{"id":492,"date":"2022-04-14T20:15:03","date_gmt":"2022-04-14T12:15:03","guid":{"rendered":"http:\/\/120.55.184.7\/?p=492"},"modified":"2025-04-27T17:56:37","modified_gmt":"2025-04-27T09:56:37","slug":"ac%e8%87%aa%e5%8a%a8%e6%9c%ba%ef%bc%9a%e9%ab%98%e6%95%88%e5%a4%9a%e6%a8%a1%e5%bc%8f%e5%8c%b9%e9%85%8d%e7%ae%97%e6%b3%95%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/beijian99.top\/?p=492","title":{"rendered":"AC\u81ea\u52a8\u673a\uff1a\u9ad8\u6548\u591a\u6a21\u5f0f\u5339\u914d\u7b97\u6cd5"},"content":{"rendered":"\n<p>AC \u81ea\u52a8\u673a\uff08Aho-Corasick Automaton\uff09\u8be6\u89e3<\/p>\n\n\n\n<p>AC \u81ea\u52a8\u673a\uff08Aho-Corasick Automaton\uff09\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u591a\u6a21\u5f0f\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5\uff0c\u7531 Alfred Aho \u548c Margaret Corasick \u5728 1975 \u5e74\u63d0\u51fa\u3002\u5b83\u7ed3\u5408\u4e86 Trie \u6811 \u548c KMP \u7b97\u6cd5 \u7684\u601d\u60f3\uff0c\u80fd\u591f\u5728 O(n + m + z) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u5b8c\u6210\u591a\u6a21\u5f0f\u5339\u914d\uff0c\u5176\u4e2d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>n<\/code> \u662f\u4e3b\u4e32\u7684\u957f\u5ea6\uff0c<\/li>\n\n\n\n<li><code>m<\/code> \u662f\u6240\u6709\u6a21\u5f0f\u4e32\u7684\u603b\u957f\u5ea6\uff0c<\/li>\n\n\n\n<li><code>z<\/code> \u662f\u5339\u914d\u6210\u529f\u7684\u6b21\u6570\u3002<\/li>\n<\/ul>\n\n\n\n<p>AC \u81ea\u52a8\u673a\u7279\u522b\u9002\u5408 \u591a\u6a21\u5f0f\u4e32\u5339\u914d \u573a\u666f\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u75c5\u6bd2\u626b\u63cf\uff08\u68c0\u6d4b\u6587\u672c\u4e2d\u662f\u5426\u5305\u542b\u5df2\u77e5\u75c5\u6bd2\u7279\u5f81\u7801\uff09\uff0c<\/li>\n\n\n\n<li>\u5173\u952e\u8bcd\u8fc7\u6ee4\uff08\u5982\u654f\u611f\u8bcd\u68c0\u6d4b\uff09\uff0c<\/li>\n\n\n\n<li>DNA \u5e8f\u5217\u5206\u6790\u7b49\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u4e00\u3001AC \u81ea\u52a8\u673a\u7684\u6838\u5fc3\u601d\u60f3<\/p>\n\n\n\n<p>AC \u81ea\u52a8\u673a\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Trie \u6811\uff1a\u5c06\u6240\u6709\u6a21\u5f0f\u4e32\u6784\u5efa\u6210\u4e00\u68f5 Trie \u6811\uff0c\u4fbf\u4e8e\u5feb\u901f\u67e5\u627e\u3002<\/li>\n\n\n\n<li>\u5931\u8d25\u6307\u9488\uff08Fail Pointer\uff09\uff1a\u7c7b\u4f3c\u4e8e KMP \u7b97\u6cd5\u7684 <code>next<\/code> \u6570\u7ec4\uff0c\u7528\u4e8e\u5728\u4e0d\u5339\u914d\u65f6\u8df3\u8f6c\uff0c\u907f\u514d\u4ece\u5934\u5f00\u59cb\u5339\u914d\u3002<\/li>\n\n\n\n<li>\u8f93\u51fa\u51fd\u6570\uff08Output Function\uff09\uff1a\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u5bf9\u5e94\u7684\u5339\u914d\u6a21\u5f0f\u4e32\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u4e8c\u3001AC \u81ea\u52a8\u673a\u7684\u6784\u5efa\u6b65\u9aa4<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6784\u5efa Trie \u6811<br>\u5c06\u6240\u6709\u6a21\u5f0f\u4e32\u63d2\u5165\u5230 Trie \u6811\u4e2d\uff0c\u5e76\u4e3a\u6bcf\u4e2a\u8282\u70b9\u6807\u8bb0\u662f\u5426\u4e3a\u67d0\u4e2a\u6a21\u5f0f\u4e32\u7684\u7ed3\u5c3e\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u793a\u4f8b\uff1a<br>\u6a21\u5f0f\u4e32\u96c6\u5408\uff1a<code>[\"he\", \"she\", \"his\", \"hers\"]<\/code><\/p>\n\n\n\n<p>\u6784\u5efa\u7684 Trie \u6811\u5982\u4e0b\uff1a<\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: plain; title: ; notranslate\" title=\"\">\n        (root)\n       \/  |  \\\n      h   s   ...\n     \/ \\   \\\n    e   i   h\n   \/     \\   \\\n  *       s   i\n           \\   \\\n            *   r\n                 \\\n                  s\n                   *\n<\/pre><\/div>\n\n\n<p>\u5176\u4e2d <code>*<\/code> \u8868\u793a\u8be5\u8282\u70b9\u662f\u67d0\u4e2a\u6a21\u5f0f\u4e32\u7684\u7ed3\u5c3e\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>\u6784\u5efa\u5931\u8d25\u6307\u9488\uff08Fail Pointer\uff09<br>\u5931\u8d25\u6307\u9488\u7684\u4f5c\u7528\u662f\uff1a\u5f53\u5f53\u524d\u5b57\u7b26\u5339\u914d\u5931\u8d25\u65f6\uff0c\u8df3\u8f6c\u5230\u53e6\u4e00\u4e2a\u8282\u70b9\u7ee7\u7eed\u5339\u914d\uff0c\u7c7b\u4f3c\u4e8e KMP \u7684 <code>next<\/code> \u6570\u7ec4\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6784\u5efa\u89c4\u5219\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6839\u8282\u70b9\u7684\u5931\u8d25\u6307\u9488\uff1a\u6307\u5411 <code>null<\/code>\uff08\u6216\u81ea\u8eab\uff09\u3002<\/li>\n\n\n\n<li>\u6839\u8282\u70b9\u7684\u5b50\u8282\u70b9\u7684\u5931\u8d25\u6307\u9488\uff1a\u6307\u5411\u6839\u8282\u70b9\uff08\u56e0\u4e3a\u5982\u679c\u5339\u914d\u5931\u8d25\uff0c\u53ef\u4ee5\u91cd\u65b0\u4ece\u6839\u8282\u70b9\u5f00\u59cb\u5339\u914d\uff09\u3002<\/li>\n\n\n\n<li>\u5176\u4ed6\u8282\u70b9\u7684\u5931\u8d25\u6307\u9488\uff1a \u2022 \u5982\u679c\u5f53\u524d\u8282\u70b9\u7684\u7236\u8282\u70b9\u7684\u5931\u8d25\u6307\u9488\u6709\u76f8\u540c\u5b57\u7b26\u7684\u5b50\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u6307\u5411\u8be5\u5b50\u8282\u70b9\u3002 \u2022 \u5426\u5219\uff0c\u7ee7\u7eed\u6cbf\u7740\u5931\u8d25\u6307\u9488\u5411\u4e0a\u67e5\u627e\uff0c\u76f4\u5230\u627e\u5230\u5339\u914d\u7684\u5b50\u8282\u70b9\u6216\u56de\u5230\u6839\u8282\u70b9\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u793a\u4f8b\uff1a<br>\u4ee5 <code>\"he\", \"she\", \"his\", \"hers\"<\/code> \u4e3a\u4f8b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>h<\/code> \u7684\u5931\u8d25\u6307\u9488\u6307\u5411\u6839\u8282\u70b9\uff08\u56e0\u4e3a\u5b83\u662f\u6839\u8282\u70b9\u7684\u5b50\u8282\u70b9\uff09\u3002<\/li>\n\n\n\n<li><code>e<\/code> \u7684\u5931\u8d25\u6307\u9488\uff1a<code>h<\/code> \u7684\u5931\u8d25\u6307\u9488\u662f\u6839\u8282\u70b9\uff0c\u6839\u8282\u70b9\u6ca1\u6709 <code>e<\/code> \u5b50\u8282\u70b9\uff0c\u6240\u4ee5 <code>e<\/code> \u7684\u5931\u8d25\u6307\u9488\u6307\u5411\u6839\u8282\u70b9\u3002<\/li>\n\n\n\n<li><code>s<\/code> \u7684\u5931\u8d25\u6307\u9488\uff1a<code>h<\/code> \u7684\u5931\u8d25\u6307\u9488\u662f\u6839\u8282\u70b9\uff0c\u6839\u8282\u70b9\u6709 <code>s<\/code> \u5b50\u8282\u70b9\uff0c\u6240\u4ee5 <code>s<\/code> \u7684\u5931\u8d25\u6307\u9488\u6307\u5411\u6839\u8282\u70b9\u7684 <code>s<\/code> \u5b50\u8282\u70b9\u3002<\/li>\n\n\n\n<li><code>i<\/code> \u7684\u5931\u8d25\u6307\u9488\uff1a<code>h<\/code> \u7684\u5931\u8d25\u6307\u9488\u662f\u6839\u8282\u70b9\uff0c\u6839\u8282\u70b9\u6ca1\u6709 <code>i<\/code> \u5b50\u8282\u70b9\uff0c\u6240\u4ee5 <code>i<\/code> \u7684\u5931\u8d25\u6307\u9488\u6307\u5411\u6839\u8282\u70b9\u3002<\/li>\n\n\n\n<li><code>r<\/code> \u7684\u5931\u8d25\u6307\u9488\uff1a<code>s<\/code> \u7684\u5931\u8d25\u6307\u9488\u662f <code>h<\/code> \u7684 <code>s<\/code> \u5b50\u8282\u70b9\uff0c<code>h<\/code> \u7684 <code>s<\/code> \u5b50\u8282\u70b9\u6ca1\u6709 <code>r<\/code> \u5b50\u8282\u70b9\uff0c\u7ee7\u7eed\u5411\u4e0a\u627e <code>h<\/code> \u7684\u5931\u8d25\u6307\u9488\uff08\u6839\u8282\u70b9\uff09\uff0c\u6839\u8282\u70b9\u6ca1\u6709 <code>r<\/code> \u5b50\u8282\u70b9\uff0c\u6240\u4ee5 <code>r<\/code> \u7684\u5931\u8d25\u6307\u9488\u6307\u5411\u6839\u8282\u70b9\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li>\u6784\u5efa\u8f93\u51fa\u51fd\u6570\uff08Output Function\uff09<br>\u8f93\u51fa\u51fd\u6570\u7528\u4e8e\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u5bf9\u5e94\u7684\u5339\u914d\u6a21\u5f0f\u4e32\u3002\u5982\u679c\u67d0\u4e2a\u8282\u70b9\u662f\u67d0\u4e2a\u6a21\u5f0f\u4e32\u7684\u7ed3\u5c3e\uff0c\u6216\u8005\u5b83\u7684\u5931\u8d25\u6307\u9488\u6307\u5411\u7684\u8282\u70b9\u662f\u67d0\u4e2a\u6a21\u5f0f\u4e32\u7684\u7ed3\u5c3e\uff0c\u5219\u8be5\u8282\u70b9\u9700\u8981\u8f93\u51fa\u5bf9\u5e94\u7684\u6a21\u5f0f\u4e32\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u793a\u4f8b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>e<\/code> \u662f <code>\"he\"<\/code> \u7684\u7ed3\u5c3e\uff0c\u6240\u4ee5 <code>e<\/code> \u7684\u8f93\u51fa\u662f <code>\"he\"<\/code>\u3002<\/li>\n\n\n\n<li><code>s<\/code> \u662f <code>\"she\"<\/code> \u548c <code>\"hers\"<\/code> \u7684\u7ed3\u5c3e\uff0c\u6240\u4ee5 <code>s<\/code> \u7684\u8f93\u51fa\u662f <code>\"she\"<\/code> \u548c <code>\"hers\"<\/code>\uff08\u9700\u8981\u68c0\u67e5\u5931\u8d25\u6307\u9488\u94fe\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u4e09\u3001AC \u81ea\u52a8\u673a\u7684\u5339\u914d\u8fc7\u7a0b<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u521d\u59cb\u5316\uff1a\u4ece Trie \u6811\u7684\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u9010\u4e2a\u5b57\u7b26\u5339\u914d\u4e3b\u4e32\u3002<\/li>\n\n\n\n<li>\u5339\u914d\u5b57\u7b26\uff1a<br>\u2022 \u5982\u679c\u5f53\u524d\u5b57\u7b26\u5339\u914d\u6210\u529f\uff0c\u5219\u79fb\u52a8\u5230\u5bf9\u5e94\u7684\u5b50\u8282\u70b9\uff0c\u5e76\u68c0\u67e5\u8be5\u8282\u70b9\u53ca\u5176\u5931\u8d25\u6307\u9488\u94fe\u662f\u5426\u6709\u8f93\u51fa\u3002 \u2022 \u5982\u679c\u5339\u914d\u5931\u8d25\uff0c\u5219\u6cbf\u7740\u5931\u8d25\u6307\u9488\u8df3\u8f6c\uff0c\u76f4\u5230\u627e\u5230\u5339\u914d\u7684\u5b50\u8282\u70b9\u6216\u56de\u5230\u6839\u8282\u70b9\u3002<\/li>\n\n\n\n<li>\u8f93\u51fa\u5339\u914d\u7ed3\u679c\uff1a\u6bcf\u5f53\u5230\u8fbe\u4e00\u4e2a\u8282\u70b9\u65f6\uff0c\u68c0\u67e5\u8be5\u8282\u70b9\u53ca\u5176\u5931\u8d25\u6307\u9488\u94fe\u662f\u5426\u6709\u8f93\u51fa\uff0c\u5982\u679c\u6709\u5219\u8bb0\u5f55\u5339\u914d\u7684\u6a21\u5f0f\u4e32\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u793a\u4f8b\uff1a<br>\u4e3b\u4e32\uff1a<code>\"ahishers\"<\/code><br>\u6a21\u5f0f\u4e32\u96c6\u5408\uff1a<code>[\"he\", \"she\", \"his\", \"hers\"]<\/code><\/p>\n\n\n\n<p>\u5339\u914d\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><code>'a'<\/code>\uff1a\u4e0d\u5339\u914d\uff0c\u505c\u7559\u5728\u6839\u8282\u70b9\u3002<\/li>\n\n\n\n<li><code>'h'<\/code>\uff1a\u5339\u914d\uff0c\u79fb\u52a8\u5230 <code>h<\/code> \u8282\u70b9\u3002<\/li>\n\n\n\n<li><code>'i'<\/code>\uff1a\u5339\u914d\uff0c\u79fb\u52a8\u5230 <code>i<\/code> \u8282\u70b9\uff08<code>\"his\"<\/code> \u5339\u914d\u6210\u529f\uff09\u3002<\/li>\n\n\n\n<li><code>'s'<\/code>\uff1a\u5339\u914d\uff0c\u79fb\u52a8\u5230 <code>s<\/code> \u8282\u70b9\uff08<code>\"his\"<\/code> \u548c <code>\"hers\"<\/code> \u5339\u914d\u6210\u529f\uff09\u3002<br>\u2022 \u68c0\u67e5 <code>s<\/code> \u7684\u8f93\u51fa\uff1a<code>\"hers\"<\/code>\u3002 \u2022 \u68c0\u67e5 <code>s<\/code> \u7684\u5931\u8d25\u6307\u9488\uff08\u6307\u5411 <code>h<\/code> \u7684 <code>s<\/code> \u5b50\u8282\u70b9\uff09\u7684\u8f93\u51fa\uff1a<code>\"she\"<\/code>\uff08\u56e0\u4e3a <code>h<\/code> \u7684 <code>s<\/code> \u5b50\u8282\u70b9\u662f <code>\"she\"<\/code> \u7684\u7ed3\u5c3e\uff09\u3002<\/li>\n\n\n\n<li><code>'h'<\/code>\uff1a\u4e0d\u5339\u914d\uff0c\u6cbf\u7740 <code>s<\/code> \u7684\u5931\u8d25\u6307\u9488\u8df3\u8f6c\uff08\u56de\u5230 <code>h<\/code> \u7684 <code>s<\/code> \u5b50\u8282\u70b9\u7684\u5931\u8d25\u6307\u9488\uff0c\u5373 <code>h<\/code> \u8282\u70b9\uff09\u3002<\/li>\n\n\n\n<li><code>'e'<\/code>\uff1a\u5339\u914d\uff0c\u79fb\u52a8\u5230 <code>e<\/code> \u8282\u70b9\uff08<code>\"he\"<\/code> \u5339\u914d\u6210\u529f\uff09\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6700\u7ec8\u5339\u914d\u7ed3\u679c\uff1a<code>\"his\"<\/code>, <code>\"hers\"<\/code>, <code>\"he\"<\/code>\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u56db\u3001AC \u81ea\u52a8\u673a\u7684 C++ \u5b9e\u73b0<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u662f AC \u81ea\u52a8\u673a\u7684\u5b8c\u6574 C++ \u5b9e\u73b0\uff1a<\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: cpp; title: ; notranslate\" title=\"\">\n#include &lt;iostream&gt;\n#include &lt;vector&gt;\n#include &lt;queue&gt;\n#include &lt;unordered_map&gt;\nusing namespace std;\n\nstruct TrieNode {\n    unordered_map&lt;char, TrieNode*&gt; children;\n    TrieNode* fail = nullptr;\n    vector&lt;int&gt; output; \/\/ \u5b58\u50a8\u5339\u914d\u7684\u6a21\u5f0f\u4e32\u7d22\u5f15\n};\n\nclass ACAutomaton {\nprivate:\n    TrieNode* root;\n    vector&lt;string&gt; patterns;\n\n    void buildTrie(const vector&lt;string&gt;&amp; patterns) {\n        this-&gt;patterns = patterns;\n        root = new TrieNode();\n        for (int i = 0; i &lt; patterns.size(); ++i) {\n            TrieNode* node = root;\n            for (char c : patterns&#x5B;i]) {\n                if (!node-&gt;children.count(c)) {\n                    node-&gt;children&#x5B;c] = new TrieNode();\n                }\n                node = node-&gt;children&#x5B;c];\n            }\n            node-&gt;output.push_back(i); \/\/ \u8bb0\u5f55\u6a21\u5f0f\u4e32\u7d22\u5f15\n        }\n    }\n\n    void buildFailPointers() {\n        queue&lt;TrieNode*&gt; q;\n        root-&gt;fail = nullptr;\n        for (auto&amp; &#x5B;c, child] : root-&gt;children) {\n            child-&gt;fail = root;\n            q.push(child);\n        }\n\n        while (!q.empty()) {\n            TrieNode* current = q.front();\n            q.pop();\n\n            for (auto&amp; &#x5B;c, child] : current-&gt;children) {\n                TrieNode* failNode = current-&gt;fail;\n                while (failNode != nullptr &amp;&amp; !failNode-&gt;children.count(c)) {\n                    failNode = failNode-&gt;fail;\n                }\n                child-&gt;fail = (failNode == nullptr) ? root : failNode-&gt;children&#x5B;c];\n                child-&gt;output.insert(child-&gt;output.end(), child-&gt;fail-&gt;output.begin(), child-&gt;fail-&gt;output.end());\n                q.push(child);\n            }\n        }\n    }\n\npublic:\n    ACAutomaton(const vector&lt;string&gt;&amp; patterns) {\n        buildTrie(patterns);\n        buildFailPointers();\n    }\n\n    vector&lt;int&gt; search(const string&amp; text) {\n        vector&lt;int&gt; matches;\n        TrieNode* node = root;\n        for (int i = 0; i &lt; text.size(); ++i) {\n            char c = text&#x5B;i];\n            while (node != nullptr &amp;&amp; !node-&gt;children.count(c)) {\n                node = node-&gt;fail;\n            }\n            if (node == nullptr) {\n                node = root;\n                continue;\n            }\n            node = node-&gt;children&#x5B;c];\n            for (int patternIndex : node-&gt;output) {\n                matches.push_back(patternIndex);\n            }\n        }\n        return matches;\n    }\n\n    