{"id":170,"date":"2013-10-14T02:30:26","date_gmt":"2013-10-13T18:30:26","guid":{"rendered":"http:\/\/blog.stlover.org\/?p=170"},"modified":"2013-10-14T03:34:21","modified_gmt":"2013-10-13T19:34:21","slug":"%e5%ad%97%e7%ac%a6%e4%b8%b2%e5%8c%b9%e9%85%8d%e7%b2%97%e6%8e%a2%e8%ae%a8","status":"publish","type":"post","link":"http:\/\/blog.xuhao1.me\/?p=170","title":{"rendered":"\u5b57\u7b26\u4e32\u5339\u914d\u7c97\u63a2\u8ba8"},"content":{"rendered":"

\u6700\u8fd1\u803d\u4e8eiGEM\uff0c\u603b\u60f3\u641e\u70b9\u72ec\u7279\u7684\u7b97\u6cd5\uff0c\u9700\u8981\u7528\u5230\u5b57\u7b26\u4e32\u5339\u914d\uff0c\u5199\u4e2a\u7b14\u8bb0\u5728\u8fd9\u91cc\u3002<\/p>\n

<\/h2>\n

$$P_k$$\u8868\u793aP\u7684\u524dk\u4e2a\u5b57\u7b26\u7684\u5b57\u4e32\u3002<\/p>\n

\u81ea\u52a8\u673a\uff1a<\/h2>\n

\u795e\u5947\u800c\u4f18\u7f8e\u7684\u4e1c\u897f<\/p>\n

KMP\uff1a<\/h2>\n

\u9996\u5148\u95ee\u8fd9\u6837\u4e00\u4e2a\u95ee\u9898\uff1a<\/p>\n

\u60f3\u5728T\u4e2d\u627e\u5230\u4e00\u4e2a\u4e32\u548cP\u76f8\u7b49\u3002\u90a3\u4e48\u6211\u4eec\u5df2\u77e5\u626b\u63cf\u4e86\u5230\u4e86\u8fd9\u6837\u4e00\u4e2a\u7ed3\u679c<\/p>\n

$$P[1..q]==T[s..s+q]$$<\/p>\n

\u90a3\u4e48\u4e0b\u4e00\u4e2as’\u6ee1\u8db3<\/p>\n

$$P[1..k]==T[s’..s’+k]$$\u7684s’\u662f\u4ec0\u4e48\u3002<\/p><\/blockquote>\n

\u5982\u679c\u77e5\u9053\u4e86\u8fd9\u4e2a\u95ee\u9898\u7684\u7b54\u6848\uff0c\u6211\u4eec\u53ef\u4ee5\u8f7b\u677e\u5728s\u548c\u4e0b\u4e00\u4e2as’\u5185\u8df3\u8dc3\uff08\u591a\u4e48\u8c61\u81ea\u52a8\u673a\uff09\uff0c\u4ece\u800c\u5728\u8d85\u7ea7\u77ed\u7684\u65f6\u95f4\u5185\u5b8c\u6210\u67e5\u627e\u3002<\/p>\n

\u518d\u56de\u5934\u770b\u8fd9\u4e2a\u95ee\u9898\uff0c\u5176\u5b9e\u627e\u5230\u8fd9\u4e2a$$s’$$\u5df2\u7ecf\u548cT\u6ca1\u6709\u4efb\u4f55\u7684\u5173\u7cfb\u3002\u8fd9\u4ec5\u4ec5\u662fP\u81ea\u8eab\u7684\u6027\u8d28\u3002<\/p>\n

\u4e8e\u662f\uff0c\u6211\u4eec\u62ffP\u4e0e\u81ea\u8eab\u6bd4\u8f83\uff0c\u505a\u4e00\u4e2a\u9884\u5904\u7406\uff0c\u5f88\u5bb9\u6613\u5f97\u5230\u8fd9\u4e2as\u548cs’\u7684\u5173\u7cfb\u3002<\/p>\n

