{"id":120415,"date":"2026-10-31T16:48:50","date_gmt":"2026-10-31T08:48:50","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/120415.html"},"modified":"2026-10-31T16:48:50","modified_gmt":"2026-10-31T08:48:50","slug":"2026-10-31%ef%bc%9a%e6%95%b0%e5%af%b9%e7%9a%84%e6%9c%80%e5%a4%a7%e5%bc%ba%e5%ba%a6%e3%80%82%e7%94%a8go%e8%af%ad%e8%a8%80%ef%bc%8c%e7%bb%99%e5%ae%9a%e4%b8%80%e4%b8%aa%e6%95%b4%e6%95%b0%e6%95%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/120415.html","title":{"rendered":"2026-10-31\uff1a\u6570\u5bf9\u7684\u6700\u5927\u5f3a\u5ea6\u3002\u7528go\u8bed\u8a00\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums\u3002\u9700\u8981\u4ece\u6570\u7ec4\u4e2d\u9009\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u4e0d\u540c\u7684\u5143\u7d20\uff0c\u7ec4\u6210\u4e00\u4e2a\u6570\u5bf9\u3002\u8be5\u6570\u5bf9\u7684\u5f3a\u5ea6\u7b49\u4e8e\uff1a\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u4e58\u79ef\uff0c\u9664\u4ee5\u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u7684\u5e73\u65b9\u3002\u8bf7\u8ba1\u7b97\u5e76"},"content":{"rendered":"

2026-10-31：\u6570\u5bf9\u7684\u6700\u5927\u5f3a\u5ea6\u3002\u7528go\u8bed\u8a00，\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums\u3002\u9700\u8981\u4ece\u6570\u7ec4\u4e2d\u9009\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u4e0d\u540c\u7684\u5143\u7d20，\u7ec4\u6210\u4e00\u4e2a\u6570\u5bf9\u3002\u8be5\u6570\u5bf9\u7684\u5f3a\u5ea6\u7b49\u4e8e：\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u4e58\u79ef，\u9664\u4ee5\u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u7684\u5e73\u65b9\u3002\u8bf7\u8ba1\u7b97\u5e76\u8fd4\u56de\u6240\u6709\u53ef\u80fd\u6570\u5bf9\u4e2d\u80fd\u591f\u5f97\u5230\u7684\u6700\u5927\u5f3a\u5ea6\u503c\u3002<\/p>\n

2 <= nums.length <= 2000\u3002<\/p>\n

1 <= nums[i] <= 100000\u3002<\/p>\n

\u8f93\u5165： nums = [2,3,5]\u3002<\/p>\n

\u8f93\u51fa： 15\u3002<\/p>\n

\u89e3\u91ca：<\/p>\n

\u9009\u62e9 i = 1 \u548c j = 2，\u5f97\u5230\u5f3a\u5ea6：<\/p>\n

(3 * 5) \/ gcd(3, 5)2 = 15 \/ 1 = 15，\u8fd9\u662f\u6240\u6709\u6570\u5bf9\u4e2d\u7684\u6700\u5927\u503c\u3002<\/p>\n

\u9898\u76ee\u6765\u81ea\u529b\u62634010\u3002<\/p>\n

\u5927\u4f53\u6b65\u9aa4\u5982\u4e0b：<\/h2>\n

\u4e00\u3001\u5148\u770b\u6e05"\u5f3a\u5ea6"\u8fd9\u4e2a\u5f0f\u5b50\u7684\u6570\u5b66\u672c\u8d28<\/h3>\n

\u6570\u5bf9 (x, y) \u7684\u5f3a\u5ea6\u5b9a\u4e49\u4e3a：<\/p>\n

strength=x\u22c5ygcd\u2061(x,y)2\\\\text{strength} = \\\\frac{x \\\\cdot y}{\\\\gcd(x,y)^2}<\/span><\/span>strength<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8bbe g=gcd\u2061(x,y)g = \\\\gcd(x, y)<\/span><\/span>g<\/span><\/span>=<\/span><\/span><\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u90a3\u4e48\u53ef\u4ee5\u5199\u6210 x=g\u22c5a,\u00a0y=g\u22c5bx = g \\\\cdot a,\\\\ y = g \\\\cdot b<\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>g<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span>,<\/span>\u00a0<\/span><\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>g<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>，\u4e14 gcd\u2061(a,b)=1\\\\gcd(a,b) = 1<\/span><\/span>g<\/span>cd<\/span>(<\/span>a<\/span>,<\/span><\/span>b<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3002\u4ee3\u5165\u540e：<\/p>\n

ga\u22c5gbg2=a\u22c5b=xg\u22c5yg\\\\frac{g a \\\\cdot g b}{g^2} = a \\\\cdot b = \\\\frac{x}{g} \\\\cdot \\\\frac{y}{g}<\/span><\/span><\/span><\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>a<\/span><\/span>\u22c5<\/span><\/span>g<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>b<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>g<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span><\/span>g<\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7ed3\u8bba：\u5f3a\u5ea6 = \u4e24\u4e2a\u6570\u5404\u81ea"\u7ea6\u6389\u516c\u56e0\u5b50\u4e4b\u540e"\u7684\u4e58\u79ef\u3002 \u6240\u4ee5\u8981\u8ba9\u5b83\u5927，\u9700\u8981\u4e24\u4e2a\u6761\u4ef6\u540c\u65f6\u6ee1\u8db3：<\/p>\n

  • \u4e24\u4e2a\u6570\u672c\u8eab\u5c3d\u91cf\u5927（\u4e58\u79ef\u7684\u5206\u5b50\u5927）；<\/li>\n
  • \u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u5c3d\u91cf\u5c0f（\u9664\u4ee5\u7684 g2g^2<\/span><\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c0f）\u3002<\/li>\n

