{"id":54047,"date":"2025-08-12T21:30:10","date_gmt":"2025-08-12T13:30:10","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/54047.html"},"modified":"2025-08-12T21:30:10","modified_gmt":"2025-08-12T13:30:10","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e5%88%86%e4%ba%ab%e3%80%91%e5%ad%97%e5%85%b8%e6%a0%91-%e6%8f%92%e5%85%a5%e3%80%81%e6%9f%a5%e8%af%a2%e4%b8%8e%e7%8a%b6%e6%80%81%e6%a0%87%e8%ae%b0%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/54047.html","title":{"rendered":"\u3010\u7b97\u6cd5\u5206\u4eab\u3011\u5b57\u5178\u6811 \u2014\u63d2\u5165\u3001\u67e5\u8be2\u4e0e\u72b6\u6001\u6807\u8bb0\u8be6\u89e3"},"content":{"rendered":"<h2>\u5b57\u5178\u6811(Trie)&#xff1a;\u9ad8\u6548\u7684\u5b57\u7b26\u4e32\u5904\u7406\u5229\u5668 &#x1f333;<\/h2>\n<p>\u5728\u5904\u7406\u5927\u91cf\u5b57\u7b26\u4e32\u6570\u636e\u65f6&#xff0c;\u6211\u4eec\u7ecf\u5e38\u9700\u8981\u8fdb\u884c\u524d\u7f00\u5339\u914d\u3001\u5355\u8bcd\u67e5\u627e\u3001\u81ea\u52a8\u8865\u5168\u7b49\u64cd\u4f5c\u3002\u5982\u679c\u4f7f\u7528\u666e\u901a\u7684\u6570\u7ec4\u6216\u8005\u54c8\u5e0c\u8868&#xff0c;\u867d\u7136\u80fd\u591f\u89e3\u51b3\u95ee\u9898&#xff0c;\u4f46\u662f\u6548\u7387\u90fd\u4e0d\u662f\u5f88\u7406\u60f3\u3002\u90a3\u6211\u4eec\u6765\u5b66\u4e60\u4e00\u79cd\u4e13\u95e8\u4e3a\u5b57\u7b26\u4e32\u800c\u8bbe\u8ba1\u7684\u6570\u636e\u7ed3\u6784\u2014\u2014\u5b57\u5178\u6811&#xff08;Trie&#xff09;\u3002<\/p>\n<h3>\u4ec0\u4e48\u662f\u5b57\u5178\u6811&#xff1f; &#x1f914;<\/h3>\n<p>\u5b57\u5178\u6811&#xff0c;\u53c8\u79f0\u524d\u7f00\u6811\u6216\u5355\u8bcd\u67e5\u627e\u6811&#xff0c;\u662f\u4e00\u79cd\u6709\u5e8f\u6811\u7ed3\u6784&#xff0c;\u7528\u4e8e\u4fdd\u5b58\u5173\u8054\u6570\u7ec4&#xff0c;\u5176\u4e2d\u7684\u952e\u901a\u5e38\u662f\u5b57\u7b26\u4e32\u3002\u5b83\u7684\u540d\u5b57\u6765\u6e90\u4e8eretrieval&#xff08;\u68c0\u7d22&#xff09;&#xff0c;\u56e0\u4e3a\u5b83\u80fd\u591f\u5feb\u901f\u68c0\u7d22\u5b57\u7b26\u4e32\u3002<\/p>\n<h3>\u5b57\u5178\u6811\u7684\u7279\u70b9 \u2728<\/h3>\n<ul>\n<li>\u524d\u7f00\u5171\u4eab &#x1f517;&#xff1a;\u5177\u6709\u516c\u5171\u524d\u7f00\u7684\u5b57\u7b26\u4e32\u4f1a\u5171\u4eab\u76f8\u540c\u7684\u8def\u5f84<\/li>\n<li>\u7a7a\u95f4\u4f18\u5316 &#x1f4be;&#xff1a;\u76f8\u6bd4\u5b58\u50a8\u5b8c\u6574\u5b57\u7b26\u4e32&#xff0c;\u53ef\u4ee5\u8282\u7701\u5927\u91cf\u5b58\u50a8\u7a7a\u95f4<\/li>\n<li>\u67e5\u627e\u9ad8\u6548 \u26a1&#xff1a;\u67e5\u627e\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(m)&#xff0c;\u5176\u4e2dm\u4e3a\u5b57\u7b26\u4e32\u957f\u5ea6<\/li>\n<li>\u652f\u6301\u524d\u7f00\u64cd\u4f5c &#x1f50d;&#xff1a;\u5929\u7136\u652f\u6301\u524d\u7f00\u5339\u914d\u3001\u81ea\u52a8\u8865\u5168\u7b49\u529f\u80fd<\/li>\n<\/ul>\n<h3>\u5b57\u5178\u6811\u7684\u7ed3\u6784 &#x1f3d7;\ufe0f<\/h3>\n<p>\u5b57\u5178\u6811\u662f\u4e00\u4e2a\u591a\u53c9\u6811&#xff0c;\u6bcf\u4e2a\u8282\u70b9\u5305\u542b&#xff1a;<\/p>\n<ul>\n<li>\u6307\u5411\u5b50\u8282\u70b9\u7684\u6307\u9488\u6570\u7ec4&#xff08;\u901a\u5e38\u4e3a26\u4e2a&#xff0c;\u5bf9\u5e94a-z&#xff09;<\/li>\n<li>\u4e00\u4e2a\u6807\u8bb0\u4f4d&#xff0c;\u8868\u793a\u8be5\u8282\u70b9\u662f\u5426\u4e3a\u67d0\u4e2a\u5355\u8bcd\u7684\u7ed3\u5c3e<\/li>\n<\/ul>\n<p><span class=\"token keyword\">struct<\/span> <span class=\"token class-name\">node<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">bool<\/span> end <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span>    <span class=\"token comment\">\/\/ \u6807\u8bb0\u4f4d<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> count <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>n<span