1TM KIM & SP XPBi ging Cu trc d liu v Gii thut

Tm kimTun t

Ni dung

Tun t Nh phn

Sp xp Bubble sort Selection sort Insert sort Quick sort

Tm kim3

Tm kim: duyt mt danh sch v ly ra phn t tho tiu chun cho trc.

L thao tc ph bin trn my tnh: L thao tc ph bin trn my tnh: Tm mu tin trong c s d liu Tm kim thng tin trn Internet

Kho st vic tm kim trn mng/danh sch.

Tm kimGii thut

4

Input: Mng A gm n phn t Gi tr x cn tm

Tr v: V tr phn t x trong A hoc 1 nu x khng xut hin

Thao tc c bn: So snh

Tm kim tun tGii thut

5

Gii thut: Ln lt so snh x vi cc phn t ca mng A cho n khi

gp c phn t cn tm, hoc ht mng. V d: A = {1, 25, 6, 5, 2, 37, 40}, x = 6

1 25 6 5 2 37 40

x = 6

x = 6

Dng

1 25 6 5 2 37 40

1 25 6 5 2 37 40

x = 6

Tm kim tun tnh gi

6

nh gi (thao tc so snh): Tt nht: O(1) Xu nht: O(n) Trung bnh:

Him khi xy ra. Ti sao?

Trung bnh: Gi s d liu phn b u, xc sut bt gp x ti mi v tr u nh nhau.

Mi vng lp thc hin 2 thao tc so snh. Ti sao? S thao tc = 2*(1 + 2 + + n) = n + 1 phc tp: O(n)

Tm kim tun tPhn t lnh canh

7

Mi vng lp cn 2 thao tc so snh: Kim tra ht mng Kim tra phn t hin ti c bng x

Phn t lnh canh: t gi tr x vo cui mng Phn t lnh canh: t gi tr x vo cui mng khng cn kim tra iu kin ht mng.

V d: A = {1, 25, 5, 2, 37}, x = 6

Tr v: n nu khng tm thy

1 25 5 2 37 6

Tm kim nh phn8

Khi mng gm cc phn t c sp, tn dng iu kin ny gim s thao tc.

tng: tng: Xt phn t gia A[m] Nu A[m] = x, tr v m Nu A[m] > x, tm trong cc phn t bn tri ca m Nu A[m] < x, tm trong cc phn t bn tri ca m

Tm kim nh phnV d minh ho

9

A = {2, 3, 6, 7, 10, 16, 18}, x = 16

2 3 6 7 10 16 18

[0] [1] [2] [3] [4] [5] [6][0] [1] [2] [3] [4] [5] [6][4] [5] [6]

2 3 6 7 10 16 18

10

Tm kim nh phnChng trnhint BinarySearch(int a[], int n, int x){int l = 0, r = n-1;while (l

Tm kim nh phnBi tp

11

Thc hin vic tm kim i vi cc bi tp sau: A = {1, 2, 6, 26, 28, 37, 40}, x = 40

A = {1, 2, 6, 26, 28, 37, 40}, x = -7

Tm kim nh phnnh gi

12

Mi ln lp, chiu di mng con phi xt c gim so vi mng trc .

Mng ban u c chia ti a k ln vi k =log2n.log2n.

Ti a k vng lp c thc hin trong mi vng lp thc hin 1-2 php so snh.

phc tp: O(log2n)

Mng cn c sp xp trc!!!

Sp xp13

Sp xp: t chc cc phn t trong mt danh sch theo th t.

L bi ton ph bin trn my tnh. L bi ton ph bin trn my tnh. Nhiu gii thut sp xp ra i.

Kho st v nh gi hiu qu mt s gii thut sp xp thng dng da trn mng.

Sp xpGii thut

14

Input: Mng A gm n phn t.

Output: Mt hon v ca A sao cho: A0 A1 An-1 (sp Mt hon v ca A sao cho: A0 A1 An-1 (sp

xp tng dn). Thao tc c bn:

So snh Hon v (i v tr hai phn t)

Sp xpCc gii thut

15

Cc phng php sp xp thng dng: Bubble Sort Selection Sort Insertion Sort Insertion Sort Quick Sort Merge Sort Shell Sort Heap Sort Radix Sort

Bubble sort16

Gii thut: Xut pht t cui (u) dy, i ch cc cp phn t k

cn a phn t nh hn v v tr ng u dyhin hnh.

Sau khng xt n n bc k tip. Ln x l th i s c v tr u dy l i. Lp li cho n khi khng cn cp phn t no xt.