    \u987a\u5e26\u4e00\u4e2a\u526f\u4ea7\u54c1：x\u22c5yx \\\\cdot y<\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u4e00\u5b9a\u80fd\u88ab gcd\u2061(x,y)2\\\\gcd(x,y)^2<\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6574\u9664，\u6240\u4ee5\u4ee3\u7801\u91cc\u505a\u6574\u6570\u9664\u6cd5 xyg2\\\\frac{x y}{g^2}<\/span><\/span><\/span><\/span>g<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0d\u4f1a\u6709\u4efb\u4f55\u53d6\u6574\u8bef\u5dee，\u7ed3\u679c\u662f\u7cbe\u786e\u7684\u3002\u8fd9\u4e00\u70b9\u540e\u9762\u5224\u65ad\u526a\u679d\u5b89\u5168\u6027\u65f6\u4f1a\u7528\u5230\u3002<\/p>\n

    \u9898\u76ee\u6570\u636e\u8303\u56f4 n\u22642000n \\\\le 2000<\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>2000<\/span><\/span><\/span><\/span><\/span>，\u4e24\u4e24\u6570\u5bf9\u4e00\u5171\u7ea6 n(n\u22121)2\u22482\u00d7106\\\\frac{n(n-1)}{2} \\\\approx 2 \\\\times 10^6<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span>(<\/span>n<\/span>\u2212<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5bf9，\u6240\u4ee5"\u5168\u90e8\u679a\u4e3e"\u672c\u8eab\u662f\u53ef\u884c\u7684baseline；\u8fd9\u4efd\u4ee3\u7801\u7684\u4ef7\u503c\u5728\u4e8e\u7528\u4e00\u4e2a\u4e0a\u754c\u526a\u679d\u628a\u7edd\u5927\u591a\u6570\u60c5\u51b5\u538b\u5230\u8fdc\u4f4e\u4e8e\u8fd9\u4e2a\u6570\u3002<\/p>\n

    \n

    \u4e8c\u3001\u6574\u4f53\u7b56\u7565：\u6392\u5e8f + \u6784\u9020\u4e00\u4e2a"\u53ea\u4f9d\u8d56\u4e58\u79ef"\u7684\u4e0a\u754c<\/h3>\n

    \u66b4\u529b\u679a\u4e3e\u7684\u95ee\u9898\u662f\u6bcf\u4e00\u5bf9\u90fd\u8981\u7b97\u4e00\u6b21 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span>\u3002\u4ee3\u7801\u7684\u601d\u8def\u662f：<\/p>\n

    \u80fd\u4e0d\u80fd\u5728\u4e0d\u7b97 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span> \u7684\u524d\u63d0\u4e0b，\u5148\u5224\u65ad"\u8fd9\u4e00\u5bf9\u7edd\u5bf9\u4e0d\u53ef\u80fd\u5237\u65b0\u6700\u4f18\u89e3"？\u5982\u679c\u80fd，\u5c31\u76f4\u63a5\u8df3\u8fc7\u4e0d\u505a gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    \u8981\u505a\u5230\u8fd9\u4ef6\u4e8b，\u9700\u8981\u4e24\u6837\u4e1c\u897f：<\/p>\n

      \n
    • \u4e00\u4e2a\u4fbf\u5b9c\u7684\u4e0a\u754c：\u53ea\u9760 x\u22c5yx \\\\cdot y<\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u5c31\u80fd\u7b97\u51fa"\u8fd9\u5bf9\u7684\u5f3a\u5ea6\u6700\u591a\u662f\u591a\u5c11"；<\/li>\n
    • \u4e00\u4e2a\u5355\u8c03\u7684\u679a\u4e3e\u987a\u5e8f：\u4fdd\u8bc1\u4e00\u65e6\u4e0a\u754c\u8dcc\u7834\u5f53\u524d\u6700\u4f18，\u540e\u9762\u6240\u6709\u5019\u9009\u53ea\u4f1a\u66f4\u5dee，\u53ef\u4ee5\u76f4\u63a5 break，\u800c\u4e0d\u662f\u7ee7\u7eed\u904d\u5386\u3002<\/li>\n<\/ul>\n

      \u6392\u5e8f\u8d1f\u8d23\u7b2c\u4e8c\u4ef6\u4e8b，\u5168\u5c40 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span> \u8d1f\u8d23\u7b2c\u4e00\u4ef6\u4e8b\u3002<\/p>\n

      \n

      \u4e09\u3001\u6b65\u9aa4 1：\u964d\u5e8f\u6392\u5e8f（\u4e3a\u5355\u8c03\u6027\u94fa\u8def）<\/h3>\n

      \u4ee3\u7801\u7528 slices.SortFunc \u914d\u5408\u6bd4\u8f83\u51fd\u6570 b – a，\u628a nums \u6392\u6210\u4ece\u5927\u5230\u5c0f\u3002<\/p>\n

      \u6392\u5e8f\u4e0d\u662f\u4e3a\u4e86"\u627e\u6700\u5927\u7684\u4e24\u4e2a\u6570"\u8fd9\u4e48\u7b80\u5355（\u6700\u5927\u7684\u4e24\u4e2a\u6570\u4e0d\u4e00\u5b9a\u662f\u6700\u4f18\u89e3，\u4f8b\u5982 [15, 10, 6] \u4e2d 15\u00d710 \u7684\u5f3a\u5ea6\u53ea\u6709 6，\u800c 10\u00d76 \u7684\u5f3a\u5ea6\u662f 15）\u3002\u6392\u5e8f\u7684\u771f\u6b63\u76ee\u7684\u662f\u8ba9\u540e\u9762\u53cc\u91cd\u5faa\u73af\u7684\u679a\u4e3e\u987a\u5e8f\u5177\u5907\u5355\u8c03\u6027：<\/p>\n

