{"id":78294,"date":"2026-02-26T23:05:26","date_gmt":"2026-02-26T15:05:26","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/78294.html"},"modified":"2026-02-26T23:05:26","modified_gmt":"2026-02-26T15:05:26","slug":"141-%e7%8e%af%e5%bd%a2%e9%93%be%e8%a1%a8-%e9%a2%98%e8%a7%a3%e4%b8%8e%e8%af%a6%e7%bb%86%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/78294.html","title":{"rendered":"141. \u73af\u5f62\u94fe\u8868 - \u9898\u89e3\u4e0e\u8be6\u7ec6\u5206\u6790"},"content":{"rendered":"<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<p>\u7ed9\u4f60\u4e00\u4e2a\u94fe\u8868\u7684\u5934\u8282\u70b9\u00a0head&#xff0c;\u5224\u65ad\u94fe\u8868\u4e2d\u662f\u5426\u6709\u73af\u3002<\/p>\n<p>\u5982\u679c\u94fe\u8868\u4e2d\u6709\u67d0\u4e2a\u8282\u70b9&#xff0c;\u53ef\u4ee5\u901a\u8fc7\u8fde\u7eed\u8ddf\u8e2a\u00a0next\u00a0\u6307\u9488\u518d\u6b21\u5230\u8fbe&#xff0c;\u5219\u94fe\u8868\u4e2d\u5b58\u5728\u73af\u3002\u4e3a\u4e86\u8868\u793a\u7ed9\u5b9a\u94fe\u8868\u4e2d\u7684\u73af&#xff0c;\u8bc4\u6d4b\u7cfb\u7edf\u5185\u90e8\u4f7f\u7528\u6574\u6570\u00a0pos\u00a0\u6765\u8868\u793a\u94fe\u8868\u5c3e\u8fde\u63a5\u5230\u94fe\u8868\u4e2d\u7684\u4f4d\u7f6e&#xff08;\u7d22\u5f15\u4ece 0 \u5f00\u59cb&#xff09;\u3002\u6ce8\u610f&#xff1a;pos\u00a0\u4e0d\u4f5c\u4e3a\u53c2\u6570\u8fdb\u884c\u4f20\u9012&#xff0c;\u4ec5\u4ec5\u662f\u4e3a\u4e86\u6807\u8bc6\u94fe\u8868\u7684\u5b9e\u9645\u60c5\u51b5\u3002<\/p>\n<p>\u5982\u679c\u94fe\u8868\u4e2d\u5b58\u5728\u73af&#xff0c;\u5219\u8fd4\u56de\u00a0true\u3002\u5426\u5219&#xff0c;\u8fd4\u56de\u00a0false\u3002<\/p>\n<h4>\u793a\u4f8b<\/h4>\n<p>\u793a\u4f8b 1&#xff1a;<\/p>\n<p>text<\/p>\n<p>\u8f93\u5165&#xff1a;head &#061; [3,2,0,-4], pos &#061; 1<br \/>\n\u8f93\u51fa&#xff1a;true<br \/>\n\u89e3\u91ca&#xff1a;\u94fe\u8868\u4e2d\u6709\u4e00\u4e2a\u73af&#xff0c;\u5176\u5c3e\u90e8\u8fde\u63a5\u5230\u7b2c\u4e8c\u4e2a\u8282\u70b9\u3002<\/p>\n<p>\u793a\u4f8b 2&#xff1a;<\/p>\n<p>text<\/p>\n<p>\u8f93\u5165&#xff1a;head &#061; [1,2], pos &#061; 0<br \/>\n\u8f93\u51fa&#xff1a;true<br \/>\n\u89e3\u91ca&#xff1a;\u94fe\u8868\u4e2d\u6709\u4e00\u4e2a\u73af&#xff0c;\u5176\u5c3e\u90e8\u8fde\u63a5\u5230\u7b2c\u4e00\u4e2a\u8282\u70b9\u3002<\/p>\n<p>\u793a\u4f8b 3&#xff1a;<\/p>\n<p>text<\/p>\n<p>\u8f93\u5165&#xff1a;head &#061; [1], pos &#061; -1<br \/>\n\u8f93\u51fa&#xff1a;false<br \/>\n\u89e3\u91ca&#xff1a;\u94fe\u8868\u4e2d\u6ca1\u6709\u73af\u3002<\/p>\n<h3>\u89e3\u9898\u601d\u8def<\/h3>\n<p>\u5224\u65ad\u94fe\u8868\u662f\u5426\u6709\u73af\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u94fe\u8868\u95ee\u9898&#xff0c;\u6700\u4f18\u96c5\u7684\u89e3\u51b3\u65b9\u6848\u662f\u4f7f\u7528\u5feb\u6162\u6307\u9488&#xff08;Floyd&#039;s Cycle-Finding Algorithm&#xff09;\u3002<\/p>\n<h4>\u5feb\u6162\u6307\u9488\u539f\u7406<\/h4>\n<ul>\n<li>\n<p>\u6162\u6307\u9488&#xff1a;\u6bcf\u6b21\u79fb\u52a8\u4e00\u6b65<\/p>\n<\/li>\n<li>\n<p>\u5feb\u6307\u9488&#xff1a;\u6bcf\u6b21\u79fb\u52a8\u4e24\u6b65<\/p>\n<\/li>\n<\/ul>\n<p>\u5982\u679c\u94fe\u8868\u4e2d\u5b58\u5728\u73af&#xff0c;\u5feb\u6307\u9488\u6700\u7ec8\u4f1a\u8ffd\u4e0a\u6162\u6307\u9488&#xff08;\u4e24\u8005\u76f8\u9047&#xff09;&#xff1b;\u5982\u679c\u4e0d\u5b58\u5728\u73af&#xff0c;\u5feb\u6307\u9488\u4f1a\u5148\u5230\u8fbe\u94fe\u8868\u672b\u5c3e&#xff08;NULL&#xff09;\u3002<\/p>\n<h3>\u4ee3\u7801\u5b9e\u73b0<\/h3>\n<p>c<\/p>\n<p>\/**<br \/>\n * Definition for singly-linked list.<br \/>\n * struct ListNode {<br \/>\n *     int val;<br \/>\n *     struct ListNode *next;<br \/>\n * };<br \/>\n *\/<br \/>\nbool hasCycle(struct ListNode *head) {<br \/>\n    struct ListNode *fast &#061; head;<br \/>\n    struct ListNode *slow &#061; head;<\/p>\n<p>    while(fast &amp;&amp; fast-&gt;next)<br \/>\n    {<br \/>\n        slow &#061; slow-&gt;next;          \/\/ \u6162\u6307\u9488\u79fb\u52a8\u4e00\u6b65<br \/>\n        fast &#061; fast-&gt;next-&gt;next;    \/\/ \u5feb\u6307\u9488\u79fb\u52a8\u4e24\u6b65<\/p>\n<p>        if(slow &#061;&#061; fast)            \/\/ \u5982\u679c\u76f8\u9047&#xff0c;\u8bf4\u660e\u6709\u73af<br \/>\n            return true;<br \/>\n    }<\/p>\n<p>    return false;                   \/\/ \u5feb\u6307\u9488\u5230\u8fbe\u672b\u5c3e&#xff0c;\u8bf4\u660e\u65e0\u73af<br \/>\n}<\/p>\n<h3>\u4ee3\u7801\u8be6\u89e3<\/h3>\n<h4>\u6838\u5fc3\u903b\u8f91<\/h4>\n<p>c<\/p>\n<p>while(fast &amp;&amp; fast-&gt;next)<br \/>\n{<br \/>\n    slow &#061; slow-&gt;next;          \/\/ \u6162\u6307\u9488\u79fb\u52a8\u4e00\u6b65<br \/>\n    fast &#061; fast-&gt;next-&gt;next;    \/\/ \u5feb\u6307\u9488\u79fb\u52a8\u4e24\u6b65<\/p>\n<p>    if(slow &#061;&#061; fast)            \/\/ \u68c0\u67e5\u662f\u5426\u76f8\u9047<br \/>\n        return true;<br \/>\n}<\/p>\n<p>\u5faa\u73af\u6761\u4ef6\u5206\u6790&#xff1a;<\/p>\n<ul>\n<li>\n<p>fast&#xff1a;\u786e\u4fdd\u5feb\u6307\u9488\u672c\u8eab\u4e0d\u4e3a\u7a7a<\/p>\n<\/li>\n<li>\n<p>fast-&gt;next&#xff1a;\u786e\u4fdd\u5feb\u6307\u9488\u53ef\u4ee5\u5b89\u5168\u5730\u79fb\u52a8\u4e24\u6b65<\/p>\n<\/li>\n<\/ul>\n<h4>\u6267\u884c\u8fc7\u7a0b\u53ef\u89c6\u5316<\/h4>\n<p>\u6709\u73af\u7684\u60c5\u51b5&#xff08;\u793a\u4f8b1&#xff09;&#xff1a;<\/p>\n<p>text<\/p>\n<p>\u94fe\u8868&#xff1a;3 -&gt; 2 -&gt; 0 -&gt; -4 -&gt; 2&#xff08;\u5f62\u6210\u73af&#xff09;<\/p>\n<p>\u521d\u59cb&#xff1a;slow -&gt; 3, fast -&gt; 3<\/p>\n<p>\u7b2c1\u6b21\u5faa\u73af&#xff1a;<br \/>\nslow -&gt; 2, fast -&gt; 0<br \/>\n\u6bd4\u8f83&#xff1a;2 !&#061; 0<\/p>\n<p>\u7b2c2\u6b21\u5faa\u73af&#xff1a;<br \/>\nslow -&gt; 0, fast -&gt; 2<br \/>\n\u6bd4\u8f83&#xff1a;0 !&#061; 2<\/p>\n<p>\u7b2c3\u6b21\u5faa\u73af&#xff1a;<br \/>\nslow -&gt; -4, fast -&gt; -4<br \/>\n\u6bd4\u8f83&#xff1a;-4 &#061;&#061; -4 \u2192 \u8fd4\u56detrue<\/p>\n<p>\u65e0\u73af\u7684\u60c5\u51b5&#xff1a;<\/p>\n<p>text<\/p>\n<p>\u94fe\u8868&#xff1a;1 -&gt; 2 -&gt; 3 -&gt; 4 -&gt; NULL<\/p>\n<p>\u521d\u59cb&#xff1a;slow -&gt; 1, fast -&gt; 1<\/p>\n<p>\u7b2c1\u6b21\u5faa\u73af&#xff1a;<br \/>\nslow -&gt; 2, fast -&gt; 3<br \/>\n\u6bd4\u8f83&#xff1a;2 !&#061; 3<\/p>\n<p>\u7b2c2\u6b21\u5faa\u73af&#xff1a;<br \/>\nslow -&gt; 3, fast -&gt; NULL<br \/>\n\u6761\u4ef6\u5224\u65ad&#xff1a;fast &#061;&#061; NULL \u2192 \u9000\u51fa\u5faa\u73af&#xff0c;\u8fd4\u56defalse<\/p>\n<h3>\u4e3a\u4ec0\u4e48\u5feb\u6162\u6307\u9488\u6709\u6548&#xff1f;<\/h3>\n<h4>\u6570\u5b66\u8bc1\u660e<\/h4>\n<p>\u5047\u8bbe\u94fe\u8868\u73af\u5916\u90e8\u5206\u957f\u5ea6\u4e3a\u00a0L&#xff0c;\u73af\u7684\u5468\u957f\u4e3a\u00a0C\u3002<\/p>\n<p>\u5f53\u6162\u6307\u9488\u8fdb\u5165\u73af\u65f6&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u6162\u6307\u9488\u4f4d\u7f6e&#xff1a;0&#xff08;\u73af\u7684\u8d77\u70b9&#xff09;<\/p>\n<\/li>\n<li>\n<p>\u5feb\u6307\u9488\u4f4d\u7f6e&#xff1a;L % C&#xff08;\u56e0\u4e3a\u5feb\u6307\u9488\u5df2\u7ecf\u8d70\u4e86\u00a02L\u00a0\u6b65&#xff09;<\/p>\n<\/li>\n<\/ul>\n<p>\u5feb\u6307\u9488\u76f8\u5bf9\u4e8e\u6162\u6307\u9488\u7684\u901f\u5ea6\u662f 1 \u6b65\/\u5355\u4f4d\u65f6\u95f4&#xff08;\u5feb\u6307\u9488\u6bd4\u6162\u6307\u9488\u5feb\u4e00\u6b65&#xff09;&#xff0c;\u6240\u4ee5\u5feb\u6307\u9488\u9700\u8981\u8ffd\u8d76\u7684\u8ddd\u79bb\u6700\u591a\u4e3a\u00a0C-1\u00a0\u6b65\u3002<\/p>\n<p>\u56e0\u6b64&#xff0c;\u5728\u00a0C-1\u00a0\u6b21\u5faa\u73af\u5185&#xff0c;\u5feb\u6307\u9488\u4e00\u5b9a\u4f1a\u8ffd\u4e0a\u6162\u6307\u9488\u3002<\/p>\n<h4>\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790<\/h4>\n<ul>\n<li>\n<p>\u6162\u6307\u9488\u6700\u591a\u8d70\u00a0L &#043; C\u00a0\u6b65&#xff08;\u73af\u5916\u957f\u5ea6 &#043; \u73af\u5468\u957f&#xff09;<\/p>\n<\/li>\n<li>\n<p>\u5feb\u6307\u9488\u6700\u591a\u8d70\u00a02(L &#043; C)\u00a0\u6b65<\/p>\n<\/li>\n<li>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(n)&#xff0c;\u5176\u4e2d n \u662f\u94fe\u8868\u957f\u5ea6<\/p>\n<\/li>\n<\/ul>\n<h3>\u5176\u4ed6\u89e3\u6cd5<\/h3>\n<h4>\u65b9\u6cd5\u4e8c&#xff1a;\u54c8\u5e0c\u8868\u6cd5<\/h4>\n<p>c<\/p>\n<p>#include &lt;stdbool.h&gt;<\/p>\n<p>bool hasCycle(struct ListNode *head) {<br \/>\n    struct ListNode *visited[10000] &#061; {0};  \/\/ \u7b80\u5355\u7684\u54c8\u5e0c\u8868<br \/>\n    int count &#061; 0;<\/p>\n<p>    struct ListNode *current &#061; head;<br \/>\n    while (current !&#061; NULL) {<br \/>\n        \/\/ \u68c0\u67e5\u5f53\u524d\u8282\u70b9\u662f\u5426\u5df2\u7ecf\u8bbf\u95ee\u8fc7<br \/>\n        for (int i &#061; 0; i &lt; count; i&#043;&#043;) {<br \/>\n            if (visited[i] &#061;&#061; current) {<br \/>\n                return true;<br \/>\n            }<br \/>\n        }<\/p>\n<p>        \/\/ \u8bb0\u5f55\u5df2\u8bbf\u95ee\u7684\u8282\u70b9<br \/>\n        visited[count&#043;&#043;] &#061; current;<br \/>\n        current &#061; current-&gt;next;<br \/>\n    }<\/p>\n<p>    return false;<br \/>\n}<\/p>\n<p>\u4f18\u7f3a\u70b9&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u4f18\u70b9&#xff1a;\u601d\u8def\u7b80\u5355\u76f4\u89c2<\/p>\n<\/li>\n<li>\n<p>\u7f3a\u70b9&#xff1a;\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)&#xff0c;\u9700\u8981\u5b58\u50a8\u6240\u6709\u8bbf\u95ee\u8fc7\u7684\u8282\u70b9<\/p>\n<\/li>\n<\/ul>\n<h4>\u65b9\u6cd5\u4e09&#xff1a;\u6807\u8bb0\u6cd5&#xff08;\u4fee\u6539\u8282\u70b9\u503c&#xff09;<\/h4>\n<p>c<\/p>\n<p>bool hasCycle(struct ListNode *head) {<br \/>\n    struct ListNode *current &#061; head;<\/p>\n<p>    while (current !