Difference Algorithm

- Myers Algorithm
- SES / LCS
- Edit Graph

- Paul Heckel Algorithm

Transcript

1. %J⒎FSFODF"MHPSJUIN
   :VZB)PSJUB(JU)VCIPSJUBZVZB5XJUUFSIPSJUB@ZVZB
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3. "HFOEB
   *OUSPEVDUJPO
   w ࠩ෼ͱ͸ʁ
   w ฤूͱ͍͏ߟ͑ํ
   .ZFST"MHPSJUIN
   w 'FBUVSFT
   w 4&4-$41SPCMFN
   w &EJU(SBQI
   w ݪཧ
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   w ݪཧ
   w )FDLFM0WFSWJFX
   4VNNBSZ
   

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4. *OUSPEVDUJPO
   

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5. source = [1, 2, 3, 4, 5]
   ࠩ෼ͱ͸ʁ
   target = [1, 3, 5, 7]
   EJ⒎ TPVSDF UBSHFU
   
   

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6. source = [1, 2, 3, 4, 5]
   ࠩ෼ͱ͸ʁ
   target = [1, 3, 5, 7]
   EJ⒎ TPVSDF UBSHFU
   %FMFUF %FMFUF *OTFSU
   

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7. source = [1, 2, 3, 4, 5]
   ࠩ෼ͱ͸ʁ
   target = [1, 3, 5, 7]
   EJ⒎ TPVSDF UBSHFU
   %FMFUF %FMFUF *OTFSU
   &EJU4DSJQU
   

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8. ฤूͱ͍͏ߟ͑ํ
   
   
   
   
   
   
   
   
   
   TPVSDF UBSHFU
   

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9. 
   ฤूͱ͍͏ߟ͑ํ
   
   
   
   
   
   
   
   
   
   TPVSDF UBSHFU
   EJ⒎ TPVSDF UBSHFU
   %FMFUF %FMFUF *OTFSU
   

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10. .ZFST"MHPSJUIN
    

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11. 'FBUVSFT
    w 4JNQMF
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    w 4IPSUFTU
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    IUUQTEFWFMPQFSBOESPJEDPNSFGFSFODFBOESPJETVQQPSUWVUJM%J⒎6UJM
    

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12. ࠷୹ͷ൑ఆ͸ʁ
    

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13. ࠷୹ͷఆྔత൑அ
    w 4&44IPSUFTU&EJU4DSJQU
    w -$4ɿ-POHFTU$PNNPO4VCTFRVFODF
    w &EJU4DSJQUTPVSDFˠUBSHFUͷฤूʹඞཁͳ*OTFSU %FMFUF4DSJQUͷ͜ͱ
    w 4VCTFRVFODFɿ഑ྻ͔Β͍͔ͭ͘ͷཁૉΛऔΓআ͍ͯಘΒΕΔ഑ྻ
    4&4-$41SPCMFN
    

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14. ࠷୹ͷఆྔత൑அ
    w 4&44IPSUFTU&EJU4DSJQU
    w -$4ɿ-POHFTU$PNNPO4VCTFRVFODF
    w &EJU4DSJQUTPVSDFˠUBSHFUͷฤूʹඞཁͳ*OTFSU %FMFUF4DSJQUͷ͜ͱ
    w 4VCTFRVFODFɿ഑ྻ͔Β͍͔ͭ͘ͷཁૉΛऔΓআ͍ͯಘΒΕΔ഑ྻ
    source = [1, 2, 3, 4, 5]
    FY
    [1, 2, 5]
    [2, 3, 4, 5]
    [1, 2, 4, 3]
    [1, 3, 4, 6]
    4&4-$41SPCMFN
    
    
    

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15. ࠷୹ͷఆྔత൑அ
    w 4&44IPSUFTU&EJU4DSJQU
    w -$4ɿ-POHFTU$PNNPO4VCTFRVFODF
    w &EJU4DSJQUTPVSDFˠUBSHFUͷฤूʹඞཁͳ*OTFSU %FMFUF4DSJQUͷ͜ͱ
    w 4VCTFRVFODFɿ഑ྻ͔Β͍͔ͭ͘ͷཁૉΛऔΓআ͍ͯಘΒΕΔ഑ྻ
    4&4-$41SPCMFN
    ˞EVBMQSPCMFN
    source = [1, 2, 3, 4, 5]
    FY
    [1, 2, 5]
    [2, 3, 4, 5]
    [1, 2, 4, 3]
    [1, 3, 4, 6]
    