V d: sp xp dy A: 15 2 8 7 3 6 9 17

Bubble sortV d

17

15 2 8 7 3 6 9 17

15 2 8 3 7 6 9 17

15 2 3 8 7 6 9 17

i = 0

i = 0

i = 0

j = 4

j = 3

j = 1

2 15 3 8 7 6 9 17

2 15 3 8 6 7 9 17

2 15 3 6 8 7 9 17

2 3 15 6 8 7 9 17

2 3 15 6 7 8 9 17

i = 1

i = 1

i = 1

i = 2

i = 2

j = 5

j = 4

j = 2

j = 5

j = 3

Bubble sortV d (tt)

18

2 3 6 15 7 8 9 17

2 3 6 7 15 8 9 17

2 3 6 7 8 15 9 17

j = 4

j = 5

j = 6

i = 3

i = 4

i = 5 2 3 6 7 8 15 9 17

2 3 6 7 8 9 15 17

2 3 6 7 8 9 15 17

j = 7i = 6

Bubble sortChng trnh

19

void BubbleSort(int a[], int n){for(int i=0; ii; j--){if(a[j]

Bubble sortBi tp

20

M t tnh trng dy A sau mi bc chy vi thut ton Bubble sort.A = {2, 9, 5, 12, 20, 15, -8, 10}

Bubble sortnh gi

21

Cc gii thut sp xp thng c phc tp tng t nhau.

Cn mt nh gi chi tit: Cc trng hp: xu nht, tt nht, trung bnh Cc trng hp: xu nht, tt nht, trung bnh Cc thao tc:

So snh Gn (quan trng hn v tn nhiu chi ph hn). Lu : mi

thao tc gn v tn 3 php gn

Bubble sortChng trnh

22

void BubbleSort(int a[], int n){for(int i=0; ii; j--){if(a[j]

Bubble sortnh gi

23

S php so snh: khng ph thuc vo tnh trng dy s ban u.

2

0

( 1)( 1)2

n

i

n nn i

=

=

S lng php gn: ty vo kt qu so snh Tt nht: 0 Xu nht:

2

0

3 ( 1)3( 1)2

n

i

n nn i

=

=

Shaker sort Ci tin Bubble sort

24

Nhn xt: Bubble sort c cc khuyt im: Khng nhn din c tnh trng dy c th t hay

khng c th t tng phn. Trong khi phn t nh c a v v tr ng rt

nhanh, th cc phn t ln li c a v v tr ng rt chm.Gii thut Shaker sort ci tin cc khuyt im ny.

Shaker sort Ci tin Bubble sort

25

Ci tin: Duyt mng theo 2 lt t 2 pha khc nhau:

Lt i: y phn t nh v u mng Lt v: y phn t ln v cui mng.

Ghi nhn li nhng on sp.

Shaker sortV d minh ho

26

15 2 8 7 3 6 9 17

15 2 8 3 7 6 9 17

15 2 3 8 7 6 9 17

r =7l = 0

2 15 3 8 7 6 9 17

2 3 15 8 7 6 9 17

2 3 8 15 7 6 9 17

2 3 8 7 15 6 9 17

k=1r =7l = 1

Shaker sortV d minh ho

27

2 3 8 7 6 15 9 17

2 3 8 7 6 9 15 17 k=5

2 3 8 7 6 9 15 17

r =5l = 1

2 3 8 6 7 9 15 17

2 3 6 8 7 9 15 17 k=3

2 3 6 7 8 9 15 17

r =5l = 3

Shaker sortChng trnh

28

l=0; r=n-1; k=n-1; //khi gn cc gi tr//k l v tr xy ra hon v sau cng while(ll){ if(a[j]

Shaker sortChng trnh (tt)

29

j=l; //y phn t ln v cuiwhile(ja[j+1])

{HoanVi(a[j], a[j+1]); HoanVi(a[j], a[j+1]); k=j; //lu li v tr xy ra hon v

}j++;

}r=k; //loi cc phn t c th t cui dy

}

Selection Sort30

M phng cch sp xp t nhin nht trong thc t Chn phn t nh nht v a v v tr ng l u dy

hin hnh. Sau xem dy hin hnh ch cn n-1 phn t. Lp li cho n khi dy hin hnh ch cn 1 phn t.