&#061; NULL) {<br \/>\n        \/\/ \u5982\u679c\u9047\u5230\u7279\u6b8a\u6807\u8bb0\u503c&#xff0c;\u8bf4\u660e\u6709\u73af<br \/>\n        if (current-&gt;val &#061;&#061; 1000000) {<br \/>\n            return true;<br \/>\n        }<\/p>\n<p>        \/\/ \u6807\u8bb0\u5f53\u524d\u8282\u70b9&#xff08;\u5047\u8bbe\u8282\u70b9\u503c\u4e0d\u4f1a\u7b49\u4e8e1000000&#xff09;<br \/>\n        current-&gt;val &#061; 1000000;<br \/>\n        current &#061; current-&gt;next;<br \/>\n    }<\/p>\n<p>    return false;<br \/>\n}<\/p>\n<p>\u4f18\u7f3a\u70b9&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u4f18\u70b9&#xff1a;\u7a7a\u95f4\u590d\u6742\u5ea6 O(1)<\/p>\n<\/li>\n<li>\n<p>\u7f3a\u70b9&#xff1a;\u4fee\u6539\u4e86\u539f\u59cb\u94fe\u8868\u6570\u636e&#xff0c;\u4e0d\u63a8\u8350\u5728\u5b9e\u9645\u4e2d\u4f7f\u7528<\/p>\n<\/li>\n<\/ul>\n<h3>\u590d\u6742\u5ea6\u5206\u6790<\/h3>\n<h4>\u5feb\u6162\u6307\u9488\u6cd5<\/h4>\n<ul>\n<li>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(n)&#xff0c;\u6700\u574f\u60c5\u51b5\u4e0b\u9700\u8981\u904d\u5386\u6574\u4e2a\u94fe\u8868<\/p>\n<\/li>\n<li>\n<p>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;O(1)&#xff0c;\u53ea\u4f7f\u7528\u4e24\u4e2a\u6307\u9488\u53d8\u91cf<\/p>\n<\/li>\n<\/ul>\n<h4>\u54c8\u5e0c\u8868\u6cd5<\/h4>\n<ul>\n<li>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(n)&#xff0c;\u9700\u8981\u904d\u5386\u94fe\u8868<\/p>\n<\/li>\n<li>\n<p>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;O(n)&#xff0c;\u9700\u8981\u5b58\u50a8\u6240\u6709\u8bbf\u95ee\u8fc7\u7684\u8282\u70b9<\/p>\n<\/li>\n<\/ul>\n<h3>\u6269\u5c55\u95ee\u9898<\/h3>\n<h4>\u5982\u679c\u8981\u6c42\u627e\u5230\u73af\u7684\u5165\u53e3\u8282\u70b9<\/h4>\n<p>c<\/p>\n<p>struct ListNode *detectCycle(struct ListNode *head) {<br \/>\n    struct ListNode *slow &#061; head;<br \/>\n    struct ListNode *fast &#061; head;<\/p>\n<p>    \/\/ \u7b2c\u4e00\u9636\u6bb5&#xff1a;\u5224\u65ad\u662f\u5426\u6709\u73af<br \/>\n    while (fast &amp;&amp; fast-&gt;next) {<br \/>\n        slow &#061; slow-&gt;next;<br \/>\n        fast &#061; fast-&gt;next-&gt;next;<\/p>\n<p>        if (slow &#061;&#061; fast) {<br \/>\n            \/\/ \u7b2c\u4e8c\u9636\u6bb5&#xff1a;\u627e\u5230\u73af\u7684\u5165\u53e3<br \/>\n            struct ListNode *ptr1 &#061; head;<br \/>\n            struct ListNode *ptr2 &#061; slow;<\/p>\n<p>            while (ptr1 !&#061; ptr2) {<br \/>\n                ptr1 &#061; ptr1-&gt;next;<br \/>\n                ptr2 &#061; ptr2-&gt;next;<br \/>\n            }<\/p>\n<p>            return ptr1;  \/\/ \u73af\u7684\u5165\u53e3\u8282\u70b9<br \/>\n        }<br \/>\n    }<\/p>\n<p>    return NULL;  \/\/ \u65e0\u73af<br 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