    
    

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16. Ͳ͏΍ͬͯ୳ͦ͏
    

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17. &EJU(SBQI
    ίϯϐϡʔλͰղ͚ͦ͏ͳײ͡ʹදݱ
    

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18. &EJU(SBQI
    source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    ίϯϐϡʔλͰղ͚ͦ͏ͳײ͡ʹදݱ
    

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19. source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    (0, 0) A B C A B B A
    C
    B
    A
    B
    A
    C
    0
    1
    2
    3
    4
    5
    0 1 2 3 4 5 6
    source
    target
    4UBSU
    (7, 6)
    &OE
    

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20. source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    (0, 0) A B C A B B A
    C
    B
    A
    B
    A
    C
    0
    1
    2
    3
    4
    5
    0 1 2 3 4 5 6
    source
    target
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    (7, 6)
    4UBSU
    &OE
    

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21. source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    (0, 0) A B C A B B A
    C
    B
    A
    B
    A
    C
    0
    1
    2
    3
    4
    5
    0 1 2 3 4 5 6
    source
    target
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    (7, 6)
    &EHFʹԊͬͯɺ4UBSU͔Β&OE·ͰҠಈ͢Δ
    ӈɾԼɾࣼΊํ޲ͷҠಈ㲈EFMFUF JOTFSU EPOPUIJOH
    4UBSU
    &OE
    4UBSU
    &OE
    

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22. source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    (0, 0) A B C A B B A
    C
    B
    A
    B
    A
    C
    0
    1
    2
    3
    4
    5
    0 1 2 3 4 5 6
    source
    target
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    (7, 6)
    4&4
    4UBSU
    &OE
    4UBSU࠲ඪ&OE࠲ඪͷ࠷୹ܦ࿏
    
    4UBSU
    &OE
    

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23. (0, 0)
    0
    1
    2
    3
    4
    5
    (7, 6)
    0 1 2 3 4 5 6
    Delete A
    Delete B
    3JHIU.PWFNFOU
    #PUUPN.PWFNFOU
    %JBHPOBM.PWFNFOU
    EFMFUF
    JOTFSU
    EPOPUIJOH TBNFTZNCPM
    
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    Insert B
    Insert C
    source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    A B C A B B A
    C
    B
    A
    B
    A
    C
    target
    Delete B
    4UBSU
    &OE
    source
    4UBSU
    &OE
    

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24. w&EJU(SBQIฤू࡞ۀΛίϯϐϡʔλͰղ͚ͦ͏ͳײ͡ʹදݱɻ
    wӈҠಈ%FMFUF
    wԼҠಈ*OTFSU
    wࣼΊҠಈEPOPUIJOH TBNFFMFNFOU
    
    4&4-$41SPCMFNΛղ͘4UBSU࠲ඪ͔Β&OE࠲ඪ΁ͷ࠷୹ܦ࿏Λݟ͚ͭΔ
    

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25. ݪཧ
    

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26. ҠಈίετJT%JBHPOBM
    source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    (0, 0)
    0
    1
    2
    3
    4
    5
    (7, 6)
    0 1 2 3 4 5 6
    Delete A
    Delete B
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    Insert B
    Insert C
    A B C A B B A
    C
    B
    A
    B
    A
    C
    target
    Delete B
    4UBSU
    &OE
    ࠷୹ܦ࿏ͷ૯Ҡಈίετ %
    4&4ͷεΫϦϓτ਺
    source
    4UBSU
    &OE
    

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27. Myers Algorithm
    w%͔Β࢝Ίͯɺ&OE࠲ඪΛ໨ࢦ͢
    wແཧͩͬͨΒɺ%Λ૿΍ͯ͠౸ணग़དྷΔ·Ͱ܁Γฦ͢
    w ͍͚Δ͔ͳʁ͍͚Δ͔ͳʁ͍͚
    ˞͋͘·Ͱɺ%ճͰ࠷ԕͷ࠲ඪΛ໨ࢦ͢ɻ ࣼΊҠಈ͸શͯফඅ
    
