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TOÁN RÒ I RA C Pha m Tiến So n D à La t, 2005 2 Mu c lu c MO ’̇ D À̂U 6 1 PHÉP D É̂M 9 1 1 Các nguyên lý co bȧ’n cu̇’a phép d̄ếm 9 1 1 1 Nguyên lý tô̇’ng 9 1 1 2 Nguyên lý t́ıch 10[.]

TO ´ AN R ` O . I RA C

Pha.m Tiˆe´n So.n

D - `a La.t, 2005

Mu.c lu.c

1.1 C´ac nguyˆen l´y co ba˙’n cu˙’a ph´ep d¯ˆe´m 9

1.1.1 Nguyˆen l´y tˆo˙’ng 9

1.1.2 Nguyˆen l´y t´ıch 10

1.1.3 Nguyˆen l´y bao h`am-loa.i tr`u 13

1.2 Ho´an vi v`a tˆo˙’ ho p 15

1.3 C´ac thuˆa.t to´an sinh ra ho´an vi v`a tˆo˙’ ho p 20

1.4 Ho´an vi v`a tˆo˙’ ho p suy rˆo.ng 25

1.5 C´ac hˆe sˆo´ nhi th´u.c v`a c´ac d¯ˆo`ng nhˆa´t th´u.c 32

1.6 Nguyˆen l´y chuˆo`ng chim bˆo` cˆau 36

1.6.1 Nguyˆen l´y chuˆo`ng chim bˆo` cˆau (da.ng th´u nhˆa´t) 36

1.6.2 Nguyˆen l´y chuˆo`ng chim bˆo` cˆau (da.ng th´u hai) 37

1.6.3 Nguyˆen l´y chuˆo`ng chim bˆo` cˆau (da.ng th´u ba) 39

2.3 Quan hˆe th´u tu 54

2.4 Quan hˆe tu.o.ng d¯u.o.ng 62

2.5 Bao d¯´ong cu˙’a quan hˆe 69

2.6 Lattice cu˙’a c´ac phˆan hoa.ch 75

2.6.1 Thuˆa.t to´an giao c´ac phˆan hoa.ch 77

2.6.2 Thuˆa.t to´an trˆo.n c´ac phˆan hoa.ch 78

3 D- A.I SˆO´ BOOLE 81 3.1 Lattice 81

3.2 Latiice phˆan bˆo´ 90

3.3 D- a.i sˆo´ Boole 96

3.4 H`am Boole 103

3.5 Biˆe˙’u diˆe˜n c´ac h`am Boole qua hˆe tuyˆe˙’n, hˆo.i v`a phu˙’ d¯i.nh 107

3.6 Biˆe˙’u diˆe˜n tˆo´i thiˆe˙’u cu˙’a h`am Boole 111

3.6.1 Kh´ai niˆe.m 111

3.6.2 Phu.o.ng ph´ap ba˙’n d¯ˆo` Karnaugh 112

4 M ˜A TUYˆE´N T´INH 119 4.1 Mo.˙’ d¯ˆa` u 119

4.1.1 Kh´ai niˆe.m 119

4.1.2 M˜a ph´at hiˆe.n lˆo˜i 120

4.1.3 M˜a su.˙’a sai 121

4.2 C´ac kh´ai niˆe.m 122

4.3 Khoa˙’ng c´ach Hamming 131

4.4 Hˆo.i ch´u.ng 139

4.4.1 Gia˙’i m˜a d`ung ba˙’ng chuˆa˙’n 140

4.5 M˜a ho`an ha˙’o 143

4.6 M˜a Hamming 146

5 D- ˆ` THI.O 149 5.1 C´ac kh´ai niˆe.m 149

5.2 Dˆay chuyˆe` n v`a chu tr`ınh 154

5.3 Chu tr`ınh Hamilton v`a b`ai to´an ngu.`o.i du li.ch 162

5.3.1 Quy tˇa´c t`ım chu tr`ınh Hamilton 164

5.3.2 M˜a Gray 166

5.4 D- u.`o.ng d¯i v`a ma.ch 169

5.4.1 Thuˆa.t to´an 171

5.5 Ma trˆa.n biˆe˙’u diˆe˜n d¯ˆo` thi 173

5.5.1 Ma trˆa.n kˆe` 173

5.5.2 Ma trˆa.n liˆen thuˆo.c 175

5.6 D- ˇa˙’ng cˆa´u gi˜u.a c´ac d¯ˆo` thi 179

5.7 D- ˆo` thi phˇa˙’ng 181

6 C ˆAY 191 6.1 Mo.˙’ d¯ˆa` u 191

6.1.1 C´ac kh´ai niˆe.m 191

6.1.2 M˜a Huffman 192

6.2 Cˆay bao tr`um 197

6.2.1 Thuˆa.t to´an t`ım kiˆe´m theo chiˆe` u rˆo.ng x´ac d¯i.nh cˆay bao tr`um 198

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