vector&lt;string&gt; getPatterns() const {\n        return patterns;\n    }\n};\n\nint main() {\n    vector&lt;string&gt; patterns = {&quot;he&quot;, &quot;she&quot;, &quot;his&quot;, &quot;hers&quot;};\n    ACAutomaton ac(patterns);\n\n    string text = &quot;ahishers&quot;;\n    vector&lt;int&gt; matches = ac.search(text);\n\n    cout &lt;&lt; &quot;Matches found at positions: &quot;;\n    for (int idx : matches) {\n        cout &lt;&lt; patterns&#x5B;idx] &lt;&lt; &quot; &quot;;\n    }\n    cout &lt;&lt; endl;\n\n    return 0;\n}\n<\/pre><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u4e94\u3001AC \u81ea\u52a8\u673a\u7684\u65f6\u95f4\u590d\u6742\u5ea6<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6784\u5efa Trie \u6811\uff1aO(m)\uff0c\u5176\u4e2d m \u662f\u6240\u6709\u6a21\u5f0f\u4e32\u7684\u603b\u957f\u5ea6\u3002<\/li>\n\n\n\n<li>\u6784\u5efa\u5931\u8d25\u6307\u9488\uff1aO(m)\uff0c\u4f7f\u7528 BFS \u904d\u5386 Trie \u6811\u3002<\/li>\n\n\n\n<li>\u5339\u914d\u8fc7\u7a0b\uff1aO(n + z)\uff0c\u5176\u4e2d n \u662f\u4e3b\u4e32\u957f\u5ea6\uff0cz \u662f\u5339\u914d\u6210\u529f\u7684\u6b21\u6570\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u603b\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(m + n + z)\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u516d\u3001AC \u81ea\u52a8\u673a\u7684\u5e94\u7528\u573a\u666f<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u75c5\u6bd2\u626b\u63cf\uff1a\u68c0\u6d4b\u6587\u672c\u4e2d\u662f\u5426\u5305\u542b\u5df2\u77e5\u75c5\u6bd2\u7279\u5f81\u7801\u3002<\/li>\n\n\n\n<li>\u5173\u952e\u8bcd\u8fc7\u6ee4\uff1a\u5982\u654f\u611f\u8bcd\u68c0\u6d4b\u3001\u5e7f\u544a\u5c4f\u853d\u3002<\/li>\n\n\n\n<li>DNA \u5e8f\u5217\u5206\u6790\uff1a\u5feb\u901f\u67e5\u627e DNA \u5e8f\u5217\u4e2d\u7684\u7279\u5b9a\u6a21\u5f0f\u3002<\/li>\n\n\n\n<li>\u641c\u7d22\u5f15\u64ce\uff1a\u5feb\u901f\u5339\u914d\u641c\u7d22\u5173\u952e\u8bcd\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u4e03\u3001\u603b\u7ed3<\/p>\n\n\n\n<p>AC \u81ea\u52a8\u673a\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u591a\u6a21\u5f0f\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5\uff0c\u7ed3\u5408\u4e86 Trie \u6811\u548c KMP \u7b97\u6cd5\u7684\u601d\u60f3\uff0c\u80fd\u591f\u5728 O(n + m + z) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u5b8c\u6210\u5339\u914d\u3002\u5b83\u7684\u6838\u5fc3\u662f Trie \u6811 \u548c \u5931\u8d25\u6307\u9488\uff0c\u9002\u7528\u4e8e\u9700\u8981\u540c\u65f6\u5339\u914d\u591a\u4e2a\u6a21\u5f0f\u4e32\u7684\u573a\u666f\u3002<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>AC \u81ea\u52a8\u673a\uff08Aho-Corasick Automaton\uff09\u8be6\u89e3 AC \u81ea\u52a8\u673a\uff08Aho-Corasick Au [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":497,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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