{"id":123687,"date":"2026-11-08T02:00:49","date_gmt":"2026-11-07T18:00:49","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/123687.html"},"modified":"2026-11-08T02:00:49","modified_gmt":"2026-11-07T18:00:49","slug":"c%e7%ae%97%e6%b3%95-%e6%9e%9a%e4%b8%be%ef%bc%88%e4%b8%8b%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/123687.html","title":{"rendered":"C++\u7b97\u6cd5 \u679a\u4e3e\uff08\u4e0b\uff09"},"content":{"rendered":"

\/* MD \/ \u5bcc\u6587\u672c\u4e2d\u7684 .toc\uff08\u542b\u535a\u5ba2\u56ed\u642c\u5bb6\u7b49\u5d4c\u5957\u7ed3\u6784\uff09\uff1b.toc-box \u5728\u4fa7\u680f\uff0c\u4e0d\u53d7\u5f71\u54cd *\/
\n #content_views .toc,
\n \/* \u7f16\u8f91\u5668\u5e38\u5728\u76ee\u5f55\u524d\u540e\u63d2\u5165\u7a7a p\uff08:empty \u4ecd\u5360 20px\uff09\uff0c\u4e00\u5e76\u53bb\u6389\u907f\u514d\u9876\u7a7a\u9699 *\/
\n #content_views.markdown_views > p:empty:has(+ .toc),
\n #content_views.markdown_views > .toc + p:empty,
\n \/* \u5bcc\u6587\u672c\u65e7\u7248\u76ee\u5f55\u6807\u8bb0 *\/
\n #content_views.htmledit_views #main-toc,
\n #content_views.htmledit_views #hr-toc,
\n #content_views.htmledit_views p[id*=\\”-toc\\”] {
\n display: none !important;
\n }
\n \/* \u76ee\u5f55\u53bb\u6389\u540e\uff0c\u7d27\u8ddf\u7684\u9996\u4e2a\u6807\u9898\u4e0d\u518d\u591a\u51fa\u4e00\u5757\u4e0a\u8fb9\u8ddd *\/
\n #content_views.markdown_views > .toc + h1,
\n #content_views.markdown_views > .toc + h2,
\n #content_views.markdown_views > .toc + h3,
\n #content_views.markdown_views > .toc + h4,
\n #content_views.markdown_views > .toc + p:empty + h1,
\n #content_views.markdown_views > .toc + p:empty + h2,
\n #content_views.markdown_views > .toc + p:empty + h3,
\n #content_views.markdown_views > .toc + p:empty + h4 {
\n margin-top: 0 !important;
\n }<\/p>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u0f3a \u4e2a\u4eba\u4e3b\u9875 \u00b7 \u7eaa\u5ff5229 \u0f3b<\/font><\/p>\n

🏠\u6211\u7684\u535a\u5ba2\u4e3b\u9875🏠<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300a\u6570\u636e\u7ed3\u6784\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300a\u7b97\u6cd5\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300aC++\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300aMySQL\u6570\u636e\u5e93\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300a\u524d\u7aef\u5f00\u53d1\u300b\u0f12<\/font><\/p>\n

\u0f12\u5176\u5b83\u6709\u8da3\u7684\u8ba1\u7b97\u673a\u77e5\u8bc6\u0f12<\/font><\/p>\n

\u0f3a\u4e16\u4e0a\u672c\u6ca1\u6709\u8def，\u8d70\u7684\u4eba\u591a\u4e86\u81ea\u7136\u5c31\u6709\u4e86\u0f3b<\/font><\/p>\n

\n

\u672c\u7bc7\u6587\u7ae0\u63a5\u4e0a\u56de\u626b\u96f7\u7b97\u6cd5\u9898\u8bb2\u89e3\u8fd8\u6709\u5173\u4e8c\u8fdb\u5236\u679a\u4e3e\u679a\u4e3e\u7684\u9898\u76ee,\u5e0c\u671b\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9<\/p>\n

\u9898\u76ee\u94fe\u63a5: \u626b\u96f7 \u5b50\u96c6 \u8d39\u89e3\u7684\u5f00\u5173<\/p>\n

\n

\u6587\u7ae0\u76ee\u5f55<\/h4>\n
    \n
  • 1.\u626b\u96f7<\/li>\n
  • 2.\u5b50\u96c6<\/li>\n
  • 3.\u8d39\u89e3\u7684\u5f00\u5173<\/li>\n<\/ul>\n
    \n

    1.\u626b\u96f7<\/h2>\n

    \u5177\u4f53\u7ed3\u6784\u8fd9\u91cc\u5c31\u4e0d\u8bb2\u89e3\u4e86，\u76f4\u63a5\u4e0a\u6838\u5fc3\u601d\u60f3<\/p>\n

    *<\/span>*<\/span>\/\/\u8fd9\u91cc\u96f7\u7684\u6392\u653e\u6211\u4eec\u5bf9\u7b2c\u4e00\u884c\u7b2c\u4e00\u4e2a\u8fdb\u884c\u679a\u4e3e\u5206\u4e3a\u653e\u96f7\u548c\u4e0d\u653e\u96f7<\/span><\/p>\n

