ctdl-hash

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Bi ging Cu trc d liu 1

Ging vin:Vn Ch Nam Nguyn Th Hng Nhung ng Nguyn c Tin

Kenneth H.Rosen, Ton ri rc ng dngtrong Tin hc, ltb. 5, nxb. Gio Dc, 2007,tr. 131 -143.

Mark A. Weiss, Data Structures &Algorithm Analysis in C++, 2nd edition,

Addision Wesley, 1998, p. 41 67. Nguyn Tri Tun, Hash table, Bi ging

Cu trc d liu, i hc Khoa hc Tnhin, 2007.

HCMUS - 2008 Bi ging Cu trc d liu 1 Vn Ch Nam Nguyn Th Hng Nhung ng Nguyn c Tin 2

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Gii thiu

Hm bm

Gii quyt ng

Bi tp


Gi s ang lm vic vi h thng qun lInternet cho 10 triu ngi dng.

Mi ln tm kim mt ngi chi phl bao nhiu?

Dung lng b nh cn s dng lbao nhiu?


Gii thiu Hm bm Gii quyt ng

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S php ton trung bnh s dng l baonhiu? Gi s di tn l 8. Ln 1: So snh 1 k t u Ln 2: So snh 1 k t u Ln 23: So snh ton b 8 k t

Cng gn vi kt qu, cng phi so snhnhiu k t trong chui tn.

S php so snh: 23

184 (= 23 x 8). Vi php hash, ch cn 8 php ton!



Gi s kch thc ti a d liu l c nh.

Cch lm thng thng: ghi tun t dliu. Mi thao tc tm kim, sp xp thchin trn d liu tun t ny (c th lmtrn index).

Liu c cch no xc nh trc c vtr ca mt entry mi? Hash!



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Vn : Cho trc 1 tp S gm cc phnt c c trng bi gi tr kha. Trngi tr cc kha ny c quan h th t. Tchc S nh th no tm kim 1 phn tc kha k cho trc c phc tp t nhttrong gii hn b nh cho php?

tng: Bin i kha k thnh mt s

(bng hm hash) v s dng s ny nhl a ch tm kim trn bng d liu.





1

2

999

1000

405

406

VCNam

NTHNhung

NTin

VCNam

NTHNhung

NTin

+84.91.2345678

+84.90.9345678

+84.95.8345678

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Chi ph tm kim trung bnh: O(1)

Chi ph tm kim trong trng hp xunht: O(n) (rt t gp).



nh ngha: l hm bin i kha k caphn t thnh a ch trong bng bm.

V d: H(k) = k mod M.

Tng qut v php bin i kha: L 1nh x thch hp t tp cc kha U votp cc a ch A.

H: UA

k a = h(k)



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Tp cc gi tr kha (U) c th ln hn rtnhiu so vi s kha thc t (K) rt nhiu.

V d: Qun l danh sch 1000 sinh vin,m sinh vin gm 7 ch s.

C U = 107 kha so vi K = 1000.



Tp U

Tp K



1. 2.3

.10.9. 8.7.

6. 5.4

.

1

2

3

4

5

6

7

8

9

10

3

4

8

10

T

Key Data

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k1, k

2 K:

k1 k2, H(k1) = H(k2)



Tp U

Tp K

1.

2

.

3.10.

9.

8.

7.6. 5.

4.

T

H(3)

H(4)

H(2) = H(8)

H(10)

Tnhton

nhanh.

Cc khaphn b u.

t xy rang.



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Xt li v d v danh sch sinh vin:

Vi kch thc bng l M = 1000, ta cth chn hm bm nh sau:

H(k) = k mod M.

Kha ny tha mn yu cu tnh tonnhanh v tri u trn bng.



Mc ch ban u ca bm (hash) chnh l sinh ra cc gi tr ngu nhin.

tng: bm nh cc gi tr v trn lnvi nhau c trng thi hn lon, t s c c gi tr ngu nhin.

Ln u tin c a ra bi Hans PeterLuhn IBM vo nm 1953.



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Phng php ni kt (chaining)

Phng php a ch m (Open-addressing)



ng vi mi a ch ca bng, ta c mtdanh sch lin kt cha cc phn t ckha khc nhau m c cng a ch .

Ta s c danh sch (bng bm) gm Mphn t cha a ch u ca cc danh

sch lin kt.


Phng php XL ng PP Ni kt

PP a ch m Bi tp

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Phng php XL ng PP Ni kt PP a ch m

Bi tp

1

2

999

1000

405

406

VCNam

NTHNhung

NTin

VCNam

NTHNhung

NTin

+84.91.2345678

+84.90.9345678

+84.95.8345678

TMHuTMHu +84.95.6543210

Tn gi khc: Phng php d

Phng php th

tng: Khi ng xy ra, ta s th tm n v tr k

tip no trong bng cho n khi tm thy vtr no cn trng.


Phng php XL ng PP Ni kt

PP a ch m Bi tp

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Phng php d tuyn tnh (linear probing)

Phng php d bc 2 (Quadratic probing)

Phng php bm kp (Double hashing)


Phng php XL ng PP Ni kt PP a ch m

Bi tp


Phng php XL ng PP a ch m

PP d tuyn tnh D bc 2 & bm kp

VCNam

NTHNhung

NTin

VCNam

NTHNhung

NTin

+84.91.2345678

+84.90.9345678

+84.95.8345678

TMHu TMHu +84.95.6543210

1

2

406

407

405

999

1000

tng:

H(k, i) = (H(k) + i) mod M

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Phng php d bc 2:

H(k, i) = (H(k) + i2) mod M

Phng php bm kp:

H(k, i) = (H1(k) + i*H2(k)) mod M


Phng php XL ng PP a ch m

D bc 2 & bm kp

Bi tp

n gin khi ci t.

S dng cu trc d liu c bn.

Phng php a ch m gii quyt cng nhng li c th gy ra ng mi.

Phng php ni kt khng b nh hngv tc khi mng gn y.

t tn b nh khi mng tha (t phn t).


Phng php XL ng Bi tp

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Phng php XL ng Bi tp


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