{"id":63756,"date":"2026-01-22T11:16:30","date_gmt":"2026-01-22T03:16:30","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/63756.html"},"modified":"2026-01-22T11:16:30","modified_gmt":"2026-01-22T03:16:30","slug":"%e5%87%bd%e6%95%b0%e9%80%92%e5%bd%92%ef%bc%9a%e4%bb%8e%e9%98%b6%e4%b9%98%e8%ae%a1%e7%ae%97%e7%90%86%e8%a7%a3%e9%80%92%e5%bd%92%e7%9a%84%e6%a0%b8%e5%bf%83%e6%80%9d%e6%83%b3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/63756.html","title":{"rendered":"\u51fd\u6570\u9012\u5f52\uff1a\u4ece\u9636\u4e58\u8ba1\u7b97\u7406\u89e3\u9012\u5f52\u7684\u6838\u5fc3\u601d\u60f3"},"content":{"rendered":"<h2>\u51fd\u6570\u9012\u5f52&#xff1a;\u4ece\u9636\u4e58\u8ba1\u7b97\u7406\u89e3\u9012\u5f52\u7684\u6838\u5fc3\u601d\u60f3<\/h2>\n<p>\u5728 C&#043;&#043; \u51fd\u6570\u7f16\u7a0b\u4e2d&#xff0c;\u9012\u5f52\u662f\u4e00\u79cd\u6781\u5177\u6280\u5de7\u6027\u7684\u7f16\u7a0b\u601d\u60f3\u2014\u2014\u5b83\u5141\u8bb8\u51fd\u6570\u8c03\u7528\u81ea\u8eab&#xff0c;\u5c06\u590d\u6742\u95ee\u9898\u62c6\u89e3\u4e3a\u82e5\u5e72\u4e2a\u4e0e\u539f\u95ee\u9898\u7ed3\u6784\u4e00\u81f4\u4f46\u89c4\u6a21\u66f4\u5c0f\u7684\u5b50\u95ee\u9898&#xff0c;\u76f4\u81f3\u5b50\u95ee\u9898\u7b80\u5316\u5230\u53ef\u76f4\u63a5\u6c42\u89e3\u7684\u201c\u57fa\u7ebf\u6761\u4ef6\u201d&#xff0c;\u6700\u7ec8\u901a\u8fc7\u5b50\u95ee\u9898\u7684\u89e3\u7ec4\u5408\u5f97\u5230\u539f\u95ee\u9898\u7684\u7b54\u6848\u3002\u9636\u4e58\u8ba1\u7b97\u4f5c\u4e3a\u9012\u5f52\u601d\u60f3\u7684\u7ecf\u5178\u5e94\u7528\u573a\u666f&#xff0c;\u903b\u8f91\u7b80\u6d01\u3001\u7ed3\u6784\u6e05\u6670&#xff0c;\u662f\u5165\u95e8\u9012\u5f52\u7684\u6700\u4f73\u5207\u5165\u70b9\u3002\u672c\u6587\u5c06\u4ee5\u9636\u4e58\u8ba1\u7b97\u4e3a\u6838\u5fc3&#xff0c;\u5e26\u4f60\u5403\u900f\u9012\u5f52\u7684\u6838\u5fc3\u601d\u60f3\u3001\u6267\u884c\u6d41\u7a0b\u3001\u5b9e\u73b0\u7ec6\u8282\u4e0e\u9002\u7528\u8fb9\u754c&#xff0c;\u4ece\u201c\u4f1a\u7528\u201d\u5230\u201c\u6d3b\u7528\u201d\u9012\u5f52\u3002<\/p>\n<h3>\u4e00\u3001\u5148\u660e\u786e&#xff1a;\u4ec0\u4e48\u662f\u9012\u5f52&#xff1f;<\/h3>\n<p>\u9012\u5f52\u7684\u672c\u8d28\u662f\u201c\u5206\u800c\u6cbb\u4e4b\u201d&#xff0c;\u6838\u5fc3\u903b\u8f91\u5305\u542b\u4e24\u4e2a\u4e0d\u53ef\u7f3a\u5c11\u7684\u90e8\u5206&#xff0c;\u4e8c\u8005\u5171\u540c\u6784\u6210\u9012\u5f52\u7684\u5b8c\u6574\u95ed\u73af&#xff0c;\u7f3a\u4e00\u4e0d\u53ef&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u9012\u5f52\u6761\u4ef6&#xff08;\u9012\u63a8\u5173\u7cfb&#xff09;&#xff1a;\u5c06\u539f\u95ee\u9898\u62c6\u89e3\u4e3a\u89c4\u6a21\u66f4\u5c0f\u3001\u7ed3\u6784\u76f8\u540c\u7684\u5b50\u95ee\u9898&#xff0c;\u51fd\u6570\u901a\u8fc7\u8c03\u7528\u81ea\u8eab\u6c42\u89e3\u5b50\u95ee\u9898\u3002\u4f8b\u5982\u9636\u4e58\u8ba1\u7b97\u4e2d&#xff0c;n! \u53ef\u62c6\u89e3\u4e3a n \u00d7 (n-1)!&#xff0c;\u8fd9\u5c31\u662f\u9012\u63a8\u5173\u7cfb\u3002<\/p>\n<\/li>\n<li>\n<p>\u57fa\u7ebf\u6761\u4ef6&#xff08;\u7ec8\u6b62\u6761\u4ef6&#xff09;&#xff1a;\u5f53\u5b50\u95ee\u9898\u7b80\u5316\u5230\u4e00\u5b9a\u7a0b\u5ea6&#xff0c;\u65e0\u9700\u7ee7\u7eed\u9012\u5f52&#xff0c;\u53ef\u76f4\u63a5\u8fd4\u56de\u786e\u5b9a\u7ed3\u679c&#xff0c;\u907f\u514d\u51fd\u6570\u65e0\u9650\u8c03\u7528&#xff08;\u6b7b\u9012\u5f52&#xff09;\u3002\u4f8b\u5982\u9636\u4e58\u8ba1\u7b97\u4e2d&#xff0c;0! &#061; 1\u30011! &#061; 