Selection SortGii thut

31

Cc bc ca gii thut:1. i = 0.2. Tm a[min] nh nht trong dy t a[i] n a[n-1]3. Hon v a[min] v a[i]4. Nu i n th tng i v lp li bc 2

Ngc li: Dng thut ton

Selection SortV d

32

15 2 8 7 3 6 9 17

2 15 8 7 3 6 9 17

2 3 8 7 15 6 9 17

i = 0

i = 1

i = 2

2 3 6 7 15 8 9 17

2 3 6 7 15 8 9 17

2 3 6 7 8 15 9 17

2 3 6 7 8 9 15 17

2 3 6 7 8 9 15 17

i = 3

i = 4

i = 5

i = 6

i = 7

Selection SortChng trnh

33

void SelectionSort(int a[], int n){int min; //ch s ca phn t nh nhtfor(int i=0; i

Selection Sortnh gi

34

void SelectionSort(int a[], int n){int min; for(int i=0; i

Selection Sortnh gi

35

S php so snh: Ti lt i bao gi cng cn (n-i-1) s ln so snh Khng ph thuc vo tnh trng dy s ban u

=

1 )1()1(n nnin

S php gn: Tt nht:

Xu nht:

S php so snh = =

=

0 2)1()1(

i

nnin

1

04 4

n

in

=

=

=

+=+

1

0 2)7()14(

n

i

nnin

Insertion Sort36

Cch xp cc qun bi dng thut ton Insertion Sort:

Tay tri l dy cc qun bi c th t, khi cm 1 qun bi mi ln th tm v tr ng ca n v chn vo.

Cch tm: ln lt so snh qun bi mi vi cc qun bi trong dy ban u.

Insertion SortGii thut

37

Gii thut: Xem dy a0, a1, , an-1 c i phn t u tin a0, a1, ,

ai-1 c th t. Tm cch chn phn t ai vo v tr thch hp dy a0, i 0

a1, , ai c th t.

Cho dy ban u a0, a1, , an-1, c th xem nh on gm 1 phn t a0 c sp.

Thm vo a1 s c a0, a1 c sp, tip tc thm a2, a3cho n khi thm an-1

Insertion SortV d

38

15 2 8 7 3 6 9 17

2 15 8 7 3 6 9 17

2 8 15 7 3 6 9 17

i = 1

i = 2

i = 3 2 8 15 7 3 6 9 17

2 7 8 15 3 6 9 17

2 3 7 8 15 6 9 17

2 3 6 7 8 15 9 17

2 3 6 7 8 9 15 17

i = 3

i = 4

i = 5

i = 6

i = 7

Insertion SortGii thut

39

Cc bc ca gii thut:1. Xut pht t i = 1.2. Tm v tr pos thch hp trong on a[0] n a[i-1] chn

a[i].3. Di ch cc phn t t a[pos] n a[i-1] sang 1 v tr

chn a[i].4. a[pos] = a[i]5. Tng i.

5.1 Nu i n: lp li bc 25.2 Ngc li: dng

Insertion SortChng trnh

40

void InsertionSort(int a[], int n){

for(int i=1; i=0 && a[pos] > x) //tm pos{

a[pos+1]=a[pos]; //di v sau 1 v trpos--;

}a[pos+1] = x;

}}

Insertion SortBi tp

41

Cho bit cc gi tr i, pos tng ng khi dng thut ton Insertion Sort sp xp mng A gim dn.A = {2, 9, 5, 12, 20, 15, -8, 10}

Insertion SortNhn xt

42

Nhn xt:on a[0] n a[i-1] lun lun c sp:

Vic tm v tr chn c th dng gii thut tm kim nh phn.Nu dng gii thut tm kim nh phn th vn phi tr gi Nu dng gii thut tm kim nh phn th vn phi tr gi cho thao tc di cc phn t sau x.

Sinh vin t ci t.

Insertion Sortnh gi

43

void InsertionSort(int a[], int n){

for(int i=1; i=0 && a[pos] > x)

S ln lp i

while(pos>=0 && a[pos] > x) {

a[pos+1]=a[pos]; pos--;

}a[pos+1] = x;

}}

S ln lp pos

Insertion Sortnh gi

44

So snh: Tt nht:

Xu nht:

1

12 2 ( 1)

n

in

=

= 1

2 ( 1)n

i n n

= Xu nht:

Gn: Tt nht:

Xu nht:

1

13 3( 1)

n

in

=

=

12 ( 1)

ii n n

=

=

1

1

( 1)(3 ) 3( 1)2

n

i

n ni n

=

+ = +

Quick sort45

Cc gii thut Bubble sort, Selection sort, Insertion sort: D hiu, d ci t Hiu qu thp: O(n2) Hiu qu thp: O(n )

Cc gii thut sp xp da trn so snh: phc tp n log2n.