        \n
      • \u5916\u5c42 i \u9012\u589e\u65f6，x=nums[i]x = nums[i]<\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span>u<\/span>m<\/span>s<\/span>[<\/span>i<\/span>]<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u9012\u51cf；<\/li>\n
      • \u5185\u5c42\u904d\u5386 nums[:i]，\u5373\u4e0b\u6807 0,1,\u2026,i\u221210, 1, \\\\dots, i-1<\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>i<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u56e0\u4e3a\u6570\u7ec4\u5df2\u964d\u5e8f，yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u4e5f\u662f\u9012\u51cf\u7684，\u800c\u4e14\u6052\u6709 y\u2265xy \\\\ge x<\/span><\/span>y<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n

        \u4e8e\u662f\u5bf9\u56fa\u5b9a\u7684 xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u5185\u5c42\u5faa\u73af\u4e2d\u4e58\u79ef x\u22c5yx \\\\cdot y<\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u968f\u7740 yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u4ece nums[0] \u8d70\u5230 nums[i-1] \u662f\u4e25\u683c\u5355\u8c03\u4e0d\u589e\u7684\u3002\u8fd9\u4e2a\u6027\u8d28\u662f break \u80fd\u591f\u6210\u7acb\u7684\u524d\u63d0\u3002<\/p>\n

        \u8865\u5145\u4e00\u53e5\u526f\u4f5c\u7528：\u8fd9\u662f\u539f\u5730\u6392\u5e8f，\u4f1a\u76f4\u63a5\u6253\u4e71\u8c03\u7528\u65b9\u4f20\u5165\u7684 slice \u987a\u5e8f；\u5982\u679c\u8c03\u7528\u65b9\u8fd8\u4f9d\u8d56\u539f\u987a\u5e8f，\u9700\u8981\u5148\u62f7\u8d1d\u4e00\u4efd\u3002<\/p>\n

        \n

        \u56db\u3001\u6b65\u9aa4 2：\u6c42"\u5168\u5c40 gcd"，\u6784\u9020\u5408\u6cd5\u4e0a\u754c<\/h3>\n

        \u4ee3\u7801\u63a5\u7740\u4ece\u5934\u5230\u5c3e\u628a\u6240\u6709\u5143\u7d20\u5377\u8fdb\u4e00\u4e2a gcd，\u5f97\u5230 allGcd，\u5373\u6574\u4e2a\u6570\u7ec4\u6240\u6709\u5143\u7d20\u7684\u516c\u5171\u6700\u5927\u516c\u7ea6\u6570，\u518d\u5e73\u65b9\u5f97\u5230 allGcd2\u3002<\/p>\n

        \u521d\u59cb\u503c\u662f 0，\u800c gcd\u2061(0,x)=x\\\\gcd(0, x) = x<\/span><\/span>g<\/span>cd<\/span>(<\/span>0<\/span>,<\/span><\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>（gcd \u51fd\u6570\u91cc a = 0 \u65f6\u5faa\u73af\u4e00\u6b21\u90fd\u4e0d\u8fdb，\u76f4\u63a5\u8fd4\u56de b），\u6240\u4ee5\u7b2c\u4e00\u6b21\u6eda\u52a8\u7b49\u4ef7\u4e8e"\u628a allGcd \u521d\u59cb\u5316\u6210\u7b2c\u4e00\u4e2a\u5143\u7d20"，\u8fd9\u662f\u6807\u51c6\u7684\u5199\u6cd5\u3002\u7531\u4e8e gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3\u4ea4\u6362\u5f8b\u548c\u7ed3\u5408\u5f8b，\u904d\u5386\u987a\u5e8f\u4e0d\u5f71\u54cd\u7ed3\u679c\u3002<\/p>\n

        \u5173\u952e\u7684\u4e0d\u7b49\u5f0f\u63a8\u5bfc：<\/p>\n

      • allGcd \u6574\u9664\u6570\u7ec4\u91cc\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20，\u6240\u4ee5\u5b83\u4e5f\u6574\u9664 xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u4e5f\u6574\u9664 yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>；<\/li>\n
      • \u65e2\u7136 allGcd \u540c\u65f6\u6574\u9664 xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u548c yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>，\u90a3\u5b83\u5fc5\u7136\u6574\u9664 gcd\u2061(x,y)\\\\gcd(x, y)<\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span><\/span><\/span><\/span>；<\/li>\n
      • \u56e0\u6b64 gcd\u2061(x,y)\u2265allGcd\\\\gcd(x,y) \\\\ge \\\\text{allGcd}<\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>allGcd<\/span><\/span><\/span><\/span><\/span><\/span>，\u8fdb\u800c gcd\u2061(x,y)2\u2265allGcd2\\\\gcd(x,y)^2 \\\\ge \\\\text{allGcd}^2<\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2265<\/span><\/span><\/span><\/span>allGcd<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>；<\/li>\n
      • \u5206\u5b50\u76f8\u540c\u3001\u5206\u6bcd\u66f4\u5927 \u21d2\\\\Rightarrow<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span><\/span> \u5546\u66f4\u5c0f，\u4e8e\u662f：<\/li>\n

        x\u22c5ygcd\u2061(x,y)2\u2264x\u22c5yallGcd2\\\\frac{x \\\\cdot y}{\\\\gcd(x,y)^2} \\\\le \\\\frac{x \\\\cdot y}{\\\\text{allGcd}^2}<\/span><\/span><\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span>allGcd<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u53f3\u8fb9\u5c31\u662f\u90a3\u4e2a"\u4fbf\u5b9c\u7684\u4e0a\u754c"\u2014\u2014\u5b83\u5b8c\u5168\u4e0d\u9700\u8981\u77e5\u9053\u8fd9\u4e00\u5bf9\u5177\u4f53\u7684 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span>，\u53ea\u8981\u4e00\u6b21\u4e58\u6cd5\u4e00\u6b21\u9664\u6cd5\u5c31\u80fd\u7b97\u51fa\u6765\u3002\u800c\u4e14\u5b83\u662f"\u4efb\u610f\u6570\u5bf9\u901a\u7528\u7684"，\u5bf9\u6570\u7ec4\u91cc\u6240\u6709\u6570\u5bf9\u540c\u65f6\u6210\u7acb\u3002<\/p>\n