    #<\/span>include<\/span><iostream><\/span><\/span>
    \n#<\/span>include<\/span><cstring><\/span><\/span>
    \nusing namespace std;<\/span>
    \nconst<\/span> int<\/span> N =<\/span> 1e4<\/span> +<\/span> 10<\/span>;<\/span>
    \nint<\/span> a1[<\/span>N]<\/span>,<\/span> a2[<\/span>N]<\/span>;<\/span>
    \nint<\/span> n;<\/span><\/p>\n

    int<\/span> main<\/span>(<\/span>)<\/span>
    \n{<\/span>
    \ncin >><\/span> n;<\/span><\/p>\n

    \/\/\u6211\u4eec\u4ecea1\u4e0b\u68071\u5f00\u59cb\u679a\u4e3e\u8f93\u5165\u7684\u6570\u636e \u4e0b\u68070\u8ba1\u4e3a0\u65e0\u96f7，a1[i]\u7684\u503c\u4e3aa2[i] – a1[i – 1] – a1[i – 2]\u5982\u679c\u653e\u96f7\u7b26\u5408\u89c4\u5219\u5c31\u8bb0\u4e00\u6b21 <\/span>
    \nfor<\/span>(<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span>
    \n{<\/span>
    \n cin >><\/span> a2[<\/span>i]<\/span>;<\/span>
    \n \/\/\u7b2c\u4e8c\u5217\u4e2d\u6709\u5927\u4e8e3\u7684\u6570\u65e0\u65b9\u6848 <\/span>
    \n if<\/span>(<\/span>a2[<\/span>i]<\/span> ><\/span> 3<\/span>)<\/span>{<\/span>
    \n cout <<<\/span> 0<\/span>;<\/span>
    \n return<\/span> 0<\/span>;<\/span>
    \n }<\/span>
    \n}<\/span>
    \nint<\/span> ret =<\/span> 0<\/span>;<\/span>\/\/\u5b9a\u4e49\u4e00\u4e2aret\u8ba1\u96f7\u65b9\u6848 \u4e2a\u6570 <\/span>
    \n\/\/\u6211\u4eec\u8bbe\u7f6ea1[1]\u6709\u96f7<\/span>
    \na1[<\/span>1<\/span>]<\/span> =<\/span> 1<\/span> ;<\/span>
    \nint<\/span> flag =<\/span> 1<\/span>;<\/span>\/\/\u9ed8\u8ba4\u65b9\u6848\u6210\u529f <\/span>
    \nfor<\/span>(<\/span>int<\/span> i =<\/span> 2<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span>
    \n{<\/span>
    \na1[<\/span>i]<\/span> =<\/span> a2[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 2<\/span>]<\/span>;<\/span>\/\/\u8fd9\u91cc\u662f a1[i] = a2[i – 1] – a1[i – 1] – a1[i – 2]\u4e0d\u662fa1[i] = a2[i] – a1[i – 1] – a1[i – 2] <\/span>
    \n if<\/span>(<\/span>a1[<\/span>i]<\/span> <<\/span>0<\/span> ||<\/span> a1[<\/span>i]<\/span> ><\/span> 1<\/span>)<\/span> \/\/a1[i]\u4e0d\u4e3a0\u62161\u8bf4\u660e\u6b64\u65b9\u6848\u5931\u8d25 \u8fd9\u91cc\u7528||\u7528&&\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u6570 <\/span>
    \n {<\/span>
    \n flag =<\/span> 0<\/span>;<\/span>
    \n break<\/span>;<\/span>
    \n}<\/span>
    \n}<\/span>
    \n\/\/\u6700\u540e\u6211\u4eec\u8fd8\u8981\u9a8c\u8bc1a1[n + 1] = a2[n] – a[n] – a[n – 1];\u56e0\u4e3a\u8981\u6c42a2[i] = a1[n- 1] + a1[n] + a1[n + 1]\u6211\u4eec\u8981\u6c42\u6240\u6709\u6709\u6548\u6570\u636e\u683c\u90fd\u7b26\u5408\u8be5\u89c4\u5219 <\/span>
    \nif<\/span>(<\/span>a2[<\/span>n]<\/span> !=<\/span> a1[<\/span>n –<\/span> 1<\/span>]<\/span> +<\/span> a1[<\/span>n]<\/span> +<\/span> a1[<\/span>n +<\/span> 1<\/span>]<\/span>)<\/span> flag =<\/span> 0<\/span>;<\/span>
    \nif<\/span>(<\/span>flag ==<\/span> 1<\/span>)<\/span> ret++<\/span>;<\/span><\/p>\n

