c t cnh nht t nh 1

n nh 7 ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 18 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 1 0 1 0 0 5 1 0 0 0 0 1 1 0 1 1 6 0 1 0 1 1 0 1 0 0 1 7 0 0 0 0 1 1 0 1 1 1 8 0 0 0 1 0 0 1 0 1 0 9 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm mt ng i t cnh nht t nh 3 n

nh 9 ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 19 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 0 0 0 0 1 1 2 1 0 1 1 0 0 0 1 1 1 3 0 1 0 1 1 0 0 0 0 1 4 0 1 1 0 1 1 1 1 0 0 5 0 0 1 1 0 1 0 0 0 0 6 0 0 0 1 1 0 1 0 0 0 7 0 0 0 1 0 1 0 1 0 0 8 0 0 0 1 0 0 1 0 1 0 9 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm cy bao trm ca th G, ch r kt

qu ti mi bc thc hin theo thut ton?



1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 1 0 1 0 0 5 1 0 0 0 0 1 1 0 1 1 6 0 1 0 1 1 0 1 0 0 1 7 0 0 0 0 1 1 0 1 1 1 8 0 0 0 1 0 0 1 0 1 0 9 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm cy khung ca th G, bt u t u = 3 ch r kt qu ti mi bc thc hin theo thut ton?


1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 1 1 0 0 0 5 0 0 0 0 0 1 0 0 0 0 6 0 0 0 0 0 0 1 1 0 0 7 0 0 0 1 0 0 0 1 0 0 8 1 1 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm mt ng i t cnh nht t nh

2 n nh 8 ca th G, ch r kt qu ti mi bc thc hin theo thut ton?



1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0 0 0 3 0 1 0 0 0 0 0 1 1 0 4 0 1 0 0 0 0 0 0 0 1 5 0 0 0 0 0 1 1 0 0 0 6 0 0 0 0 1 0 1 1 0 0 7 0 0 1 0 0 0 0 1 1 0 8 0 0 0 0 1 1 1 0 1 0 9 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) Chng minh rng G l th lin thng yu nhng khng lin thng mnh?


1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 1 1 0 0 0 5 0 0 0 0 0 1 0 0 0 0 6 0 0 0 0 0 0 1 1 0 0 7 0 0 0 1 0 0 0 1 0 0 8 1 1 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng chng minh rng G l th lin

thng mnh? Cu hi 24 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 0 0 1 1 0 4 0 1 0 0 0 0 0 0 0 1 5 0 0 0 0 0 1 1 0 0 0 6 0 0 0 0 1 0 1 1 0 0 7 0 0 1 0 0 0 0 1 1 0 8 0 0 0 0 1 1 1 0 1 0 9 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G?


b) S dng thut ton duyt theo chiu su tm tt c cc thnh phn lin thng mnh ca th G, ch r kt qu ti mi bc thc hin theo thut ton?

Cu hi 25 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau

1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 0 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 0 1 0 0 0 0 0 7 0 0 0 0 1 0 0 1 1 1 8 1 0 0 0 1 0 1 0 0 1 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0

Hy thc hin: a) Pht biu iu kin cn v mt th v hng l th Euler? b) Chng minh th G cho l th Euler?


1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 1 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 1 1 0 1 0 0 0 7 0 0 0 0 1 1 0 1 1 0 8 1 0 0 0 1 0 1 0 0 0 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0

Hy thc hin: a) Pht biu iu kin mt th v hng l th na Euler? b) Chng minh th G cho l th na Euler?


