Giáo trình: Giải thuật và lập trình Lê Minh Hoàng

Λ⊇ ΜΙΝΗ ΗΟℵΝΓ

Β◊ι γι νγ χηυψν đ

ι η χ Σ πη m Η◊ Ν ι, 1999−2002

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Λ ιχ m ν

Τι mυ ν β◊ψ τ λ∫νγ βι τ ν đ ι ϖ ι νη νγ νγ
đ ψ κη⌠ κη ν κηι τι m ι β

ι τη ψ đ χη δ ψ τ ν τνη τρονγ νη νγ ν m τη〈νγ

χ ϖ◊ο η χ τιν η χ ϖ◊ λ π τρνη. Σ ηι υ βι τ ϖ◊ λ∫νγ νηι τ τνη χ α χ〈χ

τη ψ κηνγ νη νγ đ χυνγ χ π χηο τι νη νγ κι ν τη χ θυ β〈υ m◊ χ∫ν λ◊ τ m γ
νοι τηεο κηι τι đ νγ τρν β χ γι νγ χ νγ ϖ ι τ χ〈χη λ◊ m τ νγ
Χυ ν τ◊ι λι υ ν◊ψ đ

χ ϖι τ δ α τρν νη νγ τ◊ι λι υ τηυ τη π đ

νγ σ〈νγ χηο τι

ι τη ψ.

χ τ νηι υ νγυ ν κη〈χ νηαυ, β ι

χνγ σ χ χ α νηι υ τη η τη ψ τρ∫ đ τ νγ γι νγ δ ψ ϖ◊ η χ τ π τ ι Κη ι Πη τηνγ χηυψν Το〈ν−
Τιν,

ι η χ Σ πη m Η◊ Ν ι, χ∫ν τι χη λ◊ νγ

ι τ νγ η π λ ι. Θυα đψ, τι mυ ν γ ι λ ι χ m ν

τ ι χ〈χ đ νγ νγηι π đ đ χ ϖ◊ đ⌠νγ γ⌠π νη νγ  κι ν θυ β〈υ, χ m ν χ〈χ β ν η χ σινη − νη νγ
χον νγ

ι đ τρ χ τι π λ◊m νν χυ ν σ〈χη ν◊ψ.

Dο τη ι γιαν η ν η π, m τ σ

χηυψν đ τυψ đ χ⌠ νη νγ χη α κ π χη νη σ α ϖ◊ đ α ϖ◊ο τ◊ι λι υ.

Β ν đ χ χ⌠ τη τηαm κη ο τηm τρονγ πη ν τρα χ υ. Ρ τ mονγ νη ν đ

χ νη νγ λ ι νη ν ξτ ϖ◊ γ⌠π

 χ α χ〈χ β ν đ ηο◊ν τηι ν χυ ν σ〈χη ν◊ψ.
Τοκψο, 28 τη〈νγ 4 ν m 2003

Λ Μινη Ηο◊νγ

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ι

Μ ΧΛ Χ
ΠΗ Ν 1. ΒℵΙ ΤΟℑΝ ΛΙ Τ Κ⊇ ................................................................................. 1
♣1. ΝΗ Χ Λ Ι Μ Τ Σ

ΚΙ Ν ΤΗ Χ

ΙΣ

Τ

Η Π......................................................................2

1.1. ΧΗ ΝΗ Η Π Λ Π..............................................................................................................................................2
1.2. ΧΗ ΝΗ Η Π ΚΗΝΓ Λ Π...............................................................................................................................2
1.3. ΗΟℑΝ ς ...........................................................................................................................................................2
1.4. Τ Η Π..............................................................................................................................................................3

♣2. ΠΗ

ΝΓ ΠΗℑΠ ΣΙΝΗ (ΓΕΝΕΡΑΤΙΟΝ) ..........................................................................................4

2.1. ΣΙΝΗ ΧℑΧ D℘Ψ ΝΗ ΠΗℜΝ

DℵΙ Ν .........................................................................................................5

2.2. ΛΙ Τ Κ⊇ ΧℑΧ Τ Π ΧΟΝ Κ ΠΗ Ν Τ ............................................................................................................6
2.3. ΛΙ Τ Κ⊇ ΧℑΧ ΗΟℑΝ ς ..................................................................................................................................8

♣3. ΤΗΥ Τ ΤΟℑΝ ΘΥΑΨ ΛΥΙ ................................................................................................................12
3.1. ΛΙ Τ Κ⊇ ΧℑΧ D℘Ψ ΝΗ ΠΗℜΝ

DℵΙ Ν..................................................................................................12