    \/\/ \u6211\u4eec\u8bbe\u7f6ea1[1]\u6ca1\u6709\u96f7<\/span>
    \n\/\/\u5148\u6e05\u7a7as1\u6570\u636e\u4e3a0<\/span>
    \nmemset<\/span>(<\/span>a1,<\/span>0<\/span>,<\/span>sizeof<\/span> a1)<\/span>;<\/span> \/\/memset\u548cmemcpy\u7684\u5934\u6587\u4ef6\u662fcstring\u4e0d\u662fstring <\/span>
    \na1[<\/span>1<\/span>]<\/span> =<\/span> 0<\/span> ;<\/span>
    \nflag =<\/span> 1<\/span>;<\/span>\/\/\u9ed8\u8ba4\u65b9\u6848\u6210\u529f <\/span>
    \nfor<\/span>(<\/span>int<\/span> i =<\/span> 2<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span>
    \n{<\/span>
    \na1[<\/span>i]<\/span> =<\/span> a2[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 2<\/span>]<\/span>;<\/span>
    \n if<\/span>(<\/span>a1[<\/span>i]<\/span> <<\/span>0<\/span> ||<\/span> a1[<\/span>i]<\/span> ><\/span> 1<\/span>)<\/span> \/\/a1[i]\u4e0d\u4e3a0\u62161\u8bf4\u660e\u6b64\u65b9\u6848\u5931\u8d25 <\/span>
    \n {<\/span>
    \n flag =<\/span> 0<\/span>;<\/span>
    \n break<\/span>;<\/span>
    \n}<\/span>
    \n}<\/span>
    \nif<\/span>(<\/span>a2[<\/span>n]<\/span> !=<\/span> a1[<\/span>n –<\/span> 1<\/span>]<\/span> +<\/span> a1[<\/span>n]<\/span> +<\/span> a1[<\/span>n +<\/span> 1<\/span>]<\/span>)<\/span> flag =<\/span> 0<\/span>;<\/span>
    \nif<\/span>(<\/span>flag ==<\/span> 1<\/span>)<\/span> ret++<\/span>;<\/span>
    \ncout <<<\/span> ret;<\/span>
    \nreturn<\/span> 0<\/span>;<\/span>
    \n}<\/span><\/p>\n

    \u8f93\u5165n\u540e\u6211\u4eec\u786e\u5b9aa2\u8981\u8f93\u5165\u591a\u5c11\u884c\u4ece1\u5f00\u59cb\u5230n\u5229\u7528for\u5faa\u73af\u904d\u5386<\/p>\n

    \u8fd9\u91cc\u53ea\u6709\u4e00\u4e2a\u8981\u6c42\u8f93\u5165\u7684\u4e1c\u897f\u4e0d\u5927\u4e8e3\u56e0\u4e3aa2[i]\u53ea\u80fd\u6d4b\u5230a1[i – 1] a1[i] a1[i + 1] \u6240\u4ee5a2[i]\u5927\u4e8e\u4e09\u662f\u4e0d\u5b58\u5728\u7684\u82e5\u662f\u6709\u76f4\u63a5\u8fd4\u56de0\u8bf4\u660e\u6b64\u96f7\u7684\u8bbe\u8ba1\u65b9\u6848\u6ca1\u6709\u6210\u7acb\u7684<\/p>\n

    for<\/span>(<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span>
    \n{<\/span>
    \n cin >><\/span> a2[<\/span>i]<\/span>;<\/span>
    \n \/\/\u7b2c\u4e8c\u5217\u4e2d\u6709\u5927\u4e8e3\u7684\u6570\u65e0\u65b9\u6848 <\/span>
    \n if<\/span>(<\/span>a2[<\/span>i]<\/span> ><\/span> 3<\/span>)<\/span>{<\/span>
    \n cout <<<\/span> 0<\/span>;<\/span>
    \n return<\/span> 0<\/span>;<\/span>
    \n }<\/span>
    \n}<\/span> <\/p>\n

    \u6211\u4eec\u77e5\u9053\u8f93\u5165\u5b8ca2\u540e\u6211\u4eec\u8981\u6839\u636ea1[1]\u679a\u4e3e\u6709\u96f7\u548c\u65e0\u96f7\u4e24\u79cd\u60c5\u51b5（a1[0]\u9ed8\u8ba4\u4e3a0\u65e0\u96f7a1[n + 1]\u9ed8\u8ba4\u4e3a\u65e0\u96f7）\u82e5\u662f\u4e24\u79cd\u60c5\u51b5\u90fd\u7b26\u5408\u89c4\u5219\u90a3\u4e48\u5c31\u67092\u79cd\u65b9\u6848\u5408\u7406（\u6700\u591a\u67092\u79cd\u65b9\u6848\u5408\u7406\u6700\u5c11\u6ca1\u6709\u65b9\u68480\u79cd）<\/p>\n

    \u6211\u4eec\u5b9a\u4e49\u4e00\u4e2aret\u4e3a\u96f7\u7684\u8bbe\u8ba1\u89c4\u5219\u5408\u7406\u6570\u76ee\u521a\u5f00\u59cb\u4e3a0<\/p>\n

    \u5728\u5b9a\u4e49\u4e00\u4e2aflag\u4e3a1\u9ed8\u8ba4\u8be5\u89c4\u5219\u7b26\u5408 \u6211\u4eec\u5148\u679a\u4e3ea[1]\u6709\u96f7<\/p>\n