1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 0 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 0 1 0 0 0 0 0 7 0 0 0 0 1 0 0 1 1 1 8 1 0 0 0 1 0 1 0 0 1 9 0 0 0 0 1 0 1 0 0 0


0 1 0 0 0 1 0 1 1 0 0 Hy thc hin:

a) Trnh by thut ton tm mt chu trnh Euler ca th? b) p dng thut ton, tm mt chu trnh Euler ca th G cho bt u t nh 1,

ch r kt qu ti mi bc thc hin theo thut ton Cu hi 28 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau

1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 1 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 1 1 0 1 0 0 0 7 0 0 0 0 1 1 0 1 1 0 8 1 0 0 0 1 0 1 0 0 0 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton tm mt ng i Euler ca th? b) p dng thut ton, tm mt ng i Euler ca th G cho, ch r kt qu ti

mi bc thc hin theo thut ton Cu hi 29 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 4 1 0 1 0 0 0 0 0 2 4 0 1 0 1 0 0 0 0 0 3 1 1 0 1 0 0 1 0 0 0 4 0 0 1 0 0 1 2 0 0 0 5 1 1 0 0 0 0 0 1 1 0 6 0 0 0 1 0 0 1 0 0 0 7 0 0 1 2 0 1 0 0 0 0 8 0 0 0 0 1 0 0 0 2 1 9 0 0 0 0 1 0 0 2 0 1 0 0 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Pht biu iu kin cn v mt th v hng l th Euler? b) Chng minh th G cho l th Euler?


1 2 3 4 5 6 7 8 9 0 1 0 2 0 2 0 0 0 0 0 0 2 2 0 1 1 0 0 0 0 0 0 3 0 1 0 1 1 0 0 0 0 0 4 2 1 1 0 2 0 0 0 0 0 5 0 0 1 2 0 2 1 0 0 0


6 0 0 0 0 2 0 0 2 0 0 7 0 0 0 0 1 0 0 1 0 0 8 0 0 0 0 0 2 1 0 1 2 9 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 0

Hy thc hin: a) Pht biu iu kin mt th v hng l th na Euler? b) Chng minh th G cho l th na Euler?


1 2 3 4 5 6 7 8 9 0 1 0 4 1 0 1 0 0 0 0 0 2 4 0 1 0 1 0 0 0 0 0 3 1 1 0 1 0 0 1 0 0 0 4 0 0 1 0 0 1 2 0 0 0 5 1 1 0 0 0 0 0 1 1 0 6 0 0 0 1 0 0 1 0 0 0 7 0 0 1 2 0 1 0 0 0 0 8 0 0 0 0 1 0 0 0 2 1 9 0 0 0 0 1 0 0 2 0 1 0 0 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton tm mt chu trnh Euler ca th? b) p dng thut ton, tm mt chu trnh Euler ca th G cho bt u t nh 6,

ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 32 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 2 0 2 0 0 0 0 0 0 2 2 0 1 1 0 0 0 0 0 0 3 0 1 0 1 1 0 0 0 0 0 4 2 1 1 0 2 0 0 0 0 0 5 0 0 1 2 0 2 1 0 0 0 6 0 0 0 0 2 0 0 2 0 0 7 0 0 0 0 1 0 0 1 0 0 8 0 0 0 0 0 2 1 0 1 2 9 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 0

Hy thc hin: a) Trnh by thut ton tm mt ng i Euler ca th? a) p dng thut ton, tm mt ng i Euler ca th G cho, ch r kt qu ti

mi bc thc hin theo thut ton?


Cu hi 33 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau

1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 1 1 0 0 0 5 0 0 0 0 0 1 0 0 0 0 6 0 0 0 0 0 0 1 1 0 0 7 0 0 0 1 0 0 0 1 0 0 8 1 1 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0

Hy thc hin: a) Pht biu iu kin cn v mt th c hng l th Euler? b) Chng minh th G cho l th Euler?



