2014.4.28 輪講
TRANSCRIPT
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emmasan525
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1.1-1.1-2.
2.2-1.2-2.
3. 3-1.3-2.(LCS)
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3
1.
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Mdc=(c1,c2,cd)2 Md 4
1-1.
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:c1,c2,c3MM-c1c1M-c2c2M-c3c3
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1-1.
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1-1.:1,3,777761743707
7776+1=74+3=70+7
7675+1=73+3=69+7
7574+1=72+3=68+7
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:c1,c2,c3MM-c1c1M-c2c2M-c3c3
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1-1.
Mm1=M-ci(i=1,2,)+1m2=m1-ci, m3=m2-ci, mnci-ci=0M
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1-1.RECURSIVECHANGE
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M:c: c=(c1,c2,,ci)d:(c)
bestNumCoins:M
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1-1.RECURSIVECHANGE
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Mci =
M:c: c=(c1,c2,,ci)d:(c)
M-ci+1(ci)
bestNumCoins:M
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1-1.
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RECURSIVECHANGE
7776,74,7017675,73,6917574,72,6817473,71,6717372,70,6617271,69,6517170,68,64170
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1-1.
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RECURSIVECHANGE
7776,74,7017675,73,6917574,72,6817473,71,6717372,70,6617271,69,6517170,68,64170
7070=77RECURSIVECHANGE
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1-2.MM-ci(i=1,,d)1Mm(m=1,2,,M)
!
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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
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1-2.
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m1
mmm-ci
DPCHANGE
77DPCHANGE
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1-2.2d1MO(Md)DPCHANGEMd1O(Md)M
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2.
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2-1.
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()()
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2-1.
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()()
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2-1.
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()()
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2-1.
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(0,0)
(0,0)(n,m)()
(n,m)
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2-1.
170
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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
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2-1.
2:
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2-1.
(Dynamic Programming):
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2-1.
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S(0,0)S(i,j)(i=0,1,,n, j=0,1,,m)i,jS(n,m)
S(0,0)
S(n,m)
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2-1.
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S(i,0)S(0,j)
S(0,0)
S(n,m)
0+3+2+4+0=9
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2-1.
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S(1,1)S(1,0)S(0,1)23+0=31+3=44
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2-1.
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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
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2-1.
MANHATTANTOURIST
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w:(55)w:(55)n:m:
Sn,m:
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2-1.
MANHATTANTOURIST
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2-1.
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2-1.
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2-2.
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2-2.()
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2-2.()
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2-2.v
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vv(DAG)
3,2
v
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2-2.
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SvSvSuSvSuDAG
Su1 + u1v Su2 + u2v Su3 + u3vSv=max
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3.
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3-1.2vw2(pq)
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3-1.
TGCATAT ATCCGAT
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cf.42l-mer
TGCATAT** ** ATCCGAT
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ATATATTATATA2
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3-1.
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2vw2
()
522()0
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3-1.
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+1
0 1 2 2 3 4 5 6 7 70 1 2 3 4 5 5 6 6 7
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3-1.
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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)
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3-1.
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2()
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3-2.(LCS)
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A T T G C T A AGCATGTT2
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3-2.(LCS)
(LCS)2()
LCSATGTA
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3-2.(LCS)(LCS)1
TGCATA ATCTGAT
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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
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3-2.(LCS)LCS
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v,wLCS2
Sn,m:b:
0
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3-2.(LCS)
PRINTLCS
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b:LCSv:i,jLCSn,m
vi