{"id":94841,"date":"2026-08-15T12:56:50","date_gmt":"2026-08-15T04:56:50","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/94841.html"},"modified":"2026-08-15T12:56:50","modified_gmt":"2026-08-15T04:56:50","slug":"%e9%a2%98%e8%a7%a3%ef%bc%9a%e7%91%9e%e5%ad%a6%e5%a0%82-%e5%be%90%e8%80%81%e5%b8%88%e7%9a%84%e9%98%b6%e4%b9%98%e8%ae%a1%e7%ae%97%e5%99%a8","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/94841.html","title":{"rendered":"\u9898\u89e3\uff1a\u745e\u5b66\u5802 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| \u6c47\u603b<\/p>\n<hr \/>\n<p>\u3010\u9898\u76ee\u6765\u6e90\u3011<\/p>\n<p>\u745e\u5b66\u5802&#xff1a;\u5f90\u8001\u5e08\u7684\u9636\u4e58\u8ba1\u7b97\u5668<\/p>\n<p>\u3010\u9898\u76ee\u63cf\u8ff0\u3011<\/p>\n<p>\u5f90\u8001\u5e08\u53d1\u73b0\u5f88\u591a\u6570\u5b66\u95ee\u9898\u90fd\u9700\u8981\u91cd\u590d\u8ba1\u7b97\u9636\u4e58\u3002\u4e3a\u4e86\u7b80\u5316\u4ee3\u7801\u548c\u63d0\u9ad8\u6548\u7387&#xff0c;\u4ed6\u51b3\u5b9a\u7f16\u5199\u4e00\u4e2a\u51fd\u6570\u00a0factorial(n)\u00a0\u6765\u8ba1\u7b97\u4e00\u4e2a\u975e\u8d1f\u6574\u6570\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>       n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>\u00a0\u7684\u9636\u4e58\u3002<\/p>\n<p>\u9636\u4e58\u7684\u5b9a\u4e49\u662f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        !<\/p>\n<p>        &#061;<\/p>\n<p>        1<\/p>\n<p>        \u00d7<\/p>\n<p>        2<\/p>\n<p>        \u00d7<\/p>\n<p>        3<\/p>\n<p>        \u00d7<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        \u00d7<\/p>\n<p>        n<\/p>\n<p>       n!&#061;1\u00d72\u00d73\u00d7&#8230;\u00d7n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">!<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">&#8230;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 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class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u73b0\u5728&#xff0c;\u8bf7\u4f60\u5e2e\u52a9\u5f90\u8001\u5e08\u5b8c\u6210\u8fd9\u4e2a\u4efb\u52a1\u3002\u4f60\u9700\u8981\u7f16\u5199\u4e00\u4e2a\u7a0b\u5e8f&#xff0c;\u8be5\u7a0b\u5e8f\u5305\u542b\u4e00\u4e2a\u540d\u4e3a\u00a0factorial\u00a0\u7684\u51fd\u6570&#xff0c;\u7528\u4e8e\u8ba1\u7b97\u9636\u4e58\u3002\u4e3b\u7a0b\u5e8f\u5c06\u8bfb\u53d6\u4e00\u4e2a\u6574\u6570\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8868\u793a\u6709\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>\u00a0\u7ec4\u6d4b\u8bd5\u6570\u636e\u3002\u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e&#xff0c;\u8bfb\u53d6\u4e00\u4e2a\u6574\u6570\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>       n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7136\u540e\u8c03\u7528\u00a0factorial\u00a0\u51fd\u6570\u8ba1\u7b97\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        !<\/p>\n<p>       n!<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">!<\/span><\/span><\/span><\/span><\/span>\u00a0\u5e76\u8f93\u51fa\u7ed3\u679c\u3002<\/p>\n<p>\u3010\u8f93\u5165\u3011<\/p>\n<p>\u7b2c\u4e00\u884c\u5305\u542b\u4e00\u4e2a\u6574\u6570\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>        \u00a0<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        \u2264<\/p>\n<p>        T<\/p>\n<p>        \u2264<\/p>\n<p>        10<\/p>\n<p>        )<\/p>\n<p>       T\u00a0(1\u2264T\u226410)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mord\">\u00a0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span 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class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">10<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u3010\u8f93\u51fa\u3011<\/p>\n<p>\u8f93\u51fa\u5171\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>\u00a0\u884c&#xff0c;\u6bcf\u884c\u4e00\u4e2a\u6574\u6570&#xff0c;\u8868\u793a\u5bf9\u5e94\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>       n<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>\u00a0\u7684\u9636\u4e58\u00a0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        !<\/p>\n<p>       n!<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">!