        \u8fd8\u6709\u4e2a\u7ec6\u8282\u503c\u5f97\u4e00\u63d0：x\u22c5yx \\\\cdot y<\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u672a\u5fc5\u80fd\u88ab allGcd2\\\\text{allGcd}^2<\/span><\/span>allGcd<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6574\u9664（\u56e0\u4e3a allGcd \u53ea\u662f gg<\/span><\/span>g<\/span><\/span><\/span><\/span><\/span> \u7684\u4e0b\u754c，\u4e0d\u4e00\u5b9a\u7b49\u4e8e gg<\/span><\/span>g<\/span><\/span><\/span><\/span><\/span>），\u6240\u4ee5 mul \/ allGcd2 \u662f\u5411\u4e0b\u53d6\u6574\u7684\u6574\u6570\u9664\u6cd5\u3002\u5411\u4e0b\u53d6\u6574\u53ea\u4f1a\u8ba9\u8fd9\u4e2a\u4e0a\u754c\u66f4\u5c0f（\u66f4\u7d27），\u800c\u4e0d\u4f1a\u8ba9\u5b83\u5931\u6548\u2014\u2014\u230aU\u230b\u2264\\\\lfloor U \\\\rfloor \\\\le<\/span><\/span>\u230a<\/span>U<\/span>\u230b<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span> \u771f\u5b9e\u5f3a\u5ea6 \u4f9d\u7136\u6210\u7acb\u5417？\u8fd9\u91cc\u8981\u5c0f\u5fc3\u65b9\u5411：\u771f\u5b9e\u5f3a\u5ea6 \u2264xyallGcd2\\\\le \\\\frac{xy}{\\\\text{allGcd}^2}<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span>allGcd<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（\u5b9e\u6570\u9664\u6cd5），\u800c\u771f\u5b9e\u5f3a\u5ea6\u662f\u6574\u6570，\u6240\u4ee5\u771f\u5b9e\u5f3a\u5ea6 \u2264\u230axyallGcd2\u230b\\\\le \\\\lfloor\\\\frac{xy}{\\\\text{allGcd}^2}\\\\rfloor<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>\u230a<\/span><\/span><\/span>allGcd<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230b<\/span><\/span><\/span><\/span><\/span>\u3002\u662f\u7684，\u56e0\u4e3a\u4e00\u4e2a\u6574\u6570\u82e5\u4e0d\u8d85\u8fc7\u5b9e\u6570 tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>，\u90a3\u5b83\u4e5f\u4e0d\u8d85\u8fc7 \u230at\u230b\\\\lfloor t \\\\rfloor<\/span><\/span>\u230a<\/span>t<\/span>\u230b<\/span><\/span><\/span><\/span><\/span>\u3002\u6240\u4ee5\u53d6\u6574\u540e\u7684\u4e0a\u754c\u4f9d\u7136\u662f\u5408\u6cd5\u4e0a\u754c，\u526a\u679d\u5b89\u5168\u3002<\/p>\n

        \n

        \u4e94\u3001\u6b65\u9aa4 3：\u53cc\u91cd\u5faa\u73af + \u4e0a\u754c\u526a\u679d<\/h3>\n

        \u5916\u5c42\u679a\u4e3e ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>（\u4ece 0 \u5230 n\u22121n-1<\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>），x=nums[i]x = nums[i]<\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span>u<\/span>m<\/span>s<\/span>[<\/span>i<\/span>]<\/span><\/span><\/span><\/span><\/span>；\u5185\u5c42\u679a\u4e3e j<ij < i<\/span><\/span>j<\/span><\/span><<\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>，y=nums[j]y = nums[j]<\/span><\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span>u<\/span>m<\/span>s<\/span>[<\/span>j<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u6837\u6bcf\u4e2a\u65e0\u5e8f\u6570\u5bf9\u6070\u597d\u88ab\u8bbf\u95ee\u4e00\u6b21，\u4e0d\u91cd\u4e0d\u6f0f\u3002<\/p>\n