    \u5224\u65ad\u89c4\u5219\u4e3aa1[i] = a2[i -1] – a1[i – 1] – a1[i – 2];\u8fd9\u4e48\u8bbe\u8ba1\u662f\u56e0\u4e3aa1[0]\u548ca1[1]\u5df2\u7ecf\u8bbe\u8ba1\u597d\u4e86\u6211\u4eec\u8981\u4ecea1[2]\u5f00\u59cb\u6240\u4ee5 a1[2] = a2[1] – a1[1] – a1[0];\u4ee5\u6b64\u7c7b\u63a8\u6211\u4eec\u7684for\u5faa\u73af\u4ece2\u5f00\u59cb\u5230n\u5373\u53ef\u5728\u8fd0\u7b97\u8fc7\u7a0b\u4e2d\u82e5\u662fa1[i]\u5927\u4e8e1\u6216\u5c0f\u4e8e0\u5c31\u8bbe\u7f6eflag\u4e3a0brak\u9000\u51fa\u5faa\u73af，\u51fa\u4e86\u5faa\u73af\u540e\u6700\u540e\u6211\u4eec\u8fd8\u8981\u5224\u65ada1[n + 1] = a2[n] – a1[n] – a1[n – 1];\u4e0d\u6210\u7acb\u7684\u8bdd\u5c31\u5c06flag\u4e3a0<\/p>\n

    \u7136\u540e\u6211\u4eec\u5224\u65adflag\u4e3a1\u4e3a1\u7684\u8bdd\u5c31\u7b26\u5408\u96f7\u7684\u8bbe\u8ba1\u89c4\u5219\u5c06ret ++<\/p>\n

    for<\/span>(<\/span>int<\/span> i =<\/span> 2<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span>
    \n{<\/span>
    \na1[<\/span>i]<\/span> =<\/span> a2[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 2<\/span>]<\/span>;<\/span>\/\/\u8fd9\u91cc\u662f a1[i] = a2[i – 1] – a1[i – 1] – a1[i – 2]\u4e0d\u662fa1[i] = a2[i] – a1[i – 1] – a1[i – 2] <\/span>
    \n if<\/span>(<\/span>a1[<\/span>i]<\/span> <<\/span>0<\/span> ||<\/span> a1[<\/span>i]<\/span> ><\/span> 1<\/span>)<\/span> \/\/a1[i]\u4e0d\u4e3a0\u62161\u8bf4\u660e\u6b64\u65b9\u6848\u5931\u8d25 \u8fd9\u91cc\u7528||\u7528&&\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u6570 <\/span>
    \n {<\/span>
    \n flag =<\/span> 0<\/span>;<\/span>
    \n break<\/span>;<\/span>
    \n}<\/span>
    \n}<\/span>
    \n\/\/\u6700\u540e\u6211\u4eec\u8fd8\u8981\u9a8c\u8bc1a1[n + 1] = a2[n] – a[n] – a[n – 1];\u56e0\u4e3a\u8981\u6c42a2[i] = a1[n- 1] + a1[n] + a1[n + 1]\u6211\u4eec\u8981\u6c42\u6240\u6709\u6709\u6548\u6570\u636e\u683c\u90fd\u7b26\u5408\u8be5\u89c4\u5219 <\/span>
    \nif<\/span>(<\/span>a2[<\/span>n]<\/span> !=<\/span> a1[<\/span>n –<\/span> 1<\/span>]<\/span> +<\/span> a1[<\/span>n]<\/span> +<\/span> a1[<\/span>n +<\/span> 1<\/span>]<\/span>)<\/span> flag =<\/span> 0<\/span>;<\/span>
    \nif<\/span>(<\/span>flag ==<\/span> 1<\/span>)<\/span> ret++<\/span>;<\/span><\/p>\n

    \u7136\u540e\u6211\u4eec\u63a5\u7740\u679a\u4e3ea1[1]\u65e0\u96f7<\/p>\n

    \u5728\u679a\u4e3e\u524d\u6211\u4eec\u8981memset(a1, 0, sizeof a1);\u4e0d\u7528\u6ca1\u5173\u7cfb\u53cd\u6b63\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u90fd\u662f0\u5176\u5b83\u7684\u90fd\u662f\u8d4b\u503c\u7684<\/p>\n

    \u903b\u8f91\u4e0e\u6709\u96f7\u6ca1\u533a\u522b\u8fd9\u91cc\u6211\u5c31\u4e0d\u8bb2\u4e86 \u5c31\u662f\u628aa1[1] = 0 \u800c\u4e0d\u662f a1[1] = 1;<\/p>\n

    \/\/ \u6211\u4eec\u8bbe\u7f6ea1[1]\u6ca1\u6709\u96f7<\/span>
    \n\/\/\u5148\u6e05\u7a7as1\u6570\u636e\u4e3a0<\/span>
    \nmemset<\/span>(<\/span>a1,<\/span>0<\/span>,<\/span>sizeof<\/span> a1)<\/span>;<\/span> \/\/memset\u548cmemcpy\u7684\u5934\u6587\u4ef6\u662fcstring\u4e0d\u662fstring <\/span>
    \na1[<\/span>1<\/span>]<\/span> =<\/span> 0<\/span> ;<\/span>
    \nflag =<\/span> 1<\/span>;<\/span>\/\/\u9ed8\u8ba4\u65b9\u6848\u6210\u529f <\/span>
    \nfor<\/span>(<\/span>int<\/span> i =<\/span> 2<\/span>;<\/span> i <=<\/span> n;<\/span> i++<\/span>)<\/span>
    \n{<\/span>
    \na1[<\/span>i]<\/span> =<\/span> a2[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 1<\/span>]<\/span> –<\/span> a1[<\/span>i –<\/span> 2<\/span>]<\/span>;<\/span>
    \n if<\/span>(<\/span>a1[<\/span>i]<\/span> <<\/span>0<\/span> ||<\/span> a1[<\/span>i]<\/span> ><\/span> 1<\/span>)<\/span> \/\/a1[i]\u4e0d\u4e3a0\u62161\u8bf4\u660e\u6b64\u65b9\u6848\u5931\u8d25 <\/span>
    \n {<\/span>
    \n flag =<\/span> 0<\/span>;<\/span>
    \n break<\/span>;<\/span>
    \n}<\/span>
    \n}<\/span>
    \nif<\/span>(<\/span>a2[<\/span>n]<\/span> !=<\/span> a1[<\/span>n –<\/span> 1<\/span>]<\/span> +<\/span> a1[<\/span>n]<\/span> +<\/span> a1[<\/span>n +<\/span> 1<\/span>]<\/span>)<\/span> flag =<\/span> 0<\/span>;<\/span>
    \nif<\/span>(<\/span>flag ==<\/span> 1<\/span>)<\/span> ret++<\/span>;<\/span><\/p>\n

