{"id":2241,"date":"2022-08-17T18:15:32","date_gmt":"2022-08-17T10:15:32","guid":{"rendered":"http:\/\/47.101.202.111\/?p=2241"},"modified":"2023-04-07T22:23:12","modified_gmt":"2023-04-07T14:23:12","slug":"%e8%b7%b3%e8%a1%a8%e5%ae%9e%e7%8e%b0%e5%8e%9f%e7%90%86-skip-lists%e5%8e%9f%e8%ae%ba%e6%96%87%e8%a7%a3%e6%9e%90","status":"publish","type":"post","link":"http:\/\/139.196.114.170\/?p=2241","title":{"rendered":"Skip Lists – \u8df3\u8868\u539f\u8bba\u6587\u89e3\u6790"},"content":{"rendered":"

\u672c\u6587\u57fa\u4e8e\u8df3\u8868\u4f5c\u8005William Pugh\u539f\u8bba\u6587\u8fdb\u884c\u539f\u7406\u89e3\u8bfb\u548c\u4ee3\u7801\u5b9e\u73b0\u5206\u6790<\/p>\n

<\/p>\n

\u8df3\u8868\u601d\u60f3<\/h3>\n

\u8df3\u8868\u662f\u6709\u5e8f\u94fe\u8868\u5b58\u50a8\u6570\u636e\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5176\u5728\u94fe\u8868\u4e0a\u5efa\u7acb\u4e86\u591a\u7ea7\u7d22\u5f15\u3002\u8fd9\u4e9b\u7d22\u5f15\u5c06\u94fe\u8868\u5212\u5206\u4e3a\u591a\u4e2a\u533a\u95f4\uff0c\u540c\u65f6\u7d22\u5f15\u6307\u5411\u81ea\u8eab\u5212\u5206\u7684\u533a\u95f4\u8d77\u70b9\uff0c\u7528\u4ee5\u52a0\u5feb\u8303\u56f4\u67e5\u8be2\uff1a<\/p>\n

1\uff09\u9ad8\u5c42\u7d22\u5f15\u8282\u70b9\u6570\u91cf\u5c11\uff0c\u5212\u5206\u533a\u95f4\u6570\u91cf\u5c11\u8de8\u5ea6\u5927\uff0c\u6392\u9664\u5927\u8303\u56f4\u65e0\u6548\u67e5\u8be2<\/p>\n

2\uff09\u4f4e\u5c42\u7d22\u5f15\u8282\u70b9\u6570\u91cf\u591a\uff0c\u5212\u5206\u533a\u95f4\u6570\u91cf\u591a\u8de8\u5ea6\u5c0f\uff0c\u641c\u7d22\u6570\u91cf\u5c11\uff0c\u67e5\u8be2\u8ddd\u79bb\u8282\u70b9\u8d8a\u8fd1\uff0c\u7cbe\u5ea6\u66f4\u9ad8<\/p>\n

\"SkipList\"<\/p>\n

\u5982\u56fe\u8282\u70b99\u5efa\u7acb\u4e86\u533a\u95f4[9,21)\u3001[9,17)\u3001[9,12)\u7684\u7d22\u5f15<\/p>\n

\u67e5\u8be2\u64cd\u4f5c<\/h3>\n

\u8df3\u8868\u67e5\u8be2\u65f6\u4e0d\u65ad\u786e\u5b9a\u5143\u7d20\u6240\u5728\u533a\u95f4\uff1a\u540c\u5c42\u4e4b\u95f4\u4ece\u5de6\u5230\u53f3\uff1b\u4e0d\u540c\u5c42\u4e4b\u95f4\u4ece\u4e0a\u5230\u4e0b\u3001\u8de8\u5ea6\u7531\u5927\u5230\u5c0f\u3002\u5f53\u533a\u95f4\u957f\u5ea6\u4e3a1\uff0c\u4e14\u5de6\u7aef\u70b9\u4e3a\u4e0d\u8d85\u8fc7\u5143\u7d20\u503c\u7684\u6700\u5927\u533a\u95f4\u5de6\u7aef\u70b9\u65f6\uff0c\u5230\u8fbe\u6b63\u786e\u67e5\u8be2\u533a\u95f4<\/p>\n