1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 0 0 0 2 0 0 1 1 0 1 0 0 0 0 3 0 0 0 1 0 0 0 0 0 0 4 0 0 0 0 0 1 1 0 0 0 5 0 0 0 0 0 0 0 1 1 0 6 0 0 0 0 1 0 1 0 0 0 7 0 0 0 0 0 0 0 1 0 1 8 1 0 0 0 0 0 0 0 0 0 9 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

Hy thc hin:

a) Pht biu iu kin mt th cos hng l th na Euler? b) Chng minh th G cho l th na Euler?


c) Cu hi 35 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau

1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 1 1 0 0 0 5 0 0 0 0 0 1 0 0 0 0 6 0 0 0 0 0 0 1 1 0 0 7 0 0 0 1 0 0 0 1 0 0 8 1 1 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton tm mt chu trnh Euler ca th? b) p dng thut ton, tm mt chu trnh Euler ca th G cho bt u t nh 1,

ch r kt qu ti mi bc thc hin theo thut ton?



1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 1 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 0 1 0 1 0 0 0 7 0 0 0 0 1 0 0 1 1 1 8 1 0 0 0 1 0 1 0 0 0 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0

Hy thc hin: a) Trnh by thut ton tm mt ng i Euler ca th? b) p dng thut ton, tm mt ng i Euler ca th G cho, ch r kt qu ti

mi bc thc hin theo thut ton? Cu hi 37 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 0 0 0 0 1 1 2 1 0 1 1 0 0 0 1 1 1 3 0 1 0 1 1 0 0 0 0 1 4 0 1 1 0 1 1 1 1 0 0 5 0 0 1 1 0 1 0 0 0 0 6 0 0 0 1 1 0 1 0 0 0 7 0 0 0 1 0 1 0 1 0 0 8 0 1 0 1 0 0 1 0 0 1 9 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton quay lui tm mt chu trnh Hamilton ca th? b) p dng thut ton quay lui tm mt chu trnh Hamilton ca th G cho bt u

t nh 1, khi c nhiu kh nng la chn cc nh lun u tin chn nh c ch s nh nht v gii thch cc bc thc hin?


1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 1 1 0 0 0 5 1 0 0 0 0 1 1 1 0 0 6 0 0 0 0 0 0 1 1 0 0 7 0 0 0 0 1 0 0 1 0 0 8 1 0 0 0 1 0 0 0 0 0


9 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton quay lui tm mt chu trnh Hamilton ca th? b) p dng thut ton quay lui tm mt chu trnh Hamilton ca th G cho bt u

t nh 1, khi c nhiu kh nng la chn cc nh lun u tin chn nh c ch s nh nht v gii thch cc bc thc hin?

Cu hi 39 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 7

1 0 20 5 17 2 20 0 1 1 3 5 0 25 3 10 4 17 1 25 0 15 5 3 15 0 1 6 10 1 0 1 7 1 1 0

Hy thc hin: a) Trnh by thut ton Dijkstra tm ng i ngn nht xut pht t nh u V? b) p dng thut ton Dijkstra, tm ng i ngn nht t nh 1 n nh 7 ca th

G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 40 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 7

1 0 10 15 20 1 2 0 3 30 3 0 25 3 45 4 10 25 0 35 5 2 3 0 3 6 1 1 0 25 7 1 30 1 0


G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 41 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 7

1 0 15 1 9

2 0 8 3 0 4 1 4 7 0 1 5 10 2 0


6 14 2 0 7 2 0


G cho, ch r kt qu ti mi bc thc hin theo thut ton Cu hi 42 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 7

1 0 25 27 30 2 25 0 1 15 3 0 15 3 1 4 27 15 0 25 5 1 3 25 0 6 1 0 1 7 15 1 0

Hy thc hin:

a) Trnh by thut ton Dijkstra tm ng i ngn nht xut pht t nh u V? b) p dng thut ton Dijkstra, tm ng i ngn nht t nh 2 n nh 6 ca th

G cho, ch r kt qu ti mi bc thc hin theo thut ton Cu hi 43 Cho n th G = gm 6 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 1 0 15 5 20 2 1 0 17 10 3 0 2 50 4 15 1 0 70 5 20 30 10 0 10 6 18 23 20 0