    \u6700\u540e\u6253\u5370ret\u5373\u53ef cout << ret;<\/p>\n

    \n

    \u4e8c\u8fdb\u5236\u679a\u4e3e<\/p>\n

    2.\u5b50\u96c6<\/h2>\n

    \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u8fd9\u91cc\u5229\u7528\u7684\u662f\u4e8c\u8fdb\u5236\u679a\u4e3e\u7684\u65b9\u5f0f\u5c06\u8be5\u6574\u5f62\u6570\u7ec4\u7684\u5b50\u96c6\u679a\u4e3e\u51fa\u6765<\/p>\n

    \u6211\u4eec\u9996\u5148\u5f97\u5230\u8be5\u6574\u5f62\u6570\u7ec4\u7684\u4e2a\u6570n\u5c06 1 << n （2^n）\u5229\u7528\u8fd9\u4e2a\u6211\u4eec\u53ef\u4ee5\u904d\u5386\u51fa\u6240\u6709\u5b50\u96c6\u7684\u60c5\u51b5\u6bd4\u5982\u8bf432\u4f4d\u20261011\u6211\u4eec\u5c31\u679a\u4e3e\u51fa\u6574\u5f62\u6570\u7ec4\u4e0b\u6807\u4e3a0，1，3\u6240\u6307\u5411\u7684\u6570\u636e\u4f5c\u4e3a\u4e00\u4e2a\u5b50\u96c6\u6211\u4eec\u4ece0\u5f00\u59cb\u5230 2 ^ n – 1 00000001 00000010 \u2026\u53ef\u4ee5\u679a\u4e3e\u51fa\u6240\u6709\u6574\u5f62\u6570\u7ec4\u7684\u5b50\u96c6\u6700\u540e\u6253\u5370\u51fa\u8fd9\u4e2a\u6570\u7ec4\u5b57\u7b26\u4e32\u5373\u53ef<\/p>\n

    \/\/\u4e00\u4e2a\u6570\u7ec4\u96c6\u5408\u627e\u5b50\u96c6\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u4e8c\u8fdb\u5236\u679a\u4e3e\u89e3\u9898(\u5c31\u662f\u5229\u7528\u7ed9\u51fa\u6570\u7ec4\u7684\u4e2a\u6570\u5229\u7528\u4e8c\u8fdb\u5236\u679a\u4e3e\u89e3\u9898)<\/span>
    \n\/\/ \u7528\u5230\u8be5\u4f4d\u662f\u5426\u4e3a1 x >> i & 1\u548c 1 << n\u4e2d\u4ece0\u5230 2^n – 1\u7684\u6570<\/span>
    \n\/\/\u6211\u4eec\u5229\u752832\u4e3a\u7b2c0\u4e3a\u4e3a1\u5c31\u67091\u7b2c1\u4e3a\u4e3a1\u5c31\u4e3a2….\u7c7b\u63a8\u5206\u51fa\u5b50\u96c6\u7ec4\u5408<\/span>
    \n\/\/\u6211\u4eec\u627e\u5230\u5b50\u96c6\u5143\u7d20\u4e2d\u6700\u5927\u7684\u6570\u636e\u572832\u4f4d\u7684\u7b2c\u51e0\u4f4d(\u5f53\u8be5\u4f4d\u5df2\u53ca\u4e4b\u524d\u7684\u4f4e\u4f4d\u90fd\u4e3a1\u65f6\u8bf4\u660e\u679a\u4e3e\u7ed3\u675f)<\/span><\/p>\n