1&#xff0c;\u8fd9\u5c31\u662f\u7ec8\u6b62\u6761\u4ef6\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u7c7b\u6bd4\u751f\u6d3b\u573a\u666f&#xff1a;\u9012\u5f52\u5c31\u50cf\u5265\u6d0b\u8471&#xff0c;\u4ece\u5916\u5c42&#xff08;\u539f\u95ee\u9898&#xff09;\u4e00\u5c42\u5c42\u5265\u5230\u5185\u5c42&#xff08;\u57fa\u7ebf\u6761\u4ef6&#xff09;&#xff0c;\u518d\u4ece\u5185\u5c42\u4e00\u5c42\u5c42\u8fd4\u56de\u7ed3\u679c&#xff0c;\u6700\u7ec8\u7ec4\u5408\u5f97\u5230\u5916\u5c42\u7684\u7b54\u6848\u3002\u82e5\u7f3a\u5c11\u7ec8\u6b62\u6761\u4ef6&#xff0c;\u5c31\u50cf\u5265\u4e0d\u5b8c\u7684\u6d0b\u8471&#xff0c;\u51fd\u6570\u4f1a\u4e00\u76f4\u8c03\u7528\u81ea\u8eab&#xff0c;\u76f4\u81f3\u6808\u6ea2\u51fa\u7a0b\u5e8f\u5d29\u6e83\u3002<\/p>\n<h3>\u4e8c\u3001\u7ecf\u5178\u6848\u4f8b&#xff1a;\u7528\u9012\u5f52\u5b9e\u73b0\u9636\u4e58\u8ba1\u7b97<\/h3>\n<p>\u9636\u4e58\u7684\u6570\u5b66\u5b9a\u4e49\u7684\u662f&#xff1a;\u5bf9\u4e8e\u975e\u8d1f\u6574\u6570 n&#xff0c;n!&#xff08;\u8bfb\u4f5c\u201cn \u7684\u9636\u4e58\u201d&#xff09;\u8868\u793a\u4ece 1 \u5230 n \u7684\u6240\u6709\u6b63\u6574\u6570\u7684\u4e58\u79ef&#xff0c;\u4e14\u89c4\u5b9a 0! &#061; 1\u3002\u5176\u6570\u5b66\u8868\u8fbe\u5f0f\u53ef\u5199\u4e3a&#xff1a;<\/p>\n<p>n! &#061; n \u00d7 (n-1) \u00d7 (n-2) \u00d7 \u2026 \u00d7 1&#xff08;n \u2265 1&#xff09;<\/p>\n<p>n! &#061; 1&#xff08;n &#061; 0 \u6216 n &#061; 1&#xff09;<\/p>\n<p>\u89c2\u5bdf\u8868\u8fbe\u5f0f\u53ef\u53d1\u73b0\u660e\u663e\u7684\u9012\u63a8\u5173\u7cfb&#xff1a;n! &#061; n \u00d7 (n-1)!&#xff0c;\u800c\u7ec8\u6b62\u6761\u4ef6\u4e3a n &#061; 0 \u6216 n &#061; 1 \u65f6&#xff0c;\u7ed3\u679c\u4e3a 1&#xff0c;\u5b8c\u5168\u5951\u5408\u9012\u5f52\u7684\u6838\u5fc3\u903b\u8f91\u3002<\/p>\n<h4>1. \u9012\u5f52\u5b9e\u73b0\u9636\u4e58\u7684\u4ee3\u7801<\/h4>\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;iostream&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u9012\u5f52\u51fd\u6570&#xff1a;\u8ba1\u7b97n\u7684\u9636\u4e58<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">factorial<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u57fa\u7ebf\u6761\u4ef6&#xff08;\u7ec8\u6b62\u6761\u4ef6&#xff09;&#xff1a;n&#061;0\u6216n&#061;1\u65f6&#xff0c;\u8fd4\u56de1<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">||<\/span> n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/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><br \/>\n    <span class=\"token comment\">\/\/ \u9012\u5f52\u6761\u4ef6&#xff08;\u9012\u63a8\u5173\u7cfb&#xff09;&#xff1a;n! &#061; n \u00d7 (n-1)!&#xff0c;\u8c03\u7528\u81ea\u8eab\u6c42\u89e3\u5b50\u95ee\u9898<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> n <span class=\"token operator\">*<\/span> <span class=\"token function\">factorial<\/span><span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/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    <span class=\"token keyword\">int<\/span> num<span class=\"token punctuation\">;<\/span><br \/>\n    cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\u8bf7\u8f93\u5165\u4e00\u4e2a\u975e\u8d1f\u6574\u6570&#xff1a;&#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cin <span class=\"token operator\">&gt;&gt;<\/span> num<span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u8f93\u5165\u5408\u6cd5\u6027\u6821\u9a8c&#xff08;\u9636\u4e58\u4ec5\u9002\u7528\u4e8e\u975e\u8d1f\u6574\u6570&#xff09;<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>num <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\u9519\u8bef&#xff1a;\u9636\u4e58\u4ec5\u652f\u6301\u975e\u8d1f\u6574\u6570&#xff01;&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<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>    