        \u5185\u5c42\u6bcf\u4e00\u6b65\u505a\u4e09\u4ef6\u4e8b：<\/p>\n

      • \u5148\u7b97 mul = x * y（\u4e00\u6b21\u4e58\u6cd5，\u6781\u4fbf\u5b9c）；<\/li>\n
      • \u7b97\u4e0a\u754c mul \/ allGcd2，\u4e0e\u5f53\u524d\u6700\u4f18 ans \u6bd4\u8f83：\n
          \n
        • \u5982\u679c \u4e0a\u754c \u2264 ans：\u8bf4\u660e\u8fd9\u5bf9\u7684\u771f\u5b9e\u5f3a\u5ea6 \u2264\\\\le<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span> \u4e0a\u754c \u2264\\\\le<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span> ans，\u7edd\u5bf9\u4e0d\u53ef\u80fd\u5237\u65b0\u6700\u4f18；\u800c\u4e14\u56e0\u4e3a yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u7ee7\u7eed\u5f80\u4e0b\u8d70\u65f6 mul \u53ea\u4f1a\u66f4\u5c0f\u3001\u4e0a\u754c\u53ea\u4f1a\u66f4\u4f4e，\u540e\u9762\u6240\u6709 yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u4e5f\u90fd\u4e0d\u53ef\u80fd\u5237\u65b0\u6700\u4f18 \u2014\u2014 \u4e8e\u662f\u76f4\u63a5 break，\u8fde gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span> \u90fd\u4e0d\u7528\u7b97\u3002<\/li>\n
        • \u5982\u679c \u4e0a\u754c > ans：\u8bf4\u660e\u8fd9\u5bf9"\u8fd8\u6709\u5e0c\u671b"，\u8fd9\u65f6\u624d\u4ed8\u51fa\u4ee3\u4ef7\u771f\u6b63\u53bb\u7b97 g=gcd\u2061(x,y)g = \\\\gcd(x, y)<\/span><\/span>g<\/span><\/span>=<\/span><\/span><\/span><\/span>g<\/span>cd<\/span>(<\/span>x<\/span>,<\/span><\/span>y<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u518d\u7528 mul\/(g\u22c5g)mul\/(g \\\\cdot g)<\/span><\/span>m<\/span>u<\/span>l<\/span>\/<\/span>(<\/span>g<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>g<\/span>)<\/span><\/span><\/span><\/span><\/span> \u66f4\u65b0 ans\u3002<\/li>\n<\/ul>\n<\/li>\n
        • ans \u521d\u59cb\u4e3a 0，\u800c\u9898\u76ee\u4fdd\u8bc1\u5143\u7d20 \u22651\\\\ge 1<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u6240\u4ee5\u7b2c\u4e00\u5bf9\u7684\u4e0a\u754c\u4e00\u5b9a >0> 0<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，\u4e0d\u4f1a\u4e00\u5f00\u59cb\u5c31\u8bef\u526a\u3002<\/li>\n

          \u8fd9\u4e2a break \u7684\u6b63\u786e\u6027\u5b8c\u5168\u5efa\u7acb\u5728\u7b2c\u56db\u8282\u7684\u7ee7\u627f\u548c\u7b2c\u4e09\u8282\u7684\u5355\u8c03\u6027\u4e4b\u4e0a，\u7f3a\u4e00\u4e0d\u53ef：<\/p>\n

            \n
          • \u6ca1\u6709\u5355\u8c03\u7684\u679a\u4e3e\u987a\u5e8f（\u6bd4\u5982\u4e71\u5e8f），\u5373\u4f7f\u67d0\u4e00\u5bf9\u7684\u4e0a\u754c\u4e0d\u8fbe\u6807，\u4e5f\u4e0d\u80fd\u63a8\u65ad\u540e\u9762\u7684\u5bf9\u4e0d\u8fbe\u6807，\u5c31\u53ea\u80fd continue \u800c\u975e break，\u526a\u679d\u6536\u76ca\u5927\u6253\u6298\u6263；<\/li>\n
          • \u6ca1\u6709\u5408\u6cd5\u4e0a\u754c，break \u5c31\u53ef\u80fd\u628a\u771f\u6b63\u7684\u7b54\u6848\u526a\u6389\u3002<\/li>\n<\/ul>\n
            \n

            \u516d\u3001\u7528 nums = [2, 3, 5] \u5b8c\u6574\u8d70\u4e00\u904d<\/h3>\n
          • \u964d\u5e8f\u6392\u5e8f \u2192 [5, 3, 2]\u3002<\/li>\n
          • \u6c42\u5168\u5c40 gcd：gcd\u2061(0,5)=5\\\\gcd(0,5)=5<\/span><\/span>g<\/span>cd<\/span>(<\/span>0<\/span>,<\/span><\/span>5<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>5<\/span><\/span><\/span><\/span><\/span>，gcd\u2061(5,3)=1\\\\gcd(5,3)=1<\/span><\/span>g<\/span>cd<\/span>(<\/span>5<\/span>,<\/span><\/span>3<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，gcd\u2061(1,2)=1\\\\gcd(1,2)=1<\/span><\/span>g<\/span>cd<\/span>(<\/span>1<\/span>,<\/span><\/span>2<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u6240\u4ee5 allGcd = 1，allGcd2 = 1\u3002\u4e0a\u754c\u9000\u5316\u6210"\u5c31\u662f\u4e58\u79ef\u672c\u8eab"\u3002<\/li>\n
          • \u5916\u5c42 i = 0：nums[:0] \u4e3a\u7a7a，\u5185\u5c42\u4e0d\u6267\u884c\u3002<\/li>\n
          • \u5916\u5c42 i = 1，x=3x = 3<\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>：\n
              \n
            • \u5185\u5c42 y=5y = 5<\/span><\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>5<\/span><\/span><\/span><\/span><\/span>：mul = 15，\u4e0a\u754c 15\/1=15>15 \/ 1 = 15 ><\/span><\/span>15\/1<\/span><\/span>=<\/span><\/span><\/span><\/span>15<\/span><\/span>><\/span><\/span><\/span><\/span><\/span> ans = 0，\u6709\u5e0c\u671b \u2192 \u7b97 gcd\u2061(3,5)=1\\\\gcd(3,5) = 1<\/span><\/span>g<\/span>cd<\/span>(<\/span>3<\/span>,<\/span><\/span>5<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u2192 \u5f3a\u5ea6 15\/1=1515 \/ 1 = 15<\/span><\/span>15\/1<\/span><\/span>=<\/span><\/span><\/span><\/span>15<\/span><\/span><\/span><\/span><\/span> \u2192 ans = 15\u3002<\/li>\n<\/ul>\n<\/li>\n
            • \u5916\u5c42 i = 2，x=2x = 2<\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>：\n
                \n
              • \u5185\u5c42\u7b2c\u4e00\u4e2a y=5y = 5<\/span><\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>5<\/span><\/span><\/span><\/span><\/span>：mul = 10，\u4e0a\u754c 10\/1=10\u226410 \/ 1 = 10 \\\\le<\/span><\/span>10\/1<\/span><\/span>=<\/span><\/span><\/span><\/span>10<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span> ans = 15 \u2192 \u7acb\u523b break，\u5269\u4e0b\u7684 y=3y = 3<\/span><\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u76f4\u63a5\u8df3\u8fc7\u3002<\/li>\n<\/ul>\n<\/li>\n
              • \u8fd4\u56de 15\u3002<\/li>\n