    

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28. Lઢɿx - y = kͰ&EJU(SBQI্ʹͰ͖Δର֯ઢ
    

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29. (0, 0)
    0
    1
    2
    3
    4
    5
    (7, 6)
    0 1 2 3 4 5 6
    Delete A
    Delete B
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    Insert B
    Insert C
    source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    A B C A B B A
    source
    C
    B
    A
    B
    A
    C
    target
    Delete B
    4UBSU
    &OE
    3
    1
    x - y = k
    0
    -1 2
    Y
    Z
    4UBSU
    &OE
    

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30. (0, 0)
    0
    1
    2
    3
    4
    5
    (7, 6)
    0 1 2 3 4 5 6
    Delete A
    Delete B
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    Insert B
    Insert C
    source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    A B C A B B A
    source
    C
    B
    A
    B
    A
    C
    target
    Delete B
    4UBSU
    &OE
    3
    1
    x - y = k
    0
    -1 2
    Y
    Z
    k + 1
    k - 1
    k
    4UBSU
    &OE
    

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31. (0, 0)
    0
    1
    2
    3
    4
    5
    (7, 6)
    0 1 2 3 4 5 6
    Delete A
    Delete B
    NBUDIQPJOU
    QPJOUBTTBNFTZNCPM
    Insert B
    Insert C
    source = [A, B, C, A, B, B, A] target = [C, B, A, B, A, C]
    A B C A B B A
    source
    C
    B
    A
    B
    A
    C
    target
    Delete B
    4UBSU
    &OE
    3
    1
    0
    -1 2
    Y
    Z
    k + 1
    k - 1
    k
    ඇର֯ͳҠಈΛ%ճߦͬͨ࠷௕ͷܦ࿏
    %͕ح਺ͳΒLح਺ͷର֯ઢ
    %͕ۮ਺ͳΒLۮ਺ͷର֯ઢ্Ͱࢭ·Δ
    4UBSU
    &OE
    

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32. For D ← 0 to M + N Do
    For k ← -D to D in steps of 2 Do
    Until D Path gets to furthest point Do
    Move on edges
    If (N, M) is the reached point Then
    Found the SES.
    Array[with: k]
    M = source.count
    N = target.count
    %͕ح਺ͳΒLح਺ͷର֯ઢ
    %͕ۮ਺ͳΒLۮ਺ͷର֯ઢ্Ͱࢭ·Δ
    &EJU(SBQI্Ͱ࠷ԕͷύε͸֎प
    Complexity: O((M+N)D)
    ίετ%Ͱߦ͚ͨ࠷ԕͷ࠲ඪΛLઢຖʹه࿥
    %શͯԼҠಈ
    %શͯӈҠಈ
    &OE࠲ඪ
    

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33. .ZFST0WFSWJFX
    w 4&4-$41SPCMFNΛղͨ͘ΊͷΞϧΰϦζϜ
    w &EJU(SBQI
    w Ҡಈίετ %
    ɾLઢͷ֓೦Λ׆༻
    w %FMFUF *OTFSUऔಘޙɺͦΕΛ.PWF 6QEBUF4DSJQUʹม׵͢Δ
    ͜ͱ͸Մೳ
    

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34. 1BVM)FDLFM"MHPSJUIN
    

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35. w 4JNQMF0QUJNJ[BCMF
    w 0 /
    $PNQMFYJUZ
    w %FMFUF *OTFSU .PWF4DSJQU
    w /PU"MXBZT4IPSUFTU
    w #BTFPG
    'FBUVSFT
    3Y%BUB4PVSDFT
    

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36. ݪཧ
    

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37. TPVSDF UBSHFU
    4ZNCPM5BCMF
    
    
    
    
    
    
    
    
    
    
    
    
    &MFNFOU DPVOUJOTPVSDF DPVOUJOUBSHFU JOEFYJOTPVSDF
    
    
    