    class Solution {<\/span>
    \npublic:<\/span>
    \n vector<<\/span>vector<<\/span>int<\/span>>><\/span> subsets<\/span>(<\/span>vector<<\/span>int<\/span>><\/span>&<\/span> nums)<\/span> {<\/span>
    \n \/\/\u5b9a\u4e49\u4e00\u4e2a\u6570\u7ec4\u5143\u7d20\u6570\u6574\u5f62\u6570\u7ec4（\u88c5\u5b50\u96c6\u7684\u5bb9\u5668）<\/span>
    \n vector<<\/span>vector<<\/span>int<\/span>>><\/span> a;<\/span>
    \n int<\/span> n =<\/span> nums.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
    \n \/\/\u5217\u51fa\u5b50\u96c6<\/span>
    \n \/\/\u6211\u4eec\u5229\u7528for\u5faa\u73af\u4e0b\u6807\u5c0f\u4e8e1 << n\u7684\u6570\u636e\u4e8c\u8fdb\u5236\u5c31\u53ef\u4ee5\u904d\u5386\u4ece0\u5230\u8be5\u6570\u636e\u4f4d\u6570 – 1 \u7684\u6240\u6709\u4f4d\u6570\u4e0a\u7684\u6570\u636e<\/span>
    \n \/\/\u6211\u4eec\u5bf9\u8fd9\u4e9b\u6570\u636e\u90fd\u8fdb\u884cfor\u5faa\u73af\u4e0b\u6807\u5c0f\u4e8en（\u79fb\u52a8\u4f4d\u4e0d\u8d85\u8fc7n）\u5982\u679c\u67d0\u4f4d\u4e3a1\u90a3\u4e48\u8be5\u4e0b\u6807\u4e0a\u7684\u6570\u636e\u4f1a\u5165\u6574\u5f62\u6570\u7ec4<\/span>
    \n for<\/span>(<\/span>int<\/span> st =<\/span> 0<\/span>;<\/span> st <<\/span> (<\/span>1<\/span> <<<\/span> n)<\/span>;<\/span> st++<\/span>)<\/span>\/\/st\u4f5c\u4e3a\u6570\u636e(\u8fdb\u884cfor\u5faa\u73af\u4e0d\u662f\u4f5c\u4e3a\u4e0b\u6807)\u88ab\u7b2c\u4e8c\u4e2a\u5faa\u73af\u904d\u5386\u7ec4\u5408\u6210\u5b50\u96c6（\u4e0e\u6570\u7ec4\u7684\u7c7b\u578b\u65e0\u5173）(1 << n \u5c31\u662f 2^n – 1)<\/span>
    \n {<\/span>
    \n \/\/\u5b9a\u4e49\u4e00\u4e2a\u6574\u578b\u6570\u7ec4\u6765\u88c5\u5b50\u96c6\u6700\u540e\u5c06\u5b50\u96c6\u653e\u5165a\u5373\u53ef<\/span>
    \n vector<<\/span>int<\/span>><\/span> b;<\/span>\/\/\u4f5c\u4e3a\u5b50\u96c6\u88c5\u7ec4\u5408\u6570<\/span>
    \n for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span>
    \n {<\/span>
    \n \/\/\u5224\u65adst\u6570\u636e\u5728\u67d0\u4f4d\u4e0a\u4e3a1（\u5982\u679c\u4e3a1\u8bf4\u660e\u8be5\u4f4d（\u4e0b\u6807）\u53ef\u4ee5\u8fdb\u5165\u5b50\u96c6\u4f5c\u4e3a\u7ec4\u5408）<\/span>
    \n if<\/span>(<\/span>st >><\/span> i &<\/span> 1<\/span>)<\/span> b.<\/span>push_back<\/span>(<\/span> nums[<\/span>i]<\/span>)<\/span>;<\/span>\/\/\u6700\u5f00\u59cbst\u4e3a0\u65e0\u8bba\u5982\u4f55\u90fd\u5165\u4e0d\u4e86b\u6240\u4ee5\u4e00\u5b9a\u4f1a\u6709\u4e00\u4e2a\u7a7a\u7684b\u5b50\u96c6\u653e\u5165a\u4e2d \u8fd9\u91cc\u662f >> i\u4e0d\u662f << i(\u8fd9\u4e48\u79fb\u7684\u8bdd\u7b2c\u4e00\u4e2a\u90fd\u4e3a0) \u800c\u4e14\u8fd9\u91cc\u662f st >> i & 1 \u76ee\u7684\u770b\u6211\u4eec\u8981\u6c42\u7684\u4f4d\u662f\u5426\u4e3a1st >> i == 1\u8fd9\u6837\u4e0d\u884c\u5b83\u7684\u610f\u601d\u662f\u79fb\u52a8\u540e\u7684\u6570\u636e\u662f\u5426\u4e3a1<\/span>
    \n }<\/span>
    \n \/\/\u6700\u540e\u5c06b\u5b50\u96c6\u653e\u5165a\u4e2d<\/span>
    \n a.<\/span>push_back<\/span>(<\/span>b)<\/span>;<\/span>\/\/\u5982\u679cnums<\/span>
    \n }<\/span><\/p>\n

    return<\/span> a;<\/span>
    \n }<\/span>
    \n}<\/span>;<\/span><\/p>\n

    \u8be5\u9898\u662f\u6838\u5fc3\u4ee3\u7801\u6a21\u5f0f \u9898\u76ee\u5b83\u7ed9\u4e86\u4e00\u4e2avector nums\u6574\u5f62\u6570\u7ec4\u8fd4\u56de\u53ea\u662f\u4e00\u4e2a\u5143\u7d20\u4e3a\u5b57\u7b26\u4e32\u7684\u7684\u6570\u7ec4<\/p>\n