                \u9a8c\u8bc1\u4e00\u4e0b\u88ab\u8df3\u8fc7\u7684\u4e24\u5bf9：(2,5)(2,5)<\/span><\/span>(<\/span>2<\/span>,<\/span><\/span>5<\/span>)<\/span><\/span><\/span><\/span><\/span> \u5f3a\u5ea6 10\u3001(2,3)(2,3)<\/span><\/span>(<\/span>2<\/span>,<\/span><\/span>3<\/span>)<\/span><\/span><\/span><\/span><\/span> \u5f3a\u5ea6 6，\u786e\u5b9e\u90fd\u5c0f\u4e8e 15，\u526a\u679d\u6ca1\u6709\u526a\u9519\u3002<\/p>\n

                \n

                \u4e03\u3001\u8fd9\u4e2a\u526a\u679d\u5230\u5e95\u6709\u591a\u5f3a？（\u4ee5\u53ca\u4ec0\u4e48\u65f6\u5019\u4f1a\u5931\u6548）<\/h3>\n

                \u6709\u610f\u601d\u7684\u662f，\u8fd9\u4e2a\u526a\u679d\u5b58\u5728\u4e00\u4e2a"\u4e24\u96be"\u7ed3\u6784，\u8ba9\u5b83\u5728\u7edd\u5927\u591a\u6570\u8f93\u5165\u4e0b\u90fd\u5f02\u5e38\u9ad8\u6548：<\/p>\n

                  \n
                • \u5982\u679c\u6570\u5bf9\u7684 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span> \u666e\u904d\u5f88\u5c0f \u2192 \u5f3a\u5ea6\u503c\u5f88\u5927 \u2192 ans \u8fc5\u901f\u6da8\u5230\u4e00\u4e2a\u5f88\u5927\u7684\u6570 \u2192 \u4e0a\u754c\u5f88\u5bb9\u6613\u5c31\u649e\u4e0a ans \u2192 \u526a\u679d\u6781\u65e9\u89e6\u53d1；<\/li>\n
                • \u5982\u679c\u6570\u5bf9\u7684 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span> \u666e\u904d\u5f88\u5927 \u2192 \u8bf4\u660e\u5143\u7d20\u4e4b\u95f4\u5171\u4eab\u5927\u91cf\u56e0\u5b50 \u2192 \u5168\u5c40 allGcd \u4e5f\u503e\u5411\u4e8e\u53d8\u5927 \u2192 \u4e0a\u754c xyallGcd2\\\\frac{xy}{\\\\text{allGcd}^2}<\/span><\/span><\/span><\/span>allGcd<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u88ab\u538b\u5f97\u5f88\u4f4e \u2192 \u4e0a\u754c\u672c\u8eab\u5c31\u4e0d\u5bb9\u6613\u8d85\u8fc7 ans \u2192 \u526a\u679d\u540c\u6837\u5f88\u65e9\u89e6\u53d1\u3002<\/li>\n<\/ul>\n

                  \u4e24\u4e2a\u6781\u7aef\u90fd\u5229\u4e8e\u526a\u679d，\u6240\u4ee5\u5b9e\u8df5\u4e2d\u5185\u5c42\u5faa\u73af\u5f80\u5f80\u6bcf\u4e2a ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u53ea\u8dd1\u4e00\u4e24\u6b21\u5c31 break\u3002<\/p>\n

                  \u4f46\u5b83\u5e76\u975e\u6ca1\u6709\u6700\u574f\u60c5\u51b5：\u6f0f\u6d1e\u5728\u4e8e"\u5168\u5c40 gcd \u5c0f\u3001\u5c40\u90e8\u4e24\u4e24 gcd \u5927"\u7684\u8f93\u5165\u3002\u5178\u578b\u6784\u9020\u662f\u53d6\u4e00\u6279\u5927\u8d28\u6570 q1\u2026qmq_1 \\\\dots q_m<\/span><\/span>q<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2026<\/span><\/span>q<\/span><\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u4ee4\u6570\u7ec4\u5143\u7d20\u662f\u8fd9\u4e9b\u8d28\u6570\u7684\u4e24\u4e24\u4e58\u79ef qiqjq_i q_j<\/span><\/span>q<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4efb\u610f\u4e24\u4e2a\u5143\u7d20\u5171\u4eab\u4e00\u4e2a\u8d28\u56e0\u5b50（\u5c40\u90e8 gcd \u2248 300），\u4f46\u4efb\u610f\u4e09\u4e2a\u5143\u7d20\u7684\u516c\u5171 gcd = 1（\u5168\u5c40 allGcd = 1）\u3002\u6b64\u65f6：<\/p>\n

