6

emmasan525

1

1.1-1.1-2.

2.2-1.2-2.

3. 3-1.3-2.(LCS)

2

3

1.

Mdc=(c1,c2,cd)2 Md 4

1-1.

:c1,c2,c3MM-c1c1M-c2c2M-c3c3

5

1-1.

6

1-1.:1,3,777761743707

7776+1=74+3=70+7

7675+1=73+3=69+7

7574+1=72+3=68+7

:c1,c2,c3MM-c1c1M-c2c2M-c3c3

7

1-1.

Mm1=M-ci(i=1,2,)+1m2=m1-ci, m3=m2-ci, mnci-ci=0M

1-1.RECURSIVECHANGE

8

M:c: c=(c1,c2,,ci)d:(c)

bestNumCoins:M

1-1.RECURSIVECHANGE

9

Mci =

M:c: c=(c1,c2,,ci)d:(c)

M-ci+1(ci)

bestNumCoins:M

1-1.

10

RECURSIVECHANGE

7776,74,7017675,73,6917574,72,6817473,71,6717372,70,6617271,69,6517170,68,64170

1-1.

11

RECURSIVECHANGE

7776,74,7017675,73,6917574,72,6817473,71,6717372,70,6617271,69,6517170,68,64170

7070=77RECURSIVECHANGE

1-2.MM-ci(i=1,,d)1Mm(m=1,2,,M)

!

12

1-2.1,3,7m=1111m=2(m=1)+112m=331 (m=2)+11=2

1m=4(m=1)+31 (m=3)+11

2m=5(m=2)+31 (m=4)+11

3m=6(m=3)+31 (m=5)+11

2m=771 (m=4)+31 (m=6)+11 1

13

1-2.

14

m1

mmm-ci

DPCHANGE

77DPCHANGE

1-2.2d1MO(Md)DPCHANGEMd1O(Md)M

15

16

2.

2-1.

17

()()

2-1.

18

()()

2-1.

19

()()

2-1.

20

(0,0)

(0,0)(n,m)()

(n,m)

2-1.

170

21

1 1 1 1 1

1 2 3 4 5

1 3 6 10 15

1 4 10 20 35

1 5 15 35 70

2-1.

2:

22

2-1.

(Dynamic Programming):

23

2-1.

24

S(0,0)S(i,j)(i=0,1,,n, j=0,1,,m)i,jS(n,m)

S(0,0)

S(n,m)

2-1.

25

S(i,0)S(0,j)

S(0,0)

S(n,m)

0+3+2+4+0=9

2-1.

26

S(1,1)S(1,0)S(0,1)23+0=31+3=44

2-1.

27

S(i,j)S(i-1,j)S(i,j-1)S(i,j) s(i-1,j)+(i-1,j),(i,j) s(i,j-1)+(i,j-1),(i,j)S(n,m)

max

2-1.

MANHATTANTOURIST

28

w:(55)w:(55)n:m:

Sn,m:

2-1.

MANHATTANTOURIST

29

2-1.

30

2-1.

31

2-2.

32

2-2.()

33

2-2.()

34

2-2.v

35

vv(DAG)

3,2

v

2-2.

36

SvSvSuSvSuDAG

Su1 + u1v Su2 + u2v Su3 + u3vSv=max

37

3.

3-1.2vw2(pq)

38

3-1.

TGCATAT ATCCGAT

39

cf.42l-mer

TGCATAT** ** ATCCGAT

4

ATATATTATATA2

6

3-1.

40

2vw2

()

522()0

3-1.

41

+1

0 1 2 2 3 4 5 6 7 70 1 2 3 4 5 5 6 6 7

3-1.

42

S(0,0)S(1,1)S(2,2)S(2,3)S(3,4)S(4,5)S(5,5)S(6,6)S(7,6)S(7,7)

3-1.

43

2()

3-2.(LCS)

44

A T T G C T A AGCATGTT2

45

3-2.(LCS)

(LCS)2()

LCSATGTA

46

3-2.(LCS)(LCS)1

TGCATA ATCTGAT

47

3-2.(LCS)(LCS)

S(i-1,j) + 0 S(i,j-1) + 0 S(i-1,j-1) + 1 (if vi=wi)S(i,j)=max

vw3

3-2.(LCS)LCS

48

v,wLCS2

Sn,m:b:

0

3-2.(LCS)

PRINTLCS

49

b:LCSv:i,jLCSn,m

vi