Hy thc hin: a) Trnh by thut ton Floyd tm ng i ngn nht gia cc cp nh trong th? b) p dng thut ton Floyd, tm ng i ngn nht gia cc cp nh (1, 2), (1, 3), (3,

4), (4, 2) ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 44 Cho n th G = gm 6 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 1 0 1 15 20 2 1 0 5 30 3 15 0 1 7 4 1 0 20 20 5 5 20 0 5 6 20 30 20 7 5 0

Hy thc hin: a) Trnh by thut ton Floyd tm ng i ngn nht gia cc cp nh trong th?


b) p dng thut ton Floyd, tm ng i ngn nht gia cc cp nh (1, 2), (1, 6), (2, 5), (5, 6) ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton?

Cu hi 45 Cho n th v hng G = gm 10 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 7 8 9 0 1 0 4 1 1 2 9 5 4 7 2 4 0 2 9 1 5 6 3 1 2 0 7 6 6 1 1 9 4 1 7 0 1 7 6 5 2 9 1 0 3 4 3 1 2 6 9 1 6 7 3 0 3 1 1 5 7 5 6 4 3 0 4 5 8 5 1 6 3 1 4 0 4 2 9 4 6 1 1 1 5 4 0 4 0 7 9 2 5 2 4 0

Hy thc hin: a) Trnh by thut ton Kruskal tm cy khung nh nht trn th v hng, lin thng,

c trng s? b) p dng thut ton Kruskal, tm cy khung nh nht ca th G cho, ch r kt qu

ti mi bc thc hin theo thut ton?


1 2 3 4 5 6 7 8 9 0 1 0 4 1 1 2 9 5 4 7 2 4 0 2 9 1 5 6 3 1 2 0 7 6 6 1 1 9 4 1 7 0 1 7 6 5 2 9 1 0 3 4 3 1 2 6 9 1 6 7 3 0 3 1 1 5 7 5 6 4 3 0 4 5 8 5 1 6 3 1 4 0 4 2 9 4 6 1 1 1 5 4 0 4 0 7 9 2 5 2 4 0

Hy thc hin: a) Trnh by thut ton Prim tm cy khung nh nht bt u t nh s = 1 trn th v

hng, lin thng, c trng s? b) p dng thut ton Prim tm cy khung nh nht ca th G cho, ch r kt qu ti

mi bc thc hin theo thut ton?


c) , Cu hi 47 Cho n th v hng G = gm 10 nh c biu din di dng ma trn trng s nh sau

1 2 3 4 5 6 7 8 9 0 1 0 4 8 8 2 9 5 4 7 2 4 0 2 9 7 5 6 3 8 2 0 7 6 6 9 9 9 4 8 7 0 7 7 6 5 2 9 7 0 3 4 3 1 2 6 9 7 6 7 3 0 3 1 1 5 7 5 6 4 3 0 4 5 8 5 9 6 3 1 4 0 4 2 9 4 6 9 1 1 5 4 0 4 0 7 9 2 5 2 4 0

Hy thc hin: a) Trnh by thut ton Kruskal tm cy khung nh nht trn th v hng, lin thng,

c trng s? b) p dng thut ton Kruskal, tm cy khung nh nht ca th G cho, ch r kt qu

ti mi bc thc hin theo thut ton?



1 2 3 4 5 6 7 8 9 0 1 0 4 8 8 2 9 5 4 7 2 4 0 2 9 7 5 6 3 8 2 0 7 6 6 9 9 9 4 8 7 0 7 7 6 5 2 9 7 0 3 4 3 1 2 6 9 7 6 7 3 0 3 1 1 5 7 5 6 4 3 0 4 5 8 5 9 6 3 1 4 0 4 2 9 4 6 9 1 1 5 4 0 4 0 7 9 2 5 2 4 0

Hy thc hin: a) Trnh by thut ton Prim tm cy khung nh nht trn th v hng, lin thng, c

trng s? b) p dng thut ton Prim tm cy khung nh nht bt u t nh s = 3 ca th G

cho, ch r kt qu ti mi bc thc hin theo thut ton?