    \u9996\u5148\u6211\u4eec\u5b9a\u4e00\u4e2avector<vector> a\u4f5c\u4e3a\u88c5\u5b50\u96c6\u7684\u5bb9\u5668 \u7136\u540e\u6211\u4eec\u5c06\u8be5\u6574\u5f62\u6570\u7ec4\u7684\u4e2a\u6570\u6570\u51fa\u6765\u5b9a\u4e49\u4e3an 0\u52301 << n -1\u5c31\u662f\u6211\u6211\u4eec\u8981\u679a\u4e3e\u679a\u4e3e\u7684\u6240\u6709\u65b9\u5f0f \u6bcf\u4e2a\u503c\u6240\u5bf9\u5e94\u7684\u4e8c\u8fdb\u5236\u503c 000110011\u4ece\u5de6\u5230\u53f3\u4e0b\u6807\u4ece0\u5f00\u59cb\u4e0b\u6807\u4e3a1\u6240\u5bf9\u5e94\u7684\u6574\u578b\u6570\u7ec4\u4e0b\u6807\u4e0a\u7684\u6570\u5b57\u5c31\u4f5c\u4e3a\u4e00\u4e2a\u6570\u636e\u52a0\u5165\u5b50\u96c6<\/p>\n

    vector<<\/span>vector<<\/span>int<\/span>>><\/span> a;<\/span>
    \n int<\/span> n =<\/span> nums.<\/span>size<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

    \u5229\u7528\u5185\u5916\u53cc\u5faa\u73af\u5916\u5faa\u73af\u6211\u4eec\u7528st\u904d\u5386\u8fd9\u4e9b\u6570\u636e\u76f4\u5230 1 << n – 1 \u5185\u5faa\u73af\u6211\u4eec\u5229\u7528\u4e0b\u6807\u4ece0\u5230n \u6211\u4eec\u7528 st >> i(\u5c06st\u8f6c\u6362\u4e3a\u4e8c\u8fdb\u5236\u5728\u5f80\u5de6\u79fb\u52a8i\u4f4d)\u7136\u540e\u5c06\u7ed3\u679c\u6309\u4f4d\u4e0e1<\/p>\n

    \u6211\u4eec\u5b9a\u4e49\u4e00\u4e2avectorb\u6570\u7ec4（\u5b50\u96c6）\u88c5\u53ef\u4ee5\u4f5c\u4e3a\u5b50\u96c6\u7684\u5143\u7d20<\/p>\n

    \u6309\u4f4d\u4e0e\u7684\u610f\u601d\u662f\u4e24\u6570\u636e\u5bf9\u5e94\u4f4d\u7684\u4e8c\u8fdb\u5236\u503c\u90fd\u4e3a1\u624d\u4e3a1\u5426\u5219\u5c31\u4e3a0 \u6309\u4f4d\u4e0e1 1\u7684\u4e8c\u8fdb\u5236\u4f4d\u4e3a 0000000001\u6240\u4ee5\u6211\u4eec st >> i\u5411\u5de6\u79fb\u52a8i\u4f4d\u5176\u5b9e\u9664\u4e86\u7b2c0\u4e3a\u5176\u5b83\u7684\u4f4d\u6570\u7ed3\u679c\u4e00\u5b9a\u90fd\u4e3a0\u56e0\u4e3a 1\u7684\u4e8c\u8fdb\u5236\u9664\u4e86\u7b2c0\u4e3a\u5176\u5b83\u90fd\u4e3a0 0\u4e0e0 \u4e0e1\u6309\u4f4d\u4e0e\u90fd\u4e3a0 \u82e5\u662fst\u79fb\u4f4d\u540e\u4f4d\u6570\u4e3a0\u7684\u6570\u636e\u4e0d\u4e3a1\u7ed3\u679c\u5c31\u4e0d\u4e3a0\u4e3a1\u6211\u4eec\u5c31\u53ef\u4ee5\u5224\u65ad\u6574\u5f62\u6570\u7ec4\u5728\u8be5\u4f4d\u4f5c\u4e3a\u679a\u4e3e\u7684\u503c（\u4f5c\u4e3a\u5b50\u96c6\u5143\u7d20）\u6211\u4eec\u5c31\u5c06b\u8c03\u7528push_back(nums[i])\u5373\u53ef<\/p>\n

    \u6bcf\u6b21st\u8fdb\u884c\u4e00\u6b21\u5faa\u73af\u6211\u4eec\u5c06\u5b50\u96c6b\u653e\u5165\u7528push_back a\u6570\u7ec4\u4e2d<\/p>\n

    \u521a\u5f00\u59cbst\u4e3a0\u6240\u4ee5b\u5faa\u73af\u7ed3\u675f\u4e3a\u7a7a\u5c06\u7a7a\u5b50\u96c6b\u653e\u5165a\u4e2d\u7136st\u6bcf\u6b21\u52a01\u5b83\u7684\u4e8c\u8fdb\u5236\u968f\u4e4b\u6539\u53d8\u5b50\u96c6\u7684\u5143\u7d20\u6bcf\u6b21\u5f53\u7136\u4e5f\u4e0d\u540c\u77e5\u9053\u6700\u540e st\u4e3a 2^n – 1\u7684\u65f6\u501932\u4f4d\u4ece0\u5230n – 1\u4f4d\u90fd\u4e3a1\u6211\u4eec\u5c06\u6574\u5f62\u6570\u7ec4\u7684\u6240\u6709\u5143\u7d20\u4f5c\u4e3a\u5b50\u96c6b\u653e\u5165a\u4e2d\u6211\u4eec\u628a\u6240\u6709\u7684\u5b50\u96c6\u679a\u4e3e\u5b8c\u6210\u8fd4\u56dea\u5373\u53ef（\u7531\u4e8eb\u5728\u5185\u5faa\u73af\u548c\u5916\u5faa\u73af\u4e4b\u95f4\u6240\u4ee5\u6211\u4eec\u4e0d\u7528\u91cd\u7f6eb\u56e0\u4e3a\u6bcf\u6b21st\u679a\u4e3e\u5b50\u96c6\u7684\u65f6\u5019b\u5b9e\u4f8b\u5316\u90fd\u4e3a\u7a7a）<\/p>\n