\u56de\u5230\u6211\u4eec\u7684\u95ee\u9898\uff0c\u6211\u4eec\u5b9e\u9645\u4e0a\u5904\u7406\u4e86\u8fd9\u6837\u4e00\u4e2a\u4e8b\u60c5\uff1a<\/p>\n

\u627e\u5230$$P_k$$\u4f7f\u5f97$$P_k$$\u4e3a$$P_q$$\u7684\u6700\u957f\u540e\u7f00\u3002<\/p>\n

\u4e8e\u662f\u6211\u4eec\u5b9a\u4e49\u524d\u7f00\u51fd\u6570\u4e3a<\/p>\n

$$\\pi[k]=max(k,P_k\u4e3aP_q\u7684\u6700\u957f\u540e\u7f00$$<\/p>\n

\u7136\u540e\u9884\u5904\u7406So easy,<\/p>\n

    \n
  1. def<\/span>\u00a0makepi<\/span>(<\/span>P<\/span>):<\/span><\/li>\n
  2. \u00a0\u00a0\u00a0\u00a0pi<\/span>=[<\/span>0<\/span>]*<\/span>len<\/span>(<\/span>P<\/span>)<\/span><\/li>\n
  3. \u00a0\u00a0\u00a0\u00a0<\/span>for<\/span>\u00a0i\u00a0<\/span>in<\/span>\u00a0range<\/span>(<\/span>len<\/span>(<\/span>P<\/span>)):<\/span><\/li>\n
  4. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>for<\/span>\u00a0j\u00a0<\/span>in<\/span>\u00a0range<\/span>(<\/span>i<\/span>,-<\/span>1<\/span>,-<\/span>1<\/span>):<\/span><\/li>\n
  5. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>if<\/span>(<\/span>houzhui<\/span>(<\/span>P<\/span>[<\/span>0<\/span>:<\/span>j<\/span>],<\/span>P<\/span>[<\/span>0<\/span>:<\/span>i<\/span>+<\/span>1<\/span>])):<\/span><\/li>\n
  6. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0pi<\/span>[<\/span>i<\/span>]=<\/span>j<\/span><\/li>\n
  7. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>break<\/span><\/li>\n
  8. \u00a0\u00a0\u00a0\u00a0<\/span>return<\/span>\u00a0pi<\/span><\/li>\n<\/ol>\n

    \u4e8e\u662f\uff0c\u6211\u4eec\u5c31\u6709\u4e86\u4e00\u4e2a\u5f3a\u529b\u7684\u7b97\u6cd5\uff0c<\/p>\n

      \n
    1. \u7f6ei\u4e3a0\uff0c\u5f00\u59cb\u505aKMP<\/li>\n
    2. \u627e\u5230i\u4ee5\u540eT,P\u7684\u6700\u957f\u5339\u914d\u3002\u5982\u679c\u957f\u5ea6l\u548cP\u76f8\u7b49\uff0c\u5219\u8f93\u51fa\u7ed3\u679c<\/li>\n
    3. \u7531\u524d\u7f00\u51fd\u6570\u627e\u5230\u4f4d\u79fb\u91cf$$(i+=l+i-\\pi[i])$$\uff0c\u82e5\u4f4d\u79fb\u91cf\u4e3a0\u5219\u81ea\u52a0.\u91cd\u590d2<\/li>\n
    4. \u76f4\u5230\u5237\u5b8c\u3002<\/li>\n<\/ol>\n

      \u5176\u5b9e\u7ed3\u5408\u524d\u9762\u81ea\u52a8\u673a\u7684\u505a\u6cd5\uff0cKMP\u4e0d\u5982\u8bf4\u662f\u81ea\u52a8\u673a\u9488\u5bf9\u5b57\u7b26\u4e32\u5339\u914d\u8fd9\u4e00\u5355\u4e00\u95ee\u9898\u7684\u795e\u7ea7\u4f18\u5316.<\/p>\n