\nSearch(list, searchKey)\n    x := list\u2192header\n    for i := list\u2192level downto 1 do                 \/\/ \u4ece\u4e0a\u5230\u4e0b\u786e\u5b9a\u5143\u7d20\u6240\u5728\u533a\u95f4\n        while x\u2192forward[i]\u2192key < searchKey do\n            x := x\u2192forward[i]                       \/\/ \u4ece\u5de6\u5230\u53f3\u786e\u5b9a\u5143\u7d20\u6240\u5728\u533a\u95f4\uff0c\u5e76\u8bb0\u5f55\u533a\u95f4\u5de6\u7aef\u70b9\n    x := x\u2192forward[1]                               \/\/ \u5e95\u5c42\u533a\u95f4\u957f\u5ea6\u4e3a1\uff0c\u5de6\u7aef\u70b9\u53f3\u4fa7\u8282\u70b9\u4e0d\u5c0f\u4e8e\u5143\u7d20\u503c\n    if x\u2192key = searchKey then return x\u2192value        \/\/ \u7b49\u4e8e\u67e5\u8be2\u6210\u529f\n    else return failure                             \/\/ \u5927\u4e8e\u5219\u5143\u7d20\u4e0d\u5728\u8df3\u8868\u4e2d\n<\/pre>\n
\u63d2\u5165\u64cd\u4f5c<\/h3>\n
\u2460\u67e5\u8be2\u5230\u6b63\u786e\u533a\u95f4\u63d2\u5165\u5143\u7d20
\n\u2461\u66f4\u65b0\u5f85\u63d2\u5143\u7d20\u5de6\u53f3\u4fa7\u8282\u70b9\u7684\u6307\u9488\u6307\u5411
\n\u2462\u63d2\u5165\u8282\u70b9\u9ad8\u4e8e\u539f\u8df3\u8868\uff0c\u9700\u5904\u7406\u9ad8\u5c42\u6307\u9488\u548c\u5168\u8868\u9ad8\u5ea6<\/p>\n
\"SkipList\"<\/p>\n
\u56fe\u4e3a\u63d2\u516517\u65f6\u7684\u67e5\u8be2\u8def\u5f84\u548c\u6307\u9488\u4fee\u6539<\/p>\n
\nInsert(list, searchKey, newValue)\n    local update[1..MaxLevel]\n    x := list\u2192header\n    for i := list\u2192level downto 1 do\n        while x\u2192forward[i]\u2192key < searchKey do\n            x := x\u2192forward[i]\n        update[i] := x                              \/\/ \u8bb0\u5f55\u5143\u7d20\u6240\u5728\u5404\u533a\u95f4\u7684\u5de6\u7aef\u70b9\uff0c\u5c0f\u4e8e\u5143\u7d20\u503c\n    x := x\u2192forward[1]                               \/\/ \u5143\u7d20\u6240\u5728\u5e95\u5c42\u533a\u95f4\u5de6\u7aef\u70b9\u53f3\u4fa7\u4e3a\u6b63\u786e\u4f4d\u7f6e\n    if x\u2192key = searchKey then x\u2192value := newValue   \/\/ \u5df2\u6709\u5f85\u63d2\u8282\u70b9\u4ec5\u66f4\u65b0\u503c\n    else                                            \/\/ \u5c1a\u65e0\u5f85\u63d2\u8282\u70b9\u5219\u63d2\u5165\u8282\u70b9\n        lvl := randomLevel()                        \/\/ \u968f\u673a\u751f\u6210\u5f85\u63d2\u8282\u70b9\u9ad8\u5ea6\n        if lvl > list\u2192level then                    \/\/ \u65b0\u8282\u70b9\u9ad8\u4e8e\u8df3\u8868\uff0c\u5934\u8282\u70b9\u9ad8\u5c42\u5e94\u6307\u5411\u8be5\u8282\u70b9\n            for i := list\u2192level + 1 to lvl do\n                update[i] := list\u2192header\n            list\u2192level := lvl\n        x := makeNode(lvl, searchKey, value)\n        for i := 1 to level do                      \/\/ \u5c06\u65b0\u8282\u70b9\"\u6321\u5165\"\u6700\u53f3\u8282\u70b9\u548c\u4e0b\u4e00\u8282\u70b9\u4e4b\u95f4\n            x\u2192forward[i] := update[i]\u2192forward[i]\n            update[i]\u2192forward[i] := x\n<\/pre>\n
\u5220\u9664\u64cd\u4f5c<\/h3>\n
\u2460\u67e5\u627e\u5220\u9664\u5143\u7d20\u6240\u5728\u4f4d\u7f6e
\n\u2461"\u62bd\u9664"\u8282\u70b9\u540e\u5e94\u8fd8\u539f\u5f85\u5220\u5143\u7d20\u5de6\u53f3\u4fa7\u8282\u70b9\u4e4b\u95f4\u7684\u6307\u9488\u6307\u5411