class=\"token punctuation\">[<\/span><span class=\"token number\">26<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token keyword\">nullptr<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>\u793a\u4f8b&#xff1a;\u63d2\u5165\u5355\u8bcd \u201ccat\u201d, \u201ccar\u201d, \u201ccard\u201d, \u201ccare\u201d, \u201ccareful\u201d<\/p>\n<p>        root<br \/>\n         |<br \/>\n         c<br \/>\n         |<br \/>\n         a<br \/>\n        \/ \\\\<br \/>\n       t   r<br \/>\n       |   |<br \/>\n      (end)<br \/>\n           \/ \\\\<br \/>\n          d   e<br \/>\n          |   |<br \/>\n        (end) (end)<br \/>\n              |<br \/>\n              f<br \/>\n              |<br \/>\n              u<br \/>\n              |<br \/>\n              l<br \/>\n              |<br \/>\n            (end)<\/p>\n<h3>\u5b57\u5178\u6811\u7684\u57fa\u672c\u64cd\u4f5c \u2699\ufe0f<\/h3>\n<h4>1. \u63d2\u5165\u64cd\u4f5c (Insert) \u2795<\/h4>\n<p>\u4ece\u6839\u8282\u70b9\u5f00\u59cb&#xff0c;\u6309\u7167\u5b57\u7b26\u4e32\u7684\u6bcf\u4e2a\u5b57\u7b26\u9010\u5c42\u5411\u4e0b\u6784\u5efa\u8def\u5f84\u3002\u5982\u679c\u8def\u5f84\u4e0d\u5b58\u5728&#xff0c;\u5219\u521b\u5efa\u65b0\u8282\u70b9\u3002<\/p>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(m)&#xff0c;m\u4e3a\u5b57\u7b26\u4e32\u957f\u5ea6 \u23f1\ufe0f<\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">add<\/span><span class=\"token punctuation\">(<\/span>node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">,<\/span> string s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>p <span class=\"token operator\">&#061;<\/span> root<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">char<\/span> c <span class=\"token operator\">:<\/span> s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> c <span class=\"token operator\">&#8211;<\/span> <span class=\"token string\">&#039;a&#039;<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5982\u679c\u8282\u70b9\u8def\u5f84\u4e0d\u5b58\u5728&#xff0c;\u5c31\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u8282\u70b9<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token function\">node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        p <span class=\"token operator\">&#061;<\/span> p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u6807\u8bb0\u5355\u8bcd\u7ed3\u5c3e<\/span><br \/>\n    p<span class=\"token operator\">-&gt;<\/span>end <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span>   <\/p>\n<h4>2. \u67e5\u627e\u64cd\u4f5c (Search) &#x1f50e;<\/h4>\n<p>\u4ece\u6839\u8282\u70b9\u5f00\u59cb&#xff0c;\u6cbf\u7740\u5b57\u7b26\u8def\u5f84\u5411\u4e0b\u67e5\u627e\u3002\u53ea\u6709\u5f53\u8def\u5f84\u5b58\u5728\u4e14\u6700\u540e\u8282\u70b9\u6807\u8bb0\u4e3a\u5355\u8bcd\u7ed3\u5c3e\u65f6&#xff0c;\u624d\u8868\u793a\u627e\u5230\u4e86\u5b8c\u6574\u5355\u8bcd\u3002<\/p>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(m) \u23f1\ufe0f<\/p>\n<p><span class=\"token keyword\">bool<\/span> <span class=\"token function\">search<\/span><span class=\"token punctuation\">(<\/span>node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">,<\/span> string s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>p <span class=\"token operator\">&#061;<\/span> root<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">char<\/span> c <span class=\"token operator\">:<\/span> s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> c <span class=\"token operator\">&#8211;<\/span> <span class=\"token