3.2. ΛΙ Τ Κ⊇ ΧℑΧ Τ Π ΧΟΝ Κ ΠΗ Ν Τ ..........................................................................................................13
3.3. ΛΙ Τ Κ⊇ ΧℑΧ ΧΗ ΝΗ Η Π ΚΗΝΓ Λ Π ΧΗ Π Κ ....................................................................................15
3.4. ΒℵΙ ΤΟℑΝ ΠΗℜΝ Τ⊆ΧΗ Σ ...........................................................................................................................16
3.5. ΒℵΙ ΤΟℑΝ Ξ Π Η Υ .....................................................................................................................................18

♣4. Κ ΤΗΥ Τ ΝΗℑΝΗ Χ Ν.................................................................................................................24
4.1. ΒℵΙ ΤΟℑΝ Τ Ι
4.2. Σ

Υ.........................................................................................................................................24

Β∧ΝΓ Ν Τ Η Π ..................................................................................................................................24

4.3. Μ Η⊂ΝΗ Κ ΤΗΥ Τ ΝΗℑΝΗ Χ Ν...........................................................................................................24
4.4. ΒℵΙ ΤΟℑΝ ΝΓ

Ι DΥ Λ ΧΗ ........................................................................................................................25

4.5. D℘Ψ ΑΒΧ ........................................................................................................................................................28

ΠΗ Ν 2. Χ Υ ΤΡ∨Χ D
♣1. ΧℑΧ Β
1.1. ΞℑΧ

ΧΧ

ΛΙ Υ ςℵ ΓΙ Ι ΤΗΥ Τ ............................................. 33

Β Ν ΚΗΙ ΤΙ Ν ΗℵΝΗ ΓΙ Ι ΧℑΧ ΒℵΙ ΤΟℑΝ ΤΙΝ Η Χ...............................34

ΝΗ ΒℵΙ ΤΟℑΝ...................................................................................................................................34

1.2. Τ⊂Μ Χ Υ ΤΡ∨Χ D

ΛΙ Υ ΒΙ Υ DΙ Ν ΒℵΙ ΤΟℑΝ ....................................................................................34

1.3. Τ⊂Μ ΤΗΥ Τ ΤΟℑΝ ........................................................................................................................................35
1.4. Λ Π ΤΡ⊂ΝΗ .....................................................................................................................................................37
1.5. ΚΙ Μ ΤΗ ......................................................................................................................................................37
1.6. Τ Ι

Υ ΧΗ

ΝΓ ΤΡ⊂ΝΗ .............................................................................................................................38

♣2. ΠΗℜΝ Τ⊆ΧΗ ΤΗ Ι ΓΙΑΝ ΤΗ Χ ΗΙ Ν ΓΙ Ι ΤΗΥ Τ .................................................................40
2.1.

ΠΗ Χ Τ Π Τ⊆ΝΗ ΤΟℑΝ Χ Α ΓΙ Ι ΤΗΥ Τ ........................................................................................40

2.2. ΞℑΧ
2.3.

ΝΗ

ΠΗ Χ Τ Π Τ⊆ΝΗ ΤΟℑΝ Χ Α ΓΙ Ι ΤΗΥ Τ ....................................................................40

ΠΗ Χ Τ Π Τ⊆ΝΗ ΤΟℑΝ ς Ι Τ⊂ΝΗ ΤΡ ΝΓ D

ΛΙ Υ ςℵΟ..............................................................43

2.4. ΧΗΙ ΠΗ⊆ ΤΗ Χ ΗΙ Ν ΤΗΥ Τ ΤΟℑΝ...........................................................................................................43

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ιι

♣3.

ΘΥΨ ςℵ ΓΙ Ι ΤΗΥ Τ

3.1. ΚΗℑΙ ΝΙ Μ ς

ΘΥΨ ............................................................................................... 45

ΘΥΨ .............................................................................................................................. 45

3.2. ΓΙ Ι ΤΗΥ Τ

ΘΥΨ .................................................................................................................................. 45

3.3. ς⊆ D ς ΓΙ Ι ΤΗΥ Τ
3.4. ΗΙ Υ Λ Χ Χ Α

♣4. Χ Υ ΤΡ∨Χ D

ΘΥΨ ................................................................................................................ 46

ΘΥΨ ............................................................................................................................. 50

ΛΙ Υ ΒΙ Υ DΙ Ν DΑΝΗ ΣℑΧΗ.......................................................................... 52

4.1. ΚΗℑΙ ΝΙ Μ DΑΝΗ ΣℑΧΗ ............................................................................................................................ 52
4.2. ΒΙ Υ DΙ Ν DΑΝΗ ΣℑΧΗ ΤΡΟΝΓ ΜℑΨ Τ⊆ΝΗ .......................................................................................... 52

♣5. ΝΓ Ν Ξ Π ςℵ ΗℵΝΓ

Ι.............................................................................................................. 58

5.1. ΝΓ Ν Ξ Π (ΣΤΑΧΚ)..................................................................................................................................... 58
5.2. ΗℵΝΓ

Ι (ΘΥΕΥΕ)..................................................................................................................................... 60

♣6. ΧℜΨ (ΤΡΕΕ)........................................................................................................................................ 64
6.1.