    
    
    
    
    OVMM
    
    
    
    OVMM
    
    source = [1, 2, 3, 4, 5, 4] target = [1, 3, 5, 2, 2, 7]
    w TPVSDF UBSHFUͷ֤ཁૉ &MFNFOU
    Λ,FZͱͯ͠ɺ%JDUJPOBSZͷ4ZNCPM5BCMFʹొ࿥
    w 7BMVFʹ͸ͦͷཁૉͷ TPVSDF಺Ͱͷ਺ɺUBSHFU಺Ͱͷ਺ɺTPVSDF಺ͰͷJOEFY
    
    ˞ݸ͚ͩͷ৔߹ ݸPS̎ݸҎ্ͷ৔߹͸OVMM
    
    

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38. TPVSDF UBSHFU
    4ZNCPM5BCMF
    
    
    
    
    
    
    
    
    
    
    
    
    &MFNFOU DPVOUJOTPVSDF DPVOUJOUBSHFU JOEFYJOTPVSDF
    
    
    
    
    
    
    
    OVMM
    
    
    
    OVMM
    
    source = [1, 2, 3, 4, 5, 4] target = [1, 3, 5, 2, 2, 7]
    w TPVSDF UBSHFUͷ֤ཁૉ &MFNFOU
    Λ,FZͱͯ͠ɺ%JDUJPOBSZͷ4ZNCPM5BCMFʹొ࿥
    w 7BMVFʹ͸ͦͷཁૉͷ TPVSDF಺Ͱͷ਺ɺUBSHFU಺Ͱͷ਺ɺTPVSDF಺ͰͷJOEFY
    
    ɾશཁૉΛ؅ཧ͢Δ4ZNCPM5BCMFΛҰͭ༻ҙ
    ɾTPVSDF UBSHFUͦΕͧΕͷཁૉͷొ࿥࡞ۀΛߦ͏
    ˞ݸ͚ͩͷ৔߹ ݸPS̎ݸҎ্ͷ৔߹͸OVMM
    
    

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39. UBSHFU
    TPVSDF
    4ZNCPM5BCMF
    
    
    
    
    
    
    &MFNFOU DPVOUJOTPVSDF DPVOUJOUBSHFU JOEFYJOTPVSDF
    
    
    
    
    
    
    
    OVMM
    
    
    
    OVMM
    
    w TPVSDF UBSHFUͷͦΕͧΕͷཁૉͱରରԠͨ͠\TPVSDF UBSHFU^3FGFSFODFTΛ༻ҙ͢Δɻ
    w ରରԠ͍ͯ͠Δཁૉ΁ͷࢀরΛอ࣋͠ɺࢀরݩ͸4ZNCPM5BCMFPS΋͏ยํͷ഑ྻ
    ˞ͲͪΒʹ΋ͦͷཁૉ͕͋Δ৔߹͸΋͏ยํͷ഑ྻ͕༏ઌ
    
    TZNCPM5BCMF
    TZNCPM5BCMF
    TZNCPM5BCMF
    TZNCPM5BCMF
    TZNCPM5BCMF
    TZNCPM5BCMF
    UBSHFU3FGFSFODFT
    

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40. UBSHFU
    TPVSDF
    4ZNCPM5BCMF
    
    
    
    
    
    
    &MFNFOU DPVOUJOTPVSDF DPVOUJOUBSHFU JOEFYJOTPVSDF
    
    
    
    
    
    
    
    OVMM
    
    
    
    OVMM
    
    w TPVSDF UBSHFUͷͦΕͧΕͷཁૉͱରରԠͨ͠\TPVSDF UBSHFU^3FGFSFODFTΛ༻ҙ͢Δɻ
    w ରରԠ͍ͯ͠Δཁૉ΁ͷࢀরΛอ࣋͠ɺࢀরݩ͸4ZNCPM5BCMFPS΋͏ยํͷ഑ྻ
    ˞ͲͪΒʹ΋ͦͷཁૉ͕͋Δ৔߹͸΋͏ยํͷ഑ྻ͕༏ઌ
    
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    TZNCPM5BCMF
    TZNCPM5BCMF
    UBSHFU3FGFSFODFT
    