string\">&#039;a&#039;<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5355\u8bcd\u8def\u5f84\u4e0d\u5b58\u5728<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u7ee7\u7eed\u5f80\u4e0b\u4e00\u4e2a\u8282\u70b9\u8d70<\/span><br \/>\n        p <span class=\"token operator\">&#061;<\/span> p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u5fc5\u987b\u68c0\u67e5\u662f\u5426\u4e3a\u5355\u8bcd\u7ed3\u5c3e<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> p<span class=\"token operator\">-&gt;<\/span>end<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h4>3. \u524d\u7f00\u67e5\u627e (StartsWith) &#x1f50d;<\/h4>\n<p>\u4e0e\u5b8c\u6574\u5355\u8bcd\u67e5\u627e\u7c7b\u4f3c&#xff0c;\u4f46\u4e0d\u9700\u8981\u68c0\u67e5\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u662f\u5426\u4e3a\u5355\u8bcd\u7ed3\u5c3e&#xff0c;\u53ea\u9700\u8981\u8def\u5f84\u5b58\u5728\u5373\u53ef\u3002<\/p>\n<p>\u5173\u952e\u533a\u522b&#xff1a;<\/p>\n<ul>\n<li>\u5b8c\u6574\u5355\u8bcd\u67e5\u627e&#xff1a;return node-&gt;end &#8211; \u5fc5\u987b\u662f\u5b8c\u6574\u5355\u8bcd<\/li>\n<li>\u524d\u7f00\u67e5\u627e&#xff1a;return true &#8211; \u53ea\u8981\u8def\u5f84\u5b58\u5728\u5373\u53ef<\/li>\n<\/ul>\n<p>\u5b9e\u9645\u4f8b\u5b50&#xff1a; \u5047\u8bbe\u5b57\u5178\u6811\u4e2d\u6709\u5355\u8bcd&#xff1a;[\u201ccar\u201d, \u201ccard\u201d, \u201ccare\u201d, \u201ccareful\u201d]<\/p>\n<ul>\n<li>search(&#034;car&#034;) \u2192 true&#xff08;&#034;car&#034;\u662f\u5b8c\u6574\u5355\u8bcd&#xff09;<\/li>\n<li>search(&#034;ca&#034;) \u2192 false&#xff08;&#034;ca&#034;\u4e0d\u662f\u5b8c\u6574\u5355\u8bcd&#xff09;<\/li>\n<li>startsWith(&#034;ca&#034;) \u2192 true&#xff08;\u5b58\u5728\u4ee5&#034;ca&#034;\u5f00\u5934\u7684\u5355\u8bcd&#xff09;<\/li>\n<li>startsWith(&#034;car&#034;) \u2192 true&#xff08;\u5b58\u5728\u4ee5&#034;car&#034;\u5f00\u5934\u7684\u5355\u8bcd&#xff09;<\/li>\n<\/ul>\n<p><span class=\"token keyword\">bool<\/span> <span class=\"token function\">startsWith<\/span><span class=\"token punctuation\">(<\/span>node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">,<\/span> string s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>p <span class=\"token operator\">&#061;<\/span> root<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">char<\/span> c <span class=\"token operator\">:<\/span> s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> c <span class=\"token operator\">&#8211;<\/span> <span class=\"token string\">&#039;a&#039;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        p <span class=\"token operator\">&#061;<\/span> p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u53ea\u8981\u80fd\u8d70\u5b8c\u6574\u4e2a\u524d\u7f00\u8def\u5f84\u5c31\u8fd4\u56detrue&#xff0c;\u4e0d\u9700\u8981\u68c0\u67e5\u662f\u5426\u662fend<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>\u4f8b\u9898\u793a\u4f8b &#x1f680;<\/h3>\n<h4>\u9898\u76ee\u6982\u8ff0&#xff08;\u4e8e\u662f\u4ed6\u9519\u8bef\u7684\u70b9\u540d\u5f00\u59cb\u4e86&#xff09;<\/h4>\n<p>\u9898\u76ee\u80cc\u666f \u4e00\u4e2a\u5316\u5b66\u7ade\u8d5b\u6559\u7ec3\u5728\u70b9\u540d\u65f6\u56e0\u4e00\u8fb9\u73a9\u6e38\u620f\u4e00\u8fb9\u70b9\u540d&#xff0c;\u5bfc\u81f4\u8fde\u7eed\u70b9\u5230\u540c\u4e00\u540c\u5b66\u4e24\u6b21\u3002\u73b0\u5728\u9700\u8981\u5199\u7a0b\u5e8f\u5224\u65ad\u70b9\u540d\u662f\u5426\u6b63\u786e\u3002<\/p>\n<p>\u5177\u4f53\u9700\u6c42 \u7ed9\u5b9a\u73ed\u7ea7\u5408\u6cd5\u5b66\u751f\u540d\u5355&#xff08;\u540d\u5b57\u4e92\u4e0d\u76f8\u540c&#xff09;\u3002<\/p>\n<p>\u6309\u987a\u5e8f\u8bfb\u53d6\u70b9\u540d\u7684\u540d\u5b57\u3002<\/p>\n<p>\u5bf9\u6bcf\u4e2a\u540d\u5b57\u8f93\u51fa&#xff1a;<\/p>\n<ul>\n<li>OK&#xff1a;\u540d\u5b57\u5728\u540d\u5355\u4e2d&#xff0c;\u4e14\u662f\u7b2c\u4e00\u6b21\u51fa\u73b0\u3002<\/li>\n<li>REPEAT&#xff1a;\u540d\u5b57\u5728\u540d\u5355\u4e2d&#xff0c;\u4f46\u5df2\u7ecf\u51fa\u73b0\u8fc7\u3002<\/li>\n<li>WRONG&#xff1a;\u540d\u5b57\u4e0d\u5728\u540d\u5355\u4e2d\u3002<\/li>\n<\/ul>\n<h3>\u4ee3\u7801\u5b9e\u73b0 &#x1f4bb;<\/h3>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;bits\/stdc&#043;&#043;.h&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">typedef<\/span> <span class=\"token keyword\">unsigned<\/span> <span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span> ull<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">typedef<\/span> <span class=\"token keyword\">unsigned<\/span> <span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span> ll<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5b9a\u4e49\u7ed3\u70b9\u7ed3\u6784<\/span><br \/>\n<span class=\"token keyword\">struct<\/span> <span class=\"token class-name\">node<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">bool<\/span> end <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">bool<\/span> isre <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>n<span class=\"token punctuation\">[<\/span><span class=\"token number\">26<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token keyword\">nullptr<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u6dfb\u52a0\u5b57\u7b26\u5230\u7ed3\u70b9<\/span><br \/>\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">add<\/span><span class=\"token punctuation\">(<\/span>node <span class=\"token operator\">*<\/span>root<span class=\"token punctuation\">,<\/span> string s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>p <span class=\"token operator\">&#061;<\/span> root<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">char<\/span> c <span class=\"token operator\">:<\/span> s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> c <span class=\"token operator\">&#8211;<\/span> <span class=\"token string\">&#039;a&#039;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token function\">node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        p <span class=\"token operator\">&#061;<\/span> p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    p<span class=\"token operator\">-&gt;<\/span>end <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u67e5\u627e<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">search<\/span><span class=\"token punctuation\">(<\/span>node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">,<\/span> string s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>p <span class=\"token operator\">&#061;<\/span> root<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">char<\/span> c <span class=\"token operator\">:<\/span> s<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> c <span class=\"token operator\">&#8211;<\/span> <span class=\"token string\">&#039;a&#039;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\">\/\/ \u8def\u5f84\u65ad\u4e86 -&gt; \u5355\u8bcd\u4e0d\u5b58\u5728<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        p <span class=\"token operator\">&#061;<\/span> p<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u8def\u5f84\u5b58\u5728&#xff0c;\u4f46\u4e0d\u662f\u5355\u8bcd\u7ed3\u5c3e<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>p<span class=\"token operator\">-&gt;<\/span>end<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u5df2\u7ecf\u88ab\u67e5\u8be2\u8fc7<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>p<span