cout <span class=\"token operator\">&lt;&lt;<\/span> num <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;! &#061; &#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token function\">factorial<\/span><span class=\"token punctuation\">(<\/span>num<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<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>\u6d4b\u8bd5\u7ed3\u679c&#xff1a;\u8f93\u5165 5&#xff0c;\u8f93\u51fa 120&#xff08;5! &#061; 5\u00d74\u00d73\u00d72\u00d71 &#061; 120&#xff09;&#xff1b;\u8f93\u5165 0&#xff0c;\u8f93\u51fa 1&#xff0c;\u7b26\u5408\u9636\u4e58\u7684\u6570\u5b66\u5b9a\u4e49\u3002<\/p>\n<h4>2. \u9012\u5f52\u6267\u884c\u6d41\u7a0b\u62c6\u89e3&#xff08;\u4ee5 5! \u4e3a\u4f8b&#xff09;<\/h4>\n<p>\u9012\u5f52\u51fd\u6570\u7684\u6267\u884c\u5206\u4e3a\u201c\u9012\u63a8\u9636\u6bb5\u201d\u548c\u201c\u56de\u6eaf\u9636\u6bb5\u201d&#xff0c;\u4e24\u4e2a\u9636\u6bb5\u901a\u8fc7\u51fd\u6570\u8c03\u7528\u6808\u5b8c\u6210&#xff0c;\u6211\u4eec\u4ee5\u8ba1\u7b97 5! \u4e3a\u4f8b&#xff0c;\u4e00\u6b65\u6b65\u62c6\u89e3\u6267\u884c\u6d41\u7a0b&#xff1a;<\/p>\n<li>\n<p>\u9012\u63a8\u9636\u6bb5&#xff08;\u4ece\u539f\u95ee\u9898\u62c6\u89e3\u5230\u57fa\u7ebf\u6761\u4ef6&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u8c03\u7528 factorial(5)&#xff0c;n\u22600\/1&#xff0c;\u6267\u884c 5 \u00d7 factorial(4)&#xff0c;\u9700\u5148\u6c42\u89e3 factorial(4)&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u8c03\u7528 factorial(4)&#xff0c;n\u22600\/1&#xff0c;\u6267\u884c 4 \u00d7 factorial(3)&#xff0c;\u9700\u5148\u6c42\u89e3 factorial(3)&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u8c03\u7528 factorial(3)&#xff0c;n\u22600\/1&#xff0c;\u6267\u884c 3 \u00d7 factorial(2)&#xff0c;\u9700\u5148\u6c42\u89e3 factorial(2)&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u8c03\u7528 factorial(2)&#xff0c;n\u22600\/1&#xff0c;\u6267\u884c 2 \u00d7 factorial(1)&#xff0c;\u9700\u5148\u6c42\u89e3 factorial(1)&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u8c03\u7528 factorial(1)&#xff0c;n&#061;1&#xff0c;\u89e6\u53d1\u57fa\u7ebf\u6761\u4ef6&#xff0c;\u8fd4\u56de 1&#xff0c;\u9012\u63a8\u9636\u6bb5\u7ed3\u675f\u3002<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u56de\u6eaf\u9636\u6bb5&#xff08;\u4ece\u57fa\u7ebf\u6761\u4ef6\u7ed3\u679c\u56de\u6eaf\u5230\u539f\u95ee\u9898&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\n<p>factorial(1) \u8fd4\u56de 1&#xff0c;\u4ee3\u5165 factorial(2)&#xff0c;\u5f97 2 \u00d7 1 &#061; 2&#xff0c;\u8fd4\u56de 2&#xff1b;<\/p>\n<\/li>\n<li>\n<p>factorial(2) \u8fd4\u56de 2&#xff0c;\u4ee3\u5165 factorial(3)&#xff0c;\u5f97 3 \u00d7 2 &#061; 6&#xff0c;\u8fd4\u56de 6&#xff1b;<\/p>\n<\/li>\n<li>\n<p>factorial(3) \u8fd4\u56de 6&#xff0c;\u4ee3\u5165 factorial(4)&#xff0c;\u5f97 4 \u00d7 6 &#061; 24&#xff0c;\u8fd4\u56de 24&#xff1b;<\/p>\n<\/li>\n<li>\n<p>factorial(4) \u8fd4\u56de 24&#xff0c;\u4ee3\u5165 factorial(5)&#xff0c;\u5f97 5 \u00d7 24 &#061; 120&#xff0c;\u8fd4\u56de 120&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u6700\u7ec8 factorial(5) \u8fd4\u56de 