<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u3010\u8f93\u5165\u6837\u4f8b\u3011<\/p>\n<p>3<br \/>\n5<br \/>\n0<br \/>\n10<\/p>\n<p>\u3010\u8f93\u51fa\u6837\u4f8b\u3011<\/p>\n<p>120<br \/>\n1<br \/>\n3628800<\/p>\n<p>\u3010\u6838\u5fc3\u601d\u60f3\u3011<\/p>\n<li>\n<p>\u95ee\u9898\u5206\u6790&#xff1a;\u7ed9\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          T<\/p>\n<p>         T<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u7ec4\u6d4b\u8bd5\u6570\u636e&#xff0c;\u6bcf\u7ec4\u7ed9\u5b9a\u4e00\u4e2a\u975e\u8d1f\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          n<\/p>\n<p>         n<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          0<\/p>\n<p>          \u2264<\/p>\n<p>          n<\/p>\n<p>          \u2264<\/p>\n<p>          10<\/p>\n<p>         0 \\\\leq n \\\\leq 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0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>&#xff08;\u7279\u522b\u5730&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          0<\/p>\n<p>          !<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>         0! &#061; 1<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">!<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u8fd9\u662f\u4e00\u4e2a\u76f4\u63a5\u6a21\u62df\u4e58\u6cd5\u8fc7\u7a0b\u7684\u95ee\u9898&#xff0c;\u5173\u952e\u5728\u4e8e\u6b63\u786e\u5b9e\u73b0\u9636\u4e58\u7684\u7d2f\u4e58\u903b\u8f91\u5e76\u5904\u7406\u8fb9\u754c\u60c5\u51b5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          n<\/p>\n<p>          &#061;<\/p>\n<p>          0<\/p>\n<p>         n&#061;0<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>          n<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>         n&#061;1<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<\/li>\n<li>\n<p>\u7b97\u6cd5\u9009\u62e9&#xff1a;<\/p>\n<ul>\n<li>\u76f4\u63a5\u6a21\u62df&#xff08;Brute-force Simulation&#xff09;&#xff1a;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           2<\/p>\n<p>          2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           n<\/p>\n<p>          n<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> \u4f9d\u6b21\u7d2f\u4e58&#xff0c;\u5229\u7528\u4e58\u6cd5\u7684\u7ed3\u5408\u5f8b\u76f4\u63a5\u8ba1\u7b97\u7ed3\u679c<\/li>\n<li>\u8fb9\u754c\u5904\u7406&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           0<\/p>\n<p>           !<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          0! &#061; 1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">!<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>           !<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          1! &#061; 1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">!<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u901a\u8fc7\u5faa\u73af\u6761\u4ef6 i &lt;&#061; x \u81ea\u7136\u8986\u76d6&#xff08;\u5faa\u73af\u4e0d\u6267\u884c\u65f6\u8fd4\u56de\u521d\u59cb\u503c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u5173\u952e\u6b65\u9aa4&#xff1a;<\/p>\n<ul>\n<li>\u521d\u59cb\u5316&#xff1a;\u8bfb\u53d6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           T<\/p>\n<p>          T<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>&#xff08;\u6d4b\u8bd5\u7ec4\u6570&#xff09;&#xff0c;\u5b9a\u4e49\u51fd\u6570 factorial(x)<\/li>\n<li>\u51fd\u6570\u5185\u90e8&#xff1a;\n<ul>\n<li>\u521d\u59cb\u5316\u7ed3\u679c\u53d8\u91cf res &#061; 1&#xff08;\u4e58\u6cd5\u5355\u4f4d\u5143&#xff0c;\u786e\u4fdd <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>             0<\/p>\n<p>             !<\/p>\n<p>            0!<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">!<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             1<\/p>\n<p>             !<\/p>\n<p>            1!<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">!<\/span><\/span><\/span><\/span><\/span> \u6b63\u786e\u8fd4\u56de <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             1<\/p>\n<p>            1<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/li>\n<li>\u904d\u5386 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>             i<\/p>\n<p>            i<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             2<\/p>\n<p>            2<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             x<\/p>\n<p>            x<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>&#xff1a;res &#061; res \\\\times i<\/li>\n<li>\u8fd4\u56de res<\/li>\n<\/ul>\n<\/li>\n<li>\u4e3b\u7a0b\u5e8f\u5faa\u73af&#xff1a;\n<ul>\n<li>\u8bfb\u5165 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>             n<\/p>\n<p>            n<\/p>\n<p>         <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u8c03\u7528 factorial(n) \u5e76\u8f93\u51fa\u7ed3\u679c<\/li>\n<\/ul>\n<\/li>\n<li>\u91cd\u590d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           T<\/p>\n<p>          