                    \n
                  • \u4e0a\u754c =x\u22c5y\u2248105\u00d7105=1010= x \\\\cdot y \\\\approx 10^5 \\\\times 10^5 = 10^{10}<\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>y<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u975e\u5e38\u677e；<\/li>\n
                  • \u800c\u771f\u5b9e\u5f3a\u5ea6\u53ea\u6709\u7ea6 qjqk\u2248105q_j q_k \\\\approx 10^5<\/span><\/span>q<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，ans \u5f88\u5c0f；<\/li>\n
                  • \u4e8e\u662f\u4e0a\u754c\u51e0\u4e4e\u6c38\u8fdc\u5927\u4e8e ans，\u526a\u679d\u51e0\u4e4e\u5b8c\u5168\u5931\u6548，\u5185\u5c42\u4f1a\u8dd1\u6ee1，\u9000\u5316\u6210 O(n2)\\\\mathcal{O}(n^2)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u6b21\u5b8c\u6574\u679a\u4e3e\u3002<\/li>\n<\/ul>\n

                    \u5373\u4fbf\u5982\u6b64，n=2000n = 2000<\/span><\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>2000<\/span><\/span><\/span><\/span><\/span> \u65f6\u4e5f\u5c31\u7ea6 2\u00d71062 \\\\times 10^6<\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6b21 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span>，\u5b8c\u5168\u5728\u9650\u5236\u5185，\u6240\u4ee5\u8fd9\u4e2a\u4e0a\u754c\u5206\u6790\u4e0a\u662f O(n2)\\\\mathcal{O}(n^2)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u3001\u5b9e\u8df5\u4e0a\u8fdc\u597d\u4e8e O(n2)\\\\mathcal{O}(n^2)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5c5e\u4e8e"\u7a33\u8d5a\u4e0d\u8d54"\u7684\u4f18\u5316\u3002<\/p>\n

                    \n

                    \u516b\u3001\u590d\u6742\u5ea6\u5206\u6790<\/h3>\n

                    \u8bb0 $n = $ \u6570\u7ec4\u957f\u5ea6（\u22642000\\\\le 2000<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>2000<\/span><\/span><\/span><\/span><\/span>），V=max\u2061(nums)V = \\\\max(nums)<\/span><\/span>V<\/span><\/span>=<\/span><\/span><\/span><\/span>max<\/span>(<\/span>n<\/span>u<\/span>m<\/span>s<\/span>)<\/span><\/span><\/span><\/span><\/span>（\u2264105\\\\le 10^5<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u3002<\/p>\n

                    \u65f6\u95f4\u590d\u6742\u5ea6<\/p>\n

                      \n
                    • \u964d\u5e8f\u6392\u5e8f：O(nlog\u2061n)\\\\mathcal{O}(n \\\\log n)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>log<\/span><\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span>（\u539f\u5730 pdqsort，\u6bd4\u8f83\u51fd\u6570 O(1)\\\\mathcal{O}(1)<\/span><\/span>O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>）；<\/li>\n
                    • \u6c42\u5168\u5c40 gcd：nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u6b21\u6b27\u51e0\u91cc\u5f97，\u5355\u6b21 O(log\u2061V)\\\\mathcal{O}(\\\\log V)<\/span><\/span>O<\/span>(<\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5408\u8ba1 O(nlog\u2061V)\\\\mathcal{O}(n \\\\log V)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>；<\/li>\n
                    • \u53cc\u91cd\u5faa\u73af：\u8fed\u4ee3\u6b21\u6570\u4e0a\u754c n(n\u22121)2=O(n2)\\\\frac{n(n-1)}{2} = \\\\mathcal{O}(n^2)<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span>(<\/span>n<\/span>\u2212<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u6bcf\u6b21\u8fed\u4ee3\u662f O(1)\\\\mathcal{O}(1)<\/span><\/span>O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684\u4e58\u6cd5+\u6bd4\u8f83，\u53ea\u6709\u672a\u89e6\u53d1\u526a\u679d\u7684\u90a3\u4e9b\u8fed\u4ee3\u624d\u989d\u5916\u4ed8\u4e00\u6b21 O(log\u2061V)\\\\mathcal{O}(\\\\log V)<\/span><\/span>O<\/span>(<\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684 gcd\u2061\\\\gcd<\/span><\/span>g<\/span>cd<\/span><\/span><\/span><\/span><\/span>\u3002\u56e0\u6b64\u6700\u574f O(n2log\u2061V)\\\\mathcal{O}(n^2 \\\\log V)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u526a\u679d\u751f\u6548\u65f6\u663e\u8457\u4f4e\u4e8e\u6b64\u3002<\/li>\n<\/ul>\n

                      \u603b\u65f6\u95f4\u590d\u6742\u5ea6：O(nlog\u2061n+n2log\u2061V)\\\\mathcal{O}(n \\\\log n + n^2 \\\\log V)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>log<\/span><\/span><\/span>n<\/span><\/span>+<\/span><\/span><\/span><\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u7531\u53cc\u91cd\u5faa\u73af\u4e3b\u5bfc，\u5373 O(n2log\u2061V)\\\\mathcal{O}(n^2 \\\\log V)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

                      \u7531\u4e8e V\u2264105V \\\\le 10^5<\/span><\/span>V<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u6b27\u51e0\u91cc\u5f97\u7684\u8fed\u4ee3\u8f6e\u6570\u6700\u591a\u5341\u51e0\u8f6e\u4e14\u5e38\u6570\u6781\u5c0f，\u5de5\u7a0b\u4e0a\u53ef\u4ee5\u76f4\u63a5\u89c6\u4f5c O(n2)\\\\mathcal{O}(n^2)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>；\u4ee3\u5165 n=2000n = 2000<\/span><\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>2000<\/span><\/span><\/span><\/span><\/span> \u5373\u7ea6 2\u00d71062 \\\\times 10^6<\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6b21\u57fa\u672c\u8fd0\u7b97，\u6beb\u79d2\u7ea7\u3002<\/p>\n