Quick sort (C. A. R. Hoare, 1962) c th t c phc tp trn.

Quick Sort tng

46

Da trn vic phn hoch dy ban u thnh 2 phn: Dy con 1: a0, a1, , ai c gi tr nh hn x Dy con 2: aj, , an-1 c gi tr ln hn x. Dy con 2: aj, , an-1 c gi tr ln hn x.Dy ban u c phn thnh 3 phn:

Phn 2 c th t Phn 1, 3: cn sp th t, tin hnh phn hoch tng dy

con theo cch phn hoch dy ban u (chia tr)

akxk = 0 i k = i+1 j k = j+1, n-1

Quick SortGii thut

47

Gii thut phn hoch thnh 2 dy con:1. Chn phn t a[k] trong dy lm gi tr mc, 0 k r-1

x=a[k], i = 0, j = r-1.Thng chn phn t gia dy: k = (l+r)/2

2. Pht hin v hiu chnh cp phn t a[i], a[j] sai v tr2. Pht hin v hiu chnh cp phn t a[i], a[j] sai v tr2.1 Trong khi (a[i] < x), tng i.2.2 Trong khi (a[j] >x), gim j.2.3 Nu i

Quick SortV d

48

Phn hoch dy ban u: l = 0, r = 7, x = a[3]

Phn hoch on l = 0, r = 3, x = a[1]

15 2 8 7 3 6 9 17

6 2 3 7 8 15 9 17i = 3, j = 3i=0, j = 5; i = 2, j = 4

Phn hoch on l = 0, r = 3, x = a[1]

Phn hoch on l = 1, r = 3, x = a[2]

6 2 3 7 8 15 9 17

2 6 3 7 8 15 9 17i=1, j = 0

i=0, j = 1

2 6 3 7 8 15 9 17

2 3 6 7 8 15 9 17i=2, j = 1

i=1, j = 2

Quick SortV d

49

Phn hoch on l = 2, r = 3, x = a[2]

Phn hoch on l = 3, r = 7, x = a[5]

2 3 6 7 8 15 9 17i=3, j = 1

Phn hoch on l = 3, r = 5, x = a[4]

Phn hoch on l = 6, r = 7, x = a[6]

2 3 6 7 8 15 9 17i=5, j = 6i=6, j = 5

2 3 6 7 8 9 15 17i=5, j = 3

2 3 6 7 8 9 15 17

Quick SortChng trnh

50

void QuickSort(int a[], int l, int r){

i = l; j = r; x = a[(l+r)/2];do {

while (a[i] < x) i++;while (a[j] > x) j--;if (i

Quick SortBi tp

51

Chy tay thut ton Quick Sort sp xp mng A trong 2 trng hp tng dn v gim dn.A = {2, 9, 5, 12, 20, 15, -8, 10}

Quick Sortnh gi

52

nh gi gii thut: Hiu qu ph thuc vo vic chn gi tr mc

Tt nht l phn t median. Nu phn t mc l cc i hay cc tiu th vic phn

hoch khng ng u.hoch khng ng u. Tt nht: O(n*log2n) Trung bnh: O(n*log2n) Xu nht: O(n2)

Quick SortDanh sch lin kt Vi danh sch lin kt:

Quick sort sp xp hiu qu nht trn danh sch lin kt.

Lu : khi ci t trn danh sch lin kt, phn t mc

53

m c duy nht hp l l phn t u xu.

Quick SortDanh sch lin kt Gii thut Quick sort cho DSLK:

Bc 1: chn x lm mc l phn t u DSLK. Bc 2: Tch DSLK thnh 2 DSLK con L1 (cc phn

t x), L2 (cc phn t >x).

54

Bc 3: QuickSort(L1) Bc 4: QuickSort(L2) Bc 5: Ni L1, X v L2 li

Quick SortDanh sch lin kt

Tch L thnh L1, X v L2

4 9 3 4 2 19 12

3 4 2 4 9 19 12

55

Tch L1 thnh L11, X1 v L1232 4

L11 X1 L12

2 3 4

L1 X

Ni L11, X, L12

L2

Quick SortDanh sch lin ktTch L2 thnh L21, X2 v L22

Tch L22 thnh L221, X22 v L222

9 19

X2 L22

19

12

12

56

Ni L221 v X22 thnh L22

Ni L21, X2 v L22 thnh L2

Ni L1, X v L2 thnh L

1912

L221 X22

19129

2 3 4 191294

1912