      \u5199\u4e3a\u4ee3\u7801\uff0c\u4e0a\u9762\u7684\u73a9\u610f\u5927\u6982\u662f\u8fd9\u4e48\u56de\u4e8b<\/p>\n

        \n
      1. def<\/span>\u00a0KMP_Difficult<\/span>(<\/span>T<\/span>,<\/span>P<\/span>):<\/span><\/li>\n
      2. \u00a0\u00a0\u00a0\u00a0pi<\/span>=<\/span>makepi<\/span>(<\/span>P<\/span>)<\/span><\/li>\n
      3. \u00a0\u00a0\u00a0\u00a0<\/span>print<\/span>\u00a0pi<\/span><\/li>\n
      4. \u00a0\u00a0\u00a0\u00a0i<\/span>=<\/span>0<\/span><\/li>\n
      5. \u00a0\u00a0\u00a0\u00a0<\/span>while<\/span>\u00a0i<\/span><<\/span>len<\/span>(<\/span>T<\/span>):<\/span><\/li>\n
      6. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>print<\/span>\u00a0i<\/span><\/li>\n
      7. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>for<\/span>\u00a0j\u00a0<\/span>in<\/span>\u00a0range<\/span>(<\/span>len<\/span>(<\/span>P<\/span>)):<\/span><\/li>\n
      8. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>if<\/span>(<\/span>i<\/span>+<\/span>j<\/span>>=<\/span>len<\/span>(<\/span>T<\/span>)):<\/span><\/li>\n
      9. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>return<\/span><\/li>\n
      10. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>if<\/span>(<\/span>P<\/span>[<\/span>j<\/span>]!=<\/span>T<\/span>[<\/span>i<\/span>+<\/span>j<\/span>]):<\/span><\/li>\n
      11. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>break<\/span><\/li>\n
      12. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>if<\/span>(<\/span>j<\/span>==<\/span>len<\/span>(<\/span>P<\/span>)-<\/span>1<\/span>):<\/span><\/li>\n
      13. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>print<\/span>\u00a0<\/span>“res”<\/span>,<\/span>i<\/span><\/li>\n
      14. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0i<\/span>=<\/span>i<\/span>+<\/span>max<\/span>(<\/span>j<\/span>–<\/span>pi<\/span>[<\/span>j<\/span>],<\/span>1<\/span>)<\/span><\/li>\n<\/ol>\n

        \u5947\u602a\uff0c\u662f\u4e00\u79cd$$O(nm)$$\u7684\u7b97\u6cd5\uff0c\u8fd9\u5e76\u4e0d\u662f\u6211\u4eec\u60f3\u8981\u7684\u3002<\/p>\n

        \u4ed4\u7ec6\u89c2\u5bdf\uff0c\u53d1\u73b0\u95ee\u9898\u51fa\u73b0\u5728j\u7684\u5faa\u73af\u4e0a\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u6211\u4eec\u505a\u4e86\u5f88\u591a\u91cd\u590d\u6027\u7684\u5de5\u4f5c\uff0c\u56e0\u4e3a\u6211\u4eec\u7684\u5b9a\u4e49\u5305\u542b\u4e86\u8fd9\u6837\u4e00\u4e2a\u4fe1\u606f<\/p>\n

        \u7531\u73b0\u5728\u7684\u4e0b\u6807s\u548c\u5339\u914d\u6570\u53ef\u4ee5\u76f4\u63a5\u5f97\u5230\u6700\u8fd1\u7684s’\u4f7f\u5f97s’\u662fs..s’\u5185\u5339\u914d\u7684\u6700\u597d\u7684\u4e00\u4e2a\u7ed3\u679c<\/p><\/blockquote>\n