120&#xff0c;\u4e3b\u51fd\u6570\u8f93\u51fa\u7ed3\u679c\u3002<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<p>\u6838\u5fc3\u8981\u70b9&#xff1a;\u6bcf\u6b21\u51fd\u6570\u8c03\u7528\u90fd\u4f1a\u88ab\u538b\u5165\u51fd\u6570\u8c03\u7528\u6808&#xff0c;\u6808\u4e2d\u5b58\u50a8\u51fd\u6570\u7684\u53c2\u6570\u3001\u5c40\u90e8\u53d8\u91cf\u7b49\u4fe1\u606f&#xff1b;\u5f53\u89e6\u53d1\u57fa\u7ebf\u6761\u4ef6\u8fd4\u56de\u65f6&#xff0c;\u51fd\u6570\u4ece\u6808\u9876\u4f9d\u6b21\u5f39\u51fa&#xff0c;\u5b8c\u6210\u56de\u6eaf\u8ba1\u7b97\u3002<\/p>\n<h3>\u4e09\u3001\u9012\u5f52\u7684\u6838\u5fc3\u7279\u6027\u4e0e\u9002\u7528\u573a\u666f<\/h3>\n<h4>1. \u6838\u5fc3\u7279\u6027<\/h4>\n<ul>\n<li>\n<p>\u4ee3\u7801\u7b80\u6d01\u76f4\u89c2&#xff1a;\u65e0\u9700\u624b\u52a8\u7f16\u5199\u5faa\u73af\u903b\u8f91&#xff0c;\u4ec5\u9700\u5b9a\u4e49\u9012\u63a8\u5173\u7cfb\u548c\u7ec8\u6b62\u6761\u4ef6&#xff0c;\u5c31\u80fd\u5c06\u590d\u6742\u95ee\u9898\u8f6c\u5316\u4e3a\u7b80\u6d01\u4ee3\u7801&#xff0c;\u5982\u9636\u4e58\u9012\u5f52\u6bd4\u5faa\u73af\u5b9e\u73b0\u66f4\u6613\u8bfb\u3002<\/p>\n<\/li>\n<li>\n<p>\u4f9d\u8d56\u51fd\u6570\u8c03\u7528\u6808&#xff1a;\u9012\u5f52\u7684\u6267\u884c\u4f9d\u8d56\u7cfb\u7edf\u5206\u914d\u7684\u51fd\u6570\u6808&#xff0c;\u6bcf\u6b21\u8c03\u7528\u90fd\u4f1a\u5360\u7528\u6808\u7a7a\u95f4&#xff0c;\u82e5\u9012\u5f52\u6df1\u5ea6\u8fc7\u5927&#xff0c;\u53ef\u80fd\u5bfc\u81f4\u6808\u6ea2\u51fa\u3002<\/p>\n<\/li>\n<li>\n<p>\u5b58\u5728\u91cd\u590d\u8ba1\u7b97\u98ce\u9669&#xff1a;\u90e8\u5206\u9012\u5f52\u573a\u666f&#xff08;\u5982\u6590\u6ce2\u90a3\u5951\u6570\u5217&#xff09;\u4f1a\u91cd\u590d\u8ba1\u7b97\u76f8\u540c\u5b50\u95ee\u9898&#xff0c;\u5bfc\u81f4\u6548\u7387\u4f4e\u4e0b&#xff0c;\u9700\u901a\u8fc7\u8bb0\u5fc6\u5316\u641c\u7d22\u7b49\u65b9\u5f0f\u4f18\u5316\u3002<\/p>\n<\/li>\n<li>\n<p>\u903b\u8f91\u53ef\u9006&#xff1a;\u9012\u5f52\u95ee\u9898\u90fd\u53ef\u8f6c\u5316\u4e3a\u5faa\u73af&#xff08;\u8fed\u4ee3&#xff09;\u5b9e\u73b0&#xff0c;\u53cd\u4e4b\u4ea6\u7136&#xff0c;\u4e8c\u8005\u662f\u7b49\u4ef7\u7684\u89e3\u9898\u601d\u8def\u3002<\/p>\n<\/li>\n<\/ul>\n<h4>2. \u9002\u7528\u573a\u666f<\/h4>\n<p>\u9012\u5f52\u5e76\u975e\u4e07\u80fd&#xff0c;\u9700\u7ed3\u5408\u95ee\u9898\u7279\u6027\u9009\u62e9&#xff0c;\u4ee5\u4e0b\u573a\u666f\u66f4\u9002\u5408\u4f7f\u7528\u9012\u5f52&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u95ee\u9898\u5177\u6709\u660e\u786e\u9012\u63a8\u5173\u7cfb&#xff1a;\u5982\u9636\u4e58\u3001\u6590\u6ce2\u90a3\u5951\u6570\u5217\u3001\u5e42\u8fd0\u7b97\u7b49\u6570\u5b66\u95ee\u9898&#xff0c;\u80fd\u6e05\u6670\u62c6\u89e3\u4e3a\u89c4\u6a21\u66f4\u5c0f\u7684\u5b50\u95ee\u9898\u3002<\/p>\n<\/li>\n<li>\n<p>\u6811\u5f62\/\u56fe\u5f62\u7ed3\u6784\u904d\u5386&#xff1a;\u5982\u4e8c\u53c9\u6811\u7684\u524d\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\u904d\u5386&#xff0c;\u56fe\u7684\u6df1\u5ea6\u4f18\u5148\u641c\u7d22&#xff08;DFS&#xff09;&#xff0c;\u9012\u5f52\u5b9e\u73b0\u6bd4\u5faa\u73af\u66f4\u7b80\u6d01\u3002<\/p>\n<\/li>\n<li>\n<p>\u5206\u6cbb\u7b97\u6cd5\u5b9e\u73b0&#xff1a;\u5982\u5feb\u901f\u6392\u5e8f\u3001\u5f52\u5e76\u6392\u5e8f&#xff0c;\u6838\u5fc3\u662f\u5c06\u6570\u7ec4\u62c6\u5206\u540e\u9012\u5f52\u5904\u7406\u5b50\u6570\u7ec4&#xff0c;\u518d\u5408\u5e76\u7ed3\u679c\u3002<\/p>\n<\/li>\n<li>\n<p>\u5d4c\u5957\u7ed3\u6784\u5904\u7406&#xff1a;\u5982\u591a\u7ea7\u83dc\u5355\u3001\u5d4c\u5957\u62ec\u53f7\u5339\u914d&#xff0c;\u95ee\u9898\u7ed3\u6784\u5b58\u5728\u5d4c\u5957\u5c42\u7ea7&#xff0c;\u9012\u5f52\u53ef\u81ea\u7136\u9002\u914d\u5c42\u7ea7\u62c6\u89e3\u3002<\/p>\n<\/li>\n<\/ul>\n<h3>\u56db\u3001\u9012\u5f52\u4e0e\u8fed\u4ee3&#xff08;\u5faa\u73af&#xff09;\u7684\u5bf9\u6bd4<\/h3>\n<p>\u9636\u4e58\u8ba1\u7b97\u65e2\u