\n\u2462\u552f\u4e00\u6700\u9ad8\u8282\u70b9\u5220\u9664\u540e\u5e94\u964d\u4f4e\u8df3\u8868\u9ad8\u5ea6\u4e3a\u7b2c\u4e8c\u9ad8\u8282\u70b9\u9ad8\u5ea6<\/p>\n
\nDelete(list, searchKey)\n    local update[1..MaxLevel]\n    x := list\u2192header\n    for i := list\u2192level downto 1 do\n        while x\u2192forward[i]\u2192key < searchKey do\n            x := x\u2192forward[i]\n        update[i] := x                              \/\/ \u8bb0\u5f55\u5143\u7d20\u6240\u5728\u5404\u533a\u95f4\u7684\u5de6\u7aef\u70b9\uff0c\u5c0f\u4e8e\u5143\u7d20\u503c\n    x := x\u2192forward[1]                               \/\/ \u6307\u5411\u5f85\u5220\u8282\u70b9\u6240\u5728\u4f4d\u7f6e\n    if x\u2192key = searchKey then                       \/\/ \u5f85\u5220\u8282\u70b9\u4ec5\u5f53\u5b58\u5728\u65f6\u5904\u7406\n        for i := 1 to list\u2192level do\n            if update[i]\u2192forward[i] \u2260 x then break  \/\/ * \u4f18\u5316\uff1a\u65e0\u9700\u5904\u7406\u552f\u4e00\u6700\u9ad8\u8282\u70b9\u72ec\u5c5e\u9ad8\u5ea6\n            update[i]\u2192forward[i] := x\u2192forward[i]    \/\/ \u8fd8\u539f\u5220\u9664\u5143\u7d20\u5de6\u53f3\u4fa7\u8282\u70b9\u7684\u6307\u9488\u6307\u5411\n        free(x)                                     \/\/ \u91ca\u653e\u5220\u9664\u8282\u70b9\u5185\u5b58\n        while list\u2192level > 1 and list\u2192header\u2192forward[list\u2192level] = NIL do\n            list\u2192level := list\u2192level \u2013 1            \/\/ \u964d\u4f4e\u8df3\u8868\u9ad8\u5ea6\u81f3\u5f53\u524d\u6700\u9ad8\u8282\u70b9\u9ad8\u5ea6\n<\/pre>\n
\u6027\u80fd\u5206\u6790<\/h3>\n
\u589e\u5220\u67e5\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6 \\scriptsize O(\\log n)<\/code>
\n\u5e73\u5747\u7a7a\u95f4\u590d\u6742\u5ea6 \\scriptsize O(\\frac{n}{1-p})<\/code><\/p>\n
\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u4ee3\u66ff\u5e73\u8861\u67e5\u627e\u6811<\/h3>\n
\u8df3\u8868\u7684\u6027\u80fd\u63a5\u8fd1\u4e8e\u5e73\u8861\u67e5\u627e\u6811
\n\u8df3\u8868\u7ef4\u62a4\u7d22\u5f15\u4ee3\u4ef7\u4f4e\u4e8e\u7ef4\u62a4\u5e73\u8861\u64cd\u4f5c\u4ee3\u4ef7
\n\u8df3\u8868\u7684\u4ee3\u7801\u5b9e\u73b0\u66f4\u7b80\u5355\uff0c\u53ef\u8bfb\u6027\u53ef\u7406\u89e3\u6027\u66f4\u5f3a<\/p>\n
\u5e94\u7528<\/h3>\n
Redis\u4e2d\u6392\u5e8f\u96c6\u5408zset\u5e95\u5c42\u5b9e\u73b0<\/p>\n
\u53c2\u8003\u8d44\u6599<\/h3>\n
W. Pugh, Skip Lists: A Probabilistic Alternative to Balanced Trees, in CACM, 1990<\/p>\n","protected":false},"excerpt":{"rendered":"
\u672c\u6587\u57fa\u4e8e\u8df3\u8868\u4f5c\u8005William Pugh\u539f\u8bba\u6587\u8fdb\u884c\u539f\u7406\u89e3\u8bfb\u548c\u4ee3\u7801\u5b9e\u73b0\u5206\u6790<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12],"tags":[59,61,60,58],"jetpack_featured_media_url":"","_links":{"self":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2241"}],"collection":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2241"}],"version-history":[{"count":23,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2241\/revisions"}],"predecessor-version":[{"id":2745,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2241\/revisions\/2745"}],"wp:attachment":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2241"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2241"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}