T<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u6b21<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u65f6\u95f4\/\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;<\/p>\n<ul>\n<li>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           O<\/p>\n<p>           (<\/p>\n<p>           T<\/p>\n<p>           \u22c5<\/p>\n<p>           n<\/p>\n<p>           )<\/p>\n<p>          O(T \\\\cdot n)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u7ec4\u6570\u636e\u6700\u591a\u8fdb\u884c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           n<\/p>\n<p>          n<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> \u6b21\u4e58\u6cd5&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           n<\/p>\n<p>           \u2264<\/p>\n<p>           10<\/p>\n<p>          n \\\\leq 10<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7719em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/li>\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           O<\/p>\n<p>           (<\/p>\n<p>           1<\/p>\n<p>           )<\/p>\n<p>          O(1)<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ec5\u4f7f\u7528\u5e38\u6570\u4e2a\u53d8\u91cf\u5b58\u50a8\u7ed3\u679c<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6a21\u62df\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3&#xff1a;<\/p>\n<ul>\n<li>\u6309\u5b9a\u4e49\u76f4\u63a5\u5b9e\u73b0&#xff1a;\u9636\u4e58\u7684\u6570\u5b66\u5b9a\u4e49\u672c\u8eab\u5c31\u662f\u7d2f\u4e58\u8fc7\u7a0b&#xff0c;\u76f4\u63a5\u7ffb\u8bd1\u4e3a\u4ee3\u7801\u5373\u53ef<\/li>\n<li>\u4e58\u6cd5\u5355\u4f4d\u5143\u7684\u5999\u7528&#xff1a;\u521d\u59cb\u5316 res &#061; 1 \u540c\u65f6\u6ee1\u8db3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           0<\/p>\n<p>           !<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          0! &#061; 1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">!<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u548c\u4f5c\u4e3a\u7d2f\u4e58\u8d77\u70b9<\/li>\n<li>\u5faa\u73af\u8d77\u70b9\u7684\u4f18\u5316&#xff1a;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           2<\/p>\n<p>          i&#061;2<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           1<\/p>\n<p>          1<\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u4e58\u4ee5\u4efb\u4f55\u6570\u4e0d\u53d8&#xff09;&#xff0c;\u51cf\u5c11\u4e00\u6b21\u65e0\u610f\u4e49\u8fd0\u7b97<\/li>\n<li>\u6570\u636e\u7c7b\u578b\u9884\u9632&#xff1a;\u4f7f\u7528 long long \u9632\u6b62\u66f4\u5927\u8303\u56f4\u9636\u4e58\u6ea2\u51fa&#xff0c;\u4f53\u73b0\u5de5\u7a0b\u4e60\u60ef<\/li>\n<li>\u9002\u7528\u4e8e\u8ba1\u7b97\u8fc7\u7a0b\u660e\u786e\u3001\u65e0\u590d\u6742\u9012\u63a8\u5173\u7cfb\u3001\u6570\u636e\u8303\u56f4\u6781\u5c0f\u7684\u573a\u666f<\/li>\n<\/ul>\n<\/li>\n<p>\u3010\u7b97\u6cd5\u6807\u7b7e\u3011<\/p>\n<p>#\u6a21\u62df<\/p>\n<p>\u3010\u4ee3\u7801\u8be6\u89e3\u3011<\/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;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 macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">define<\/span> <span class=\"token macro-name\">int<\/span> <span class=\"token expression\"><span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span>    <\/span><span class=\"token comment\">\/\/ \u5c06int\u5b9a\u4e49\u4e3along long&#xff0c;\u907f\u514d\u9636\u4e58\u7ed3\u679c\u6ea2\u51fa&#xff08;10! &#061; 3628800&#xff0c;\u867d\u7136int\u80fd\u5b58&#xff0c;\u4f46\u517b\u6210\u597d\u4e60\u60ef&#xff09;<\/span><\/span><br \/>\n<span class=\"token keyword\">int<\/span> t<span class=\"token punctuation\">,<\/span> n<span class=\"token punctuation\">;<\/span>                <span class=\"token comment\">\/\/ t\u4e3a\u6d4b\u8bd5\u6570\u636e\u7ec4\u6570&#xff0c;n\u4e3a\u6bcf\u7ec4\u6570\u636e\u8981\u8ba1\u7b97\u9636\u4e58\u7684\u6574\u6570<\/span><\/p>\n<p><span class=\"token comment\">\/\/ factorial\u51fd\u6570&#xff1a;\u8ba1\u7b97\u975e\u8d1f\u6574\u6570x\u7684\u9636\u4e58<\/span><br \/>\n<span class=\"token comment\">\/\/ \u6ce8\u610f&#xff1a;\u539f\u4ee3\u7801\u5b58\u5728bug&#xff0c;\u5faa\u73af\u53d8\u91cf\u5e94\u4f7f\u7528\u53c2\u6570x\u800c\u975e\u5168\u5c40\u53d8\u91cfn<\/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> x<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> res <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>         <span class=\"token comment\">\/\/ res\u5b58\u50a8\u9636\u4e58\u7ed3\u679c&#xff0c;\u521d\u59cb\u5316\u4e3a1&#xff08;0! &#061; 1&#xff0c;\u4e58\u6cd5\u5355\u4f4d\u5143&#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 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