53ef\u7528\u9012\u5f52\u5b9e\u73b0&#xff0c;\u4e5f\u53ef\u7528\u5faa\u73af&#xff08;\u8fed\u4ee3&#xff09;\u5b9e\u73b0&#xff0c;\u4e8c\u8005\u5404\u6709\u4f18\u52a3&#xff0c;\u5177\u4f53\u5bf9\u6bd4\u5982\u4e0b&#xff1a;<\/p>\n<table>\n<tr>\u5bf9\u6bd4\u7ef4\u5ea6\u9012\u5f52\u5b9e\u73b0\u8fed\u4ee3\u5b9e\u73b0<\/tr>\n<tbody>\n<tr>\n<td>\u4ee3\u7801\u590d\u6742\u5ea6<\/td>\n<td>\u7b80\u6d01&#xff0c;\u4ec5\u9700\u5b9a\u4e49\u9012\u63a8\u4e0e\u7ec8\u6b62\u6761\u4ef6<\/td>\n<td>\u7a0d\u7e41\u7410&#xff0c;\u9700\u624b\u52a8\u63a7\u5236\u5faa\u73af\u53d8\u91cf\u4e0e\u7d2f\u52a0\u903b\u8f91<\/td>\n<\/tr>\n<tr>\n<td>\u5185\u5b58\u5f00\u9500<\/td>\n<td>\u8f83\u9ad8&#xff0c;\u4f9d\u8d56\u51fd\u6570\u6808&#xff0c;\u9012\u5f52\u6df1\u5ea6\u8d8a\u5927\u5f00\u9500\u8d8a\u5927<\/td>\n<td>\u8f83\u4f4e&#xff0c;\u4ec5\u9700\u5c11\u91cf\u5c40\u90e8\u53d8\u91cf&#xff0c;\u65e0\u6808\u7a7a\u95f4\u5360\u7528<\/td>\n<\/tr>\n<tr>\n<td>\u6267\u884c\u6548\u7387<\/td>\n<td>\u8f83\u4f4e&#xff0c;\u51fd\u6570\u8c03\u7528\u4e0e\u6808\u64cd\u4f5c\u5b58\u5728\u989d\u5916\u5f00\u9500<\/td>\n<td>\u8f83\u9ad8&#xff0c;\u65e0\u51fd\u6570\u8c03\u7528\u5f00\u9500&#xff0c;\u6267\u884c\u66f4\u9ad8\u6548<\/td>\n<\/tr>\n<tr>\n<td>\u53ef\u8bfb\u6027<\/td>\n<td>\u5f3a&#xff0c;\u8d34\u5408\u95ee\u9898\u7684\u6570\u5b66\u903b\u8f91\u4e0e\u62c6\u89e3\u601d\u8def<\/td>\n<td>\u8f83\u5f31&#xff0c;\u9700\u68b3\u7406\u5faa\u73af\u53d8\u91cf\u7684\u53d8\u5316\u4e0e\u7d2f\u52a0\u5173\u7cfb<\/td>\n<\/tr>\n<tr>\n<td>\u98ce\u9669\u70b9<\/td>\n<td>\u6613\u51fa\u73b0\u6b7b\u9012\u5f52\u3001\u6808\u6ea2\u51fa\u3001\u91cd\u590d\u8ba1\u7b97<\/td>\n<td>\u6613\u51fa\u73b0\u5faa\u73af\u6761\u4ef6\u9519\u8bef\u3001\u7d2f\u52a0\u903b\u8f91\u504f\u5dee<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>\u9636\u4e58\u7684\u8fed\u4ee3\u5b9e\u73b0&#xff08;\u5bf9\u6bd4\u53c2\u8003&#xff09;<\/h4>\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;iostream&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u8fed\u4ee3\u51fd\u6570&#xff1a;\u8ba1\u7b97n\u7684\u9636\u4e58<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">factorialIter<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> result <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u5faa\u73af\u7d2f\u52a0&#xff0c;\u4ece2\u5230n\u76f8\u4e58&#xff08;1\u4e58\u4efb\u4f55\u6570\u4e0d\u53d8&#xff0c;\u53ef\u7701\u7565&#xff09;<\/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\">2<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/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        result <span class=\"token operator\">*&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> result<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    <span class=\"token keyword\">int<\/span> num<span class=\"token punctuation\">;<\/span><br \/>\n    cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\u8bf7\u8f93\u5165\u4e00\u4e2a\u975e\u8d1f\u6574\u6570&#xff1a;&#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cin <span class=\"token operator\">&gt;&gt;<\/span> num<span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>num <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\u9519\u8bef&#xff1a;\u9636\u4e58\u4ec5\u652f\u6301\u975e\u8d1f\u6574\u6570&#xff01;&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<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>    cout <span class=\"token operator\">&lt;&lt;<\/span> num <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;! &#061; &#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token function\">factorialIter<\/span><span class=\"token punctuation\">(<\/span>num<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<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>\u4e94\u3001\u907f\u5751\u6307\u5357&#xff1a;\u9012\u5f52\u5e38\u89c1\u9519\u8bef\u4e0e\u89c4\u907f\u65b9\u6cd5<\/h3>\n<h4>1. \u7f3a\u5c11\u57fa\u7ebf\u6761\u4ef6&#xff08;\u6b7b\u9012\u5f52&#xff09;<\/h4>\n<p>\u9519\u8bef\u573a\u666f&#xff1a;\u5fd8\u8bb0\u5b9a\u4e49\u7ec8\u6b62\u6761\u4ef6&#xff0c;\u6216\u7ec8\u6b62\u6761\u4ef6\u903b\u8f91\u9519\u8bef&#xff0c;\u5bfc\u81f4\u51fd\u6570\u65e0\u9650\u8c03\u7528\u81ea\u8eab&#xff0c;\u6700\u7ec8\u6808\u6ea2\u51fa\u7a0b\u5e8f\u5d29\u6e83\u3002<\/p>\n<p><span class=\"token comment\">\/\/ \u9519\u8bef\u793a\u4f8b&#xff1a;\u65e0\u57fa\u7ebf\u6761\u4ef6&#xff0c;\u6b7b\u9012\u5f52<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">factorialError<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> n <span class=\"token operator\">*<\/span> <span class=\"token function\">factorialError<\/span><span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u65e0\u9650\u8c03\u7528&#xff0c;\u76f4\u81f3\u6808\u6ea2\u51fa<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u89c4\u907f\u65b9\u6848&#xff1a;\u7f16\u5199\u9012\u5f52\u51fd\u6570\u65f6&#xff0c;\u5148\u660e\u786e\u57fa\u7ebf\u6761\u4ef6&#xff0c;\u786e\u4fdd\u5b50\u95ee\u9898\u80fd\u6700\u7ec8\u7b80\u5316\u5230\u53ef\u76f4\u63a5\u8fd4\u56de\u7ed3\u679c\u7684\u72b6\u6001&#xff1b;\u6d4b\u8bd5\u65f6\u91cd\u70b9\u9a8c\u8bc1\u8fb9\u754c\u503c&#xff08;\u5982 n&#061;0\u3001n&#061;1&#xff09;\u3002<\/p>\n<h4>2. \u9012\u5f52\u6df1\u5ea6\u8fc7\u5927\u5bfc\u81f4\u6808\u6ea2\u51fa<\/h4>\n<p>\u9519\u8bef\u573a\u666f&#xff1a;\u5f53 n \u8fc7\u5927&#xff08;\u5982 n&#061;10000&#xff09;&#xff0c;\u9012\u5f52\u8c03\u7528\u6b21\u6570\u8fc7\u591a&#xff0c;\u51fd\u6570\u6808\u7a7a\u95f4\u88ab\u8017\u5c3d&#xff0c;\u89e6\u53d1\u6808\u6ea2\u51fa\u9519\u8bef\u3002<\/p>\n<p>\u89c4\u907f\u65b9\u6848&#xff1a;\u2460 \u9012\u5f52\u6df1\u5ea6\u8f83\u5927\u7684\u573a\u666f&#xff0c;\u6539\u7528\u8fed\u4ee3\u5b9e\u73b0&#xff1b;\u2461 \u90e8\u5206\u8bed\u8a00\u652f\u6301\u5c3e\u9012\u5f52\u4f18\u5316&#xff08;C&#043;&#043; \u6807\u51c6\u4e0d\u5f3a\u5236\u652f\u6301&#xff0c;\u9700\u7f16\u8bd1\u5668\u4f18\u5316&#xff09;&#xff0c;\u5c06\u9012\u5f52\u6539\u5199\u4e3a\u5c3e\u9012\u5f52\u5f62\u5f0f&#xff1b;\u2462 \u624b\u52a8\u6a21\u62df\u6808\u5b9e\u73b0\u9012\u5f52&#xff08;\u81ea\u5b9a\u4e49\u6808\u66ff\u4ee3\u51fd\u6570\u8c03\u7528\u6808&#xff09;\u3002<\/p>\n<h4>3. \u91cd\u590d\u8ba1\u7b97\u5bfc\u81f4\u6548\u7387\u4f4e\u4e0b<\/h4>\n<p>\u9519\u8bef\u573a\u666f&#xff1a;\u5982\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u6734\u7d20\u9012\u5f52\u5b9e\u73b0&#xff0c;\u4f1a\u91cd\u590d\u8ba1\u7b97\u5927\u91cf\u76f8\u540c\u5b50\u95ee\u9898&#xff08;\u5982\u8ba1\u7b97 fib(5) \u9700\u91cd\u590d\u8ba1\u7b97 fib(3)\u3001fib(2) \u591a\u6b21&#xff09;&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(2\u207f)\u3002<\/p>\n<p><span class=\"token comment\">\/\/ \u6734\u7d20\u6590\u6ce2\u90a3\u5951\u9012\u5f52&#xff08;\u5b58\u5728\u91cd\u590d\u8ba1\u7b97&#xff09;<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">fib<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">||<\/span> n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token