ΝΗ ΝΓΗ Α ................................................................................................................................................. 64

6.2. ΧℜΨ ΝΗ ΠΗℜΝ (ΒΙΝΑΡΨ ΤΡΕΕ) ............................................................................................................... 65
6.3. ΒΙ Υ DΙ Ν ΧℜΨ ΝΗ ΠΗℜΝ ........................................................................................................................ 67
6.4. ΠΗ⊃Π DΥΨ Τ ΧℜΨ ΝΗ ΠΗℜΝ.................................................................................................................... 69
6.5. ΧℜΨ Κ_ΠΗℜΝ ................................................................................................................................................ 70
6.6. ΧℜΨ Τ ΝΓ ΘΥℑΤ......................................................................................................................................... 71

♣7. Κ⇑ ΠΗℑΠ ΤΙ Ν Τ , ΤΡΥΝΓ Τ
7.1. ΒΙ Υ ΤΗ Χ D

ςℵ Η Υ Τ ............................................................................. 74

Ι D ΝΓ ΧℜΨ ΝΗ ΠΗℜΝ ............................................................................................... 74

7.2. ΧℑΧ Κ⇑ ΠΗℑΠ ΧΗΟ Χ∧ΝΓ Μ Τ ΒΙ Υ ΤΗ Χ.......................................................................................... 74
7.3. ΧℑΧΗ Τ⊆ΝΗ ΓΙℑ ΤΡ ΒΙ Υ ΤΗ Χ .............................................................................................................. 75
7.4. ΧΗΥΨ Ν Τ

D ΝΓ ΤΡΥΝΓ Τ ΣΑΝΓ D ΝΓ Η Υ Τ ......................................................................... 78

7.5. ΞℜΨ D ΝΓ ΧℜΨ ΝΗ ΠΗℜΝ ΒΙ Υ DΙ Ν ΒΙ Υ ΤΗ Χ............................................................................ 80

♣8. Σ Π Ξ Π (ΣΟΡΤΙΝΓ) ........................................................................................................................ 82
8.1. ΒℵΙ ΤΟℑΝ Σ Π Ξ Π...................................................................................................................................... 82
8.2. ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π ΚΙ Υ ΧΗ Ν (ΣΕΛΕΧΤΙΟΝΣΟΡΤ)..................................................................... 84
8.3. ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π Ν Ι Β Τ (ΒΥΒΒΛΕΣΟΡΤ)................................................................................. 85
8.4. ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π ΚΙ Υ ΧΗ∪Ν......................................................................................................... 85
8.5. ΣΗΕΛΛΣΟΡΤ................................................................................................................................................... 87

8.6. ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π ΚΙ Υ ΠΗℜΝ Ο Ν (ΘΥΙΧΚΣΟΡΤ).................................................................. 88
8.7. ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π ΚΙ Υ ςΥΝ
8.8. Σ Π Ξ Π Β ΝΓ ΠΗ⊃Π
8.9. Τ⊆ΝΗ Ν

ΝΓ (ΗΕΑΠΣΟΡΤ) ...................................................................... 92

Μ ΠΗℜΝ ΠΗ Ι (DΙΣΤΡΙΒΥΤΙΟΝ ΧΟΥΝΤΙΝΓ) ............................................. 95

ΝΗ Χ Α ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π (ΣΤΑΒΙΛΙΤΨ) ................................................................. 96

8.10. ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π Β ΝΓ Χ Σ (ΡΑDΙΞΣΟΡΤ).......................................................................... 97
8.11. ΤΗΥ Τ ΤΟℑΝ Σ Π Ξ Π ΤΡ Ν (ΜΕΡΓΕΣΟΡΤ).................................................................................... 102
8.12. ΧℵΙ

Τ ..................................................................................................................................................... 105

8.13. ℑΝΗ ΓΙℑ, ΝΗ Ν Ξ⊃Τ............................................................................................................................ 112

♣9. Τ⊂Μ ΚΙ Μ (ΣΕΑΡΧΗΙΝΓ) ............................................................................................................. 116

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