    \/\/\u5217\u51fa\u5b50\u96c6<\/span>
    \n \/\/\u6211\u4eec\u5229\u7528for\u5faa\u73af\u4e0b\u6807\u5c0f\u4e8e1 << n\u7684\u6570\u636e\u4e8c\u8fdb\u5236\u5c31\u53ef\u4ee5\u904d\u5386\u4ece0\u5230\u8be5\u6570\u636e\u4f4d\u6570 – 1 \u7684\u6240\u6709\u4f4d\u6570\u4e0a\u7684\u6570\u636e<\/span>
    \n \/\/\u6211\u4eec\u5bf9\u8fd9\u4e9b\u6570\u636e\u90fd\u8fdb\u884cfor\u5faa\u73af\u4e0b\u6807\u5c0f\u4e8en（\u79fb\u52a8\u4f4d\u4e0d\u8d85\u8fc7n）\u5982\u679c\u67d0\u4f4d\u4e3a1\u90a3\u4e48\u8be5\u4e0b\u6807\u4e0a\u7684\u6570\u636e\u4f1a\u5165\u6574\u5f62\u6570\u7ec4<\/span>
    \n for<\/span>(<\/span>int<\/span> st =<\/span> 0<\/span>;<\/span> st <<\/span> (<\/span>1<\/span> <<<\/span> n)<\/span>;<\/span> st++<\/span>)<\/span>\/\/st\u4f5c\u4e3a\u6570\u636e(\u8fdb\u884cfor\u5faa\u73af\u4e0d\u662f\u4f5c\u4e3a\u4e0b\u6807)\u88ab\u7b2c\u4e8c\u4e2a\u5faa\u73af\u904d\u5386\u7ec4\u5408\u6210\u5b50\u96c6（\u4e0e\u6570\u7ec4\u7684\u7c7b\u578b\u65e0\u5173）(1 << n \u5c31\u662f 2^n – 1)<\/span>
    \n {<\/span>
    \n \/\/\u5b9a\u4e49\u4e00\u4e2a\u6574\u578b\u6570\u7ec4\u6765\u88c5\u5b50\u96c6\u6700\u540e\u5c06\u5b50\u96c6\u653e\u5165a\u5373\u53ef<\/span>
    \n vector<<\/span>int<\/span>><\/span> b;<\/span>\/\/\u4f5c\u4e3a\u5b50\u96c6\u88c5\u7ec4\u5408\u6570<\/span>
    \n for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span>
    \n {<\/span>
    \n \/\/\u5224\u65adst\u6570\u636e\u5728\u67d0\u4f4d\u4e0a\u4e3a1（\u5982\u679c\u4e3a1\u8bf4\u660e\u8be5\u4f4d（\u4e0b\u6807）\u53ef\u4ee5\u8fdb\u5165\u5b50\u96c6\u4f5c\u4e3a\u7ec4\u5408）<\/span>
    \n if<\/span>(<\/span>st >><\/span> i &<\/span> 1<\/span>)<\/span> b.<\/span>push_back<\/span>(<\/span> nums[<\/span>i]<\/span>)<\/span>;<\/span>\/\/\u6700\u5f00\u59cbst\u4e3a0\u65e0\u8bba\u5982\u4f55\u90fd\u5165\u4e0d\u4e86b\u6240\u4ee5\u4e00\u5b9a\u4f1a\u6709\u4e00\u4e2a\u7a7a\u7684b\u5b50\u96c6\u653e\u5165a\u4e2d \u8fd9\u91cc\u662f >> i\u4e0d\u662f << i(\u8fd9\u4e48\u79fb\u7684\u8bdd\u7b2c\u4e00\u4e2a\u90fd\u4e3a0) \u800c\u4e14\u8fd9\u91cc\u662f st >> i & 1 \u76ee\u7684\u770b\u6211\u4eec\u8981\u6c42\u7684\u4f4d\u662f\u5426\u4e3a1st >> i == 1\u8fd9\u6837\u4e0d\u884c\u5b83\u7684\u610f\u601d\u662f\u79fb\u52a8\u540e\u7684\u6570\u636e\u662f\u5426\u4e3a1<\/span>
    \n }<\/span>
    \n \/\/\u6700\u540e\u5c06b\u5b50\u96c6\u653e\u5165a\u4e2d<\/span>
    \n a.<\/span>push_back<\/span>(<\/span>b)<\/span>;<\/span>\/\/\u5982\u679cnums<\/span>
    \n }<\/span><\/p>\n

    return a;<\/p>\n

    \n

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    \n

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