Cu hi 49 Cho n th G = gm 10 nh c biu din di dng ma trn k nh sau

1 2 3 4 5 6 7

1 0 1 1 0 0 0 0

2 1 0 0 1 0 0 0 3 1 0 0 1 0 0 0 4 0 1 1 0 1 1 0 5 0 0 0 1 0 1 1 6 0 0 0 1 1 0 1 7 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton t mu th vi s mu cn s dng t nht? b) p dng thut ton trn tm cch t mu th G cho vi s mu t nht, ch r kt

qu ti mi bc thc hin theo thut ton? Cu hi 50 Cho n th G = gm 7 nh c biu din di dng ma trn k nh sau

1 2 3 4 5 6 7

1 0 1 1 1 0 0 0

2 1 0 1 1 0 0 0 3 1 1 0 1 0 0 0 4 1 1 1 0 1 0 0 5 0 0 0 1 0 1 1 6 0 0 0 0 1 0 1 7 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton t mu th vi s mu cn s dng t nht? b) p dng thut ton trn tm cch t mu th G cho vi s mu t nht, ch r kt

qu ti mi bc thc hin theo thut ton?

Cu hi 51 Vit hm c tn l DFS(u : int) trn C/C++ m t thut ton duyt theo chiu su cc nh ca th G = c biu din di dng ma trn k a[ ] [ ]. Cu hi 52 Vit hm c tn l BFS(u : int) trn C/C++ m t thut ton duyt theo chiu rng cc nh ca th G = c biu din di dng ma trn k a[ ] [ ]. Cu hi 53 Vit hm c tn l int TPLT_DFS(int a[ ] [ ]) trn C/C++ tm s thnh phn lin thng ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm DFS(int u) bit m t thut ton duyt theo chiu su cc nh ca th G. Cu hi 54 Vit hm c tn l int TPLT_BFS(int a[ ] [ ]) trn C/C++ tm s thnh phn lin thng ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm BFS(int u) bit m t thut ton duyt theo chiu rng cc nh ca th G. Cu hi 55


Vit hm c tn l T_DFS(int a[ ] [ ]) trn C/C++ tm cy bao trm T[ ] ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm BFS(int u) bit m t thut ton duyt theo chiu su cc nh ca th G. Cu hi 56 Vit hm c tn l T_BFS(int a[ ] [ ]) trn C/C++ tm s thnh phn lin thng ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm BFS(int u) bit m t thut ton duyt theo chiu rng cc nh ca th G. Cu hi 57 Vit hm c tn l EULER(int a[ ] [ ]) trn C/C++ tm chu trnh Euler CE[ ] ca th G = c biu din di dng ma trn k a[ ] [ ], bit rng G l th Euler. Cu hi 58 Vit hm c tn l DIJKSTRA(int u) trn C/C++ tm ng i ngn nht d[v] xut pht t nh u n cc nh v ca th G = c biu din di dng ma trn trng s a[ ] [ ]. Cu hi 59 Vit hm c tn l FLOYD(int a[ ] [ ]) trn C/C++ tm ng i ngn nht d[ ] [ ] gia cc cp nh ca th G = c biu din di dng ma trn trng s a[ ] [ ]. Cu hi 60 Vit hm c tn l PRIM(int a[ ] [ ]) trn C/C++ tm cy khung T[ ] nh nht ca th G = c biu din di dng ma trn trng s a[ ] [ ] bng cch s dng thut ton Prim. Cu hi 61 Vit hm c tn l KRUSKAL(int a[ ] [ ]) trn C/C++ tm cy khung T[ ] nh nht ca th G = c biu din di dng ma trn trng s a[ ] [ ] bng cch s dng thut ton Kruskal.

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