class=\"token operator\">-&gt;<\/span>isre<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    p<span class=\"token operator\">-&gt;<\/span>isre <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u521b\u5efa\u6839\u8282\u70b9<\/span><br \/>\nnode<span class=\"token operator\">*<\/span> <span class=\"token function\">createT<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token function\">node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    ios<span class=\"token operator\">::<\/span><span class=\"token function\">sync_with_stdio<\/span><span class=\"token punctuation\">(<\/span><span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cin<span class=\"token punctuation\">.<\/span><span class=\"token function\">tie<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">nullptr<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u521d\u59cb\u5316 Trie \u6839\u8282\u70b9<\/span><br \/>\n    node <span class=\"token operator\">*<\/span>root <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">createT<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">;<\/span><br \/>\n    cin <span class=\"token operator\">&gt;&gt;<\/span> n<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        string s<span class=\"token punctuation\">;<\/span><br \/>\n        cin <span class=\"token operator\">&gt;&gt;<\/span> s<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token function\">add<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">,<\/span> s<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ \u63d2\u5165\u5355\u8bcd\u5230\u5b57\u5178\u6811<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">int<\/span> m<span class=\"token punctuation\">;<\/span><br \/>\n    cin <span class=\"token operator\">&gt;&gt;<\/span> m<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>m<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        string s<span class=\"token punctuation\">;<\/span><br \/>\n        cin <span class=\"token operator\">&gt;&gt;<\/span> s<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> l <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">search<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">,<\/span> s<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>l <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;WRONG&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">else<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>l <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;OK&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">else<\/span><br \/>\n            cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;REPEAT&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>\u590d\u6742\u5ea6\u5206\u6790 &#x1f4ca;<\/h3>\n<table>\n<tr>\u64cd\u4f5c\u65f6\u95f4\u590d\u6742\u5ea6\u7a7a\u95f4\u590d\u6742\u5ea6<\/tr>\n<tbody>\n<tr>\n<td>\u63d2\u5165<\/td>\n<td>O(m)<\/td>\n<td>O(ALPHABET_SIZE \u00d7 N \u00d7 M)<\/td>\n<\/tr>\n<tr>\n<td>\u67e5\u627e<\/td>\n<td>O(m)<\/td>\n<td>&#8211;<\/td>\n<\/tr>\n<tr>\n<td>\u524d\u7f00\u67e5\u627e<\/td>\n<td>O(m)<\/td>\n<td>&#8211;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li>m&#xff1a;\u5b57\u7b26\u4e32\u957f\u5ea6<\/li>\n<li>N&#xff1a;\u5b57\u5178\u6811\u4e2d\u7684\u5355\u8bcd\u6570\u91cf<\/li>\n<li>M&#xff1a;\u5355\u8bcd\u7684\u5e73\u5747\u957f\u5ea6<\/li>\n<li>ALPHABET_SIZE&#xff1a;\u5b57\u7b26\u96c6\u5927\u5c0f&#xff08;\u598226\u4e2a\u82f1\u6587\u5b57\u6bcd&#xff09;<\/li>\n<\/ul>\n<h3>\u603b\u7ed3 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