                      \u989d\u5916\u7a7a\u95f4\u590d\u6742\u5ea6<\/p>\n

                        \n
                      • \u6392\u5e8f\u662f\u539f\u5730\u7684，\u4e0d\u5206\u914d\u65b0\u6570\u7ec4；nums[:i] \u53ea\u662f\u590d\u7528\u7684\u5207\u7247\u5934（\u4e09\u4e2a\u673a\u5668\u5b57），\u5faa\u73af\u4e2d\u4e0d\u4ea7\u751f\u5806\u5206\u914d；<\/li>\n
                      • \u6392\u5e8f\u9012\u5f52\u6808 O(log\u2061n)\\\\mathcal{O}(\\\\log n)<\/span><\/span>O<\/span>(<\/span>log<\/span><\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span>；<\/li>\n
                      • ans\u3001allGcd\u3001mul \u7b49\u5747\u4e3a O(1)\\\\mathcal{O}(1)<\/span><\/span>O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684\u6807\u91cf\u3002<\/li>\n<\/ul>\n

                        \u603b\u989d\u5916\u7a7a\u95f4\u590d\u6742\u5ea6：O(log\u2061n)\\\\mathcal{O}(\\\\log n)<\/span><\/span>O<\/span>(<\/span>log<\/span><\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5168\u6765\u81ea\u6392\u5e8f\u7684\u9012\u5f52\u6808；\u5ffd\u7565\u6808\u5219\u53ef\u89c6\u4e3a O(1)\\\\mathcal{O}(1)<\/span><\/span>O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

                        \n

                        \u4e5d\u3001\u4e24\u4e2a\u5b9e\u73b0\u5c42\u9762\u7684\u5c0f\u63d0\u9192<\/h3>\n
                      • \u6574\u6570\u5bbd\u5ea6：mul = x * y \u6700\u5927\u53ef\u8fbe 101010^{10}<\/span><\/span>1<\/span>0<\/span><\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5df2\u8d85\u51fa 32 \u4f4d int\u3002\u5728 64 \u4f4d\u5e73\u53f0\u4e0a Go \u7684 int \u662f 64 \u4f4d，\u6ca1\u95ee\u9898；\u82e5\u5728 32 \u4f4d\u5e73\u53f0\u7f16\u8bd1\u5219\u4f1a\u6ea2\u51fa，\u7a33\u59a5\u505a\u6cd5\u662f\u628a\u4e2d\u95f4\u53d8\u91cf\u6362\u6210 int64（\u51fd\u6570\u8fd4\u56de\u503c\u5df2\u7ecf\u662f int64，\u8bf4\u660e\u4f5c\u8005\u4e5f\u8003\u8651\u5230\u4e86\u91cf\u7ea7）\u3002<\/li>\n
                      • \u539f\u5730\u4fee\u6539：\u5982\u7b2c\u4e09\u8282\u6240\u8ff0，\u6392\u5e8f\u4f1a\u6253\u4e71\u4f20\u5165\u7684 slice，\u8fd9\u662f\u51fd\u6570\u7684\u53ef\u89c2\u5bdf\u526f\u4f5c\u7528\u3002<\/li>\n

                        Go\u5b8c\u6574\u4ee3\u7801\u5982\u4e0b：<\/h2>\n

                        package<\/span> main<\/p>\n

                        import<\/span> (<\/span>
                        \n"fmt"<\/span>
                        \n"slices"<\/span>
                        \n)<\/span><\/p>\n

                        func<\/span> maxPairStrength<\/span>(<\/span>nums [<\/span>]<\/span>int<\/span>)<\/span> int64<\/span> {<\/span>
                        \nslices.<\/span>SortFunc<\/span>(<\/span>nums,<\/span> func<\/span>(<\/span>a,<\/span> b int<\/span>)<\/span> int<\/span> {<\/span> return<\/span> b –<\/span> a }<\/span>)<\/span><\/p>\n

                        allGcd :=<\/span> 0<\/span>
                        \nfor<\/span> _<\/span>,<\/span> x :=<\/span> range<\/span> nums {<\/span>
                        \nallGcd =<\/span> gcd<\/span>(<\/span>allGcd,<\/span> x)<\/span>
                        \n}<\/span>
                        \nallGcd2 :=<\/span> allGcd *<\/span> allGcd<\/p>\n

                        ans :=<\/span> 0<\/span>
                        \nfor<\/span> i,<\/span> x :=<\/span> range<\/span> nums {<\/span>
                        \nfor<\/span> _<\/span>,<\/span> y :=<\/span> range<\/span> nums[<\/span>:<\/span>i]<\/span> {<\/span>
                        \nmul :=<\/span> x *<\/span> y
                        \nif<\/span> mul\/<\/span>allGcd2 <=<\/span> ans {<\/span>
                        \nbreak<\/span>
                        \n}<\/span>
                        \ng :=<\/span> gcd<\/span>(<\/span>x,<\/span> y)<\/span>
                        \nans =<\/span> max<\/span>(<\/span>ans,<\/span> mul\/<\/span>(<\/span>g*<\/span>g)<\/span>)<\/span>
                        \n}<\/span>
                        \n}<\/span>
                        \nreturn<\/span> int64<\/span>(<\/span>ans)<\/span>
                        \n}<\/span><\/p>\n

                        func<\/span> gcd<\/span>(<\/span>a,<\/span> b int<\/span>)<\/span> int<\/span> {<\/span>
                        \nfor<\/span> a !=<\/span> 0<\/span> {<\/span>
                        \na,<\/span> b =<\/span> b%<\/span>a,<\/span> a
                        \n}<\/span>
                        \nreturn<\/span> b
                        \n}<\/span><\/p>