function\">fib<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token function\">fib<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token operator\">&#8211;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u91cd\u590d\u8ba1\u7b97fib(n-2)\u7b49\u5b50\u95ee\u9898<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u89c4\u907f\u65b9\u6848&#xff1a;\u2460 \u8bb0\u5fc6\u5316\u641c\u7d22&#xff08;\u7528\u6570\u7ec4\u6216\u54c8\u5e0c\u8868\u5b58\u50a8\u5df2\u8ba1\u7b97\u7684\u5b50\u95ee\u9898\u7ed3\u679c&#xff0c;\u907f\u514d\u91cd\u590d\u8ba1\u7b97&#xff09;&#xff1b;\u2461 \u52a8\u6001\u89c4\u5212&#xff08;\u8fed\u4ee3\u65b9\u5f0f\u5b58\u50a8\u4e2d\u95f4\u7ed3\u679c&#xff09;&#xff1b;\u2462 \u5c3e\u9012\u5f52\u4f18\u5316\u3002<\/p>\n<h4>4. \u9012\u63a8\u5173\u7cfb\u903b\u8f91\u9519\u8bef<\/h4>\n<p>\u9519\u8bef\u573a\u666f&#xff1a;\u9012\u63a8\u5173\u7cfb\u4e0e\u95ee\u9898\u903b\u8f91\u4e0d\u7b26&#xff0c;\u5bfc\u81f4\u8ba1\u7b97\u7ed3\u679c\u9519\u8bef&#xff0c;\u5982\u9636\u4e58\u9012\u5f52\u8bef\u5199\u4e3a return (n-1) * factorial(n)&#xff08;\u53c2\u6570\u4f20\u9012\u9519\u8bef&#xff09;\u3002<\/p>\n<p>\u89c4\u907f\u65b9\u6848&#xff1a;\u5148\u68b3\u7406\u95ee\u9898\u7684\u6570\u5b66\u9012\u63a8\u5173\u7cfb&#xff0c;\u518d\u7f16\u5199\u4ee3\u7801&#xff1b;\u901a\u8fc7\u5c0f\u6848\u4f8b&#xff08;\u5982 n&#061;2\u3001n&#061;3&#xff09;\u624b\u52a8\u62c6\u89e3\u6267\u884c\u6d41\u7a0b&#xff0c;\u9a8c\u8bc1\u9012\u63a8\u903b\u8f91\u6b63\u786e\u6027\u3002<\/p>\n<h3>\u516d\u3001\u8fdb\u9636\u4f18\u5316&#xff1a;\u5c3e\u9012\u5f52\u4e0e\u8bb0\u5fc6\u5316\u641c\u7d22<\/h3>\n<h4>1. \u5c3e\u9012\u5f52\u4f18\u5316<\/h4>\n<p>\u5c3e\u9012\u5f52\u662f\u6307\u9012\u5f52\u8c03\u7528\u4f5c\u4e3a\u51fd\u6570\u7684\u6700\u540e\u4e00\u6761\u8bed\u53e5&#xff0c;\u65e0\u540e\u7eed\u8ba1\u7b97\u64cd\u4f5c&#xff0c;\u7f16\u8bd1\u5668\u53ef\u5c06\u5176\u4f18\u5316\u4e3a\u8fed\u4ee3&#xff0c;\u907f\u514d\u6808\u7a7a\u95f4\u5360\u7528\u3002\u9636\u4e58\u7684\u5c3e\u9012\u5f52\u5b9e\u73b0\u5982\u4e0b&#xff1a;<\/p>\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;iostream&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5c3e\u9012\u5f52\u8f85\u52a9\u51fd\u6570&#xff1a;acc\u4e3a\u7d2f\u52a0\u5668&#xff0c;\u5b58\u50a8\u4e2d\u95f4\u7ed3\u679c<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">factorialTail<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> acc<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">||<\/span> n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> acc<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u9012\u5f52\u8c03\u7528\u4f5c\u4e3a\u6700\u540e\u4e00\u6761\u8bed\u53e5&#xff0c;\u65e0\u540e\u7eed\u8ba1\u7b97<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token function\">factorialTail<\/span><span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> n <span class=\"token operator\">*<\/span> acc<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5bf9\u5916\u63a5\u53e3\u51fd\u6570<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">factorial<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u521d\u59cb\u5316\u7d2f\u52a0\u5668\u4e3a1&#xff0c;\u8c03\u7528\u5c3e\u9012\u5f52\u51fd\u6570<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token function\">factorialTail<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/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    cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token