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41. UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    TZNCPM5BCMF
    TZNCPM5BCMF
    
    
    
    
    
    
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    TZNCPM5BCMF
    UIF0UIFS
    TZNCPM5BCMF
    
    
    
    
    
    
    TPVSDF
    TPVSDF3FGFSFODFT
    UBSHFU
    UBSHFU3FGFSFODFT
    

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42. w UIF0UIFSࢀরͷ৔߹.PWF
    w TZNCPM5BCMFࢀরͷ৔߹TPVSDFˠ%FMFUF UBSHFUˠ*OTFSU
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    TZNCPM5BCMF
    TZNCPM5BCMF
    
    
    
    
    
    
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    TZNCPM5BCMF
    UIF0UIFS
    TZNCPM5BCMF
    
    
    
    
    
    
    TPVSDF
    TPVSDF3FGFSFODFT
    UBSHFU
    UBSHFU3FGFSFODFT
    

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43. ૬खଆͷ഑ྻʹཁૉ͕͋ΔͳΒɺJOEFYΛม͑Δ.PWFͰ0,
    4ZNCPM5BCMF͔͠ࢀরग़དྷͳ͍ͳΒɺ
    TPVSDFͳΒ%FMFUFɺUBSHFUͳΒ*OTFSU͢Δ͔͠ແ͍
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    TZNCPM5BCMF
    TZNCPM5BCMF
    
    
    
    
    
    
    UIF0UIFS
    UIF0UIFS
    UIF0UIFS
    TZNCPM5BCMF
    UIF0UIFS
    TZNCPM5BCMF
    
    
    
    
    
    
    ˞ແବͳ.PWF͕ൃੜ͢ΔՄೳੑ༗Γ
    TPVSDF
    TPVSDF3FGFSFODFT
    UBSHFU
    UBSHFU3FGFSFODFT
    w UIF0UIFSࢀরͷ৔߹.PWF
    w TZNCPM5BCMFࢀরͷ৔߹TPVSDFˠ%FMFUF UBSHFUˠ*OTFSU
    

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44. )FDLFM0WFSWJFX
    w )BTI5BCMFΛ׆༻ͨ͠ɺཁૉͷJOEFYऔಘ
    w TPVSDFͱUBSHFUͷ֤ཁૉͷࢀরؔ܎ͷߏங
    w %FMFUF *OTFSU .PWFʹՃ͑ͯɺ6QEBUFͷऔಘ΋Մೳ
    w .ZFSTͱ͸จԽ͕ҟͳΓɺ4&4-$41SPCMFN͸ؔ܎ͳ͍
    

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45. w ར༻෯ͷ޿͞ɾ$PNQMFYJUZ༏ҐੑͳͲ͕ಛ௃తͳɺ.ZFSTɾ)FDLFMͷ
    ͭͷݪཧΛղઆɻ͓໾ʹཱͯΕ͹
    w IUUQTHJUIVCDPNIPSJUBZVZB%J⒎FSFODF"MHPSJUIN$PNQBSJTPO
    w 0 /
    ͷ$PNQMFYJUZΛ࠾༻͍ͯ͠ΔϥΠϒϥϦ΋͋Δ͕ɺ6*͕བྷΉࠩ෼ߋ৽
    ϥΠϒϥϦͱͯ͋͑ͯͦ͠ΕΛબͿཧ༝͸༨Γແ͍͔΋ʁ
    w બఆΞϧΰϦζϜɾ࣍ݩߋ৽ɾશCBUDI6QEBUF0QFSBUJPOTରԠɾ଎౓ɾFUD
    4VNNBSJ[F
    
    
    IUUQTHJUIVCDPNSB%J⒎FSFODF,JU
    

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46. ɾHeckel, Paul (1978), "A Technique for Isolating Differences Between Files”,
    Communications of the ACM, 21: 264–268, doi:10.1145/359460.359467, retrieved 2011-12-04
    ɾE. W. Myers, ‘‘An O(ND) difference algorithm and its variations,’’ Algorithmica, 1 (1986), pp. 251−266.
    3FGFSFODFT
    

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