        \u6211\u4eec\u5173\u5fc3\u7684\u5b8c\u5168\u53ef\u4ee5\u4e0d\u662f\u4ece\u67d0\u70b9\u5f00\u59cb\u7684\u6700\u591a\u5339\u914d\u957f\u5ea6\uff0c\u800c\u662f\u5230\u8fd9\u4e2a\u70b9\u8fc4\u4eca\u4e3a\u6b62\u7684\u6700\u5927\u5339\u914d\u6570\u91cf\u3002\u90a3\u4e48\u6211\u4eec\u7b97\u6cd5\u53ef\u4ee5\u6539\u4e3a<\/p>\n

        i\u4ece1\u5230n\u5faa\u73af<\/p>\n

        \u5b9a\u4e49q\u4e3a\u5230i\u4e3a\u6b62\u6700\u957f\u5339\u914d\u6570\u91cf\u3002<\/p>\n

        \u4e8e\u662fP[q]==T[i]\u90a3\u4e48q\u53ef\u4ee5\u81ea\u52a0\u4e00\u4e2a\u4e86\u3002<\/p>\n

        P[q]!=T[i]\uff0c\u90a3\u5c31\u7528\u6211\u4eec\u7684\u524d\u7f00\u51fd\u6570\u5bfb\u627e\u73b0\u5728\u7684q=$$\\pi[q]$$<\/p>\n

        q=len(P)\u5339\u914d\u6b63\u786e\u3002<\/p><\/blockquote>\n

        \u4e8e\u662f\u5462\uff0c\u6211\u4eec\u8fd9\u4e48\u5199\u4e86\u4ee3\u7801<\/p>\n

          \n
        1. def<\/span>\u00a0KMP<\/span>(<\/span>T<\/span>,<\/span>P<\/span>):<\/span><\/li>\n
        2. \u00a0\u00a0\u00a0\u00a0pi<\/span>=<\/span>makepi<\/span>(<\/span>P<\/span>)<\/span><\/li>\n
        3. \u00a0\u00a0\u00a0\u00a0q<\/span>=<\/span>0<\/span><\/li>\n
        4. \u00a0\u00a0\u00a0\u00a0<\/span>print<\/span>\u00a0pi<\/span><\/li>\n
        5. \u00a0\u00a0\u00a0\u00a0<\/span>for<\/span>\u00a0i\u00a0<\/span>in<\/span>\u00a0range<\/span>(<\/span>len<\/span>(<\/span>T<\/span>)):<\/span><\/li>\n
        6. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>if<\/span>(<\/span>T<\/span>[<\/span>i<\/span>]==<\/span>P<\/span>[<\/span>q<\/span>]):<\/span><\/li>\n
        7. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0q<\/span>+=<\/span>1<\/span><\/li>\n
        8. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>if<\/span>(<\/span>q<\/span>==<\/span>len<\/span>(<\/span>P<\/span>)):<\/span><\/li>\n
        9. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>print<\/span>\u00a0<\/span>“res”<\/span>,<\/span>i<\/span>–<\/span>q<\/span>+<\/span>2<\/span><\/li>\n
        10. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0q<\/span>=<\/span>pi<\/span>[<\/span>q<\/span>–<\/span>1<\/span>]<\/span><\/li>\n
        11. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>else<\/span>:<\/span><\/li>\n
        12. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0q<\/span>=<\/span>pi<\/span>[<\/span>q<\/span>]<\/span><\/li>\n<\/ol>\n

          All Done!<\/p>\n

          That’s Cool!<\/p>\n","protected":false},"excerpt":{"rendered":"

          \u6700\u8fd1\u803d\u4e8eiGEM\uff0c\u603b\u60f3\u641e\u70b9\u72ec\u7279\u7684\u7b97\u6cd5\uff0c\u9700\u8981\u7528\u5230\u5b57\u7b26\u4e32\u5339\u914d\uff0c\u5199\u4e2a\u7b14\u8bb0\u5728\u8fd9\u91cc\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts\/170"}],"collection":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=170"}],"version-history":[{"count":3,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts\/170\/revisions"}],"predecessor-version":[{"id":173,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=\/wp\/v2\/posts\/170\/revisions\/173"}],"wp:attachment":[{"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=170"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.xuhao1.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}