number\">5<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;! &#061; &#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token function\">factorial<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u8f93\u51fa120<\/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>\u6ce8\u610f&#xff1a;C&#043;&#043; \u6807\u51c6\u4e0d\u5f3a\u5236\u7f16\u8bd1\u5668\u652f\u6301\u5c3e\u9012\u5f52\u4f18\u5316&#xff0c;\u4e0d\u540c\u7f16\u8bd1\u5668&#xff08;\u5982 GCC\u3001Clang&#xff09;\u7684\u4f18\u5316\u6548\u679c\u4e0d\u540c&#xff0c;\u5b9e\u9645\u5f00\u53d1\u4e2d\u9700\u7ed3\u5408\u7f16\u8bd1\u5668\u7279\u6027\u4f7f\u7528\u3002<\/p>\n<h4>2. \u8bb0\u5fc6\u5316\u641c\u7d22\u4f18\u5316\u91cd\u590d\u8ba1\u7b97<\/h4>\n<p>\u4ee5\u6590\u6ce2\u90a3\u5951\u6570\u5217\u4e3a\u4f8b&#xff0c;\u7528\u6570\u7ec4\u5b58\u50a8\u5df2\u8ba1\u7b97\u7684\u5b50\u95ee\u9898\u7ed3\u679c&#xff0c;\u907f\u514d\u91cd\u590d\u8ba1\u7b97&#xff0c;\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u4ece O(2\u207f) \u4f18\u5316\u4e3a O(n)&#xff1a;<\/p>\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;iostream&gt;<\/span><\/span><br \/>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;vector&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p>vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> memo<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u8bb0\u5fc6\u5316\u6570\u7ec4&#xff0c;\u5b58\u50a8\u5df2\u8ba1\u7b97\u7684\u6590\u6ce2\u90a3\u5951\u6570<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">fibMemo<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u5df2\u8ba1\u7b97\u8fc7&#xff0c;\u76f4\u63a5\u8fd4\u56de\u7ed3\u679c<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>memo<span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">!&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> memo<span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u57fa\u7ebf\u6761\u4ef6<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">||<\/span> n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        memo<span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/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><br \/>\n    <span class=\"token comment\">\/\/ \u9012\u5f52\u8ba1\u7b97\u5e76\u5b58\u50a8\u7ed3\u679c<\/span><br \/>\n    memo<span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">fibMemo<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token function\">fibMemo<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token operator\">&#8211;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> memo<span class=\"token punctuation\">[<\/span>n<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\">fib<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    memo<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token operator\">&#043;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u521d\u59cb\u5316\u8bb0\u5fc6\u5316\u6570\u7ec4<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token function\">fibMemo<\/span><span class=\"token punctuation\">(<\/span>n<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    cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;fib(10) &#061; &#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token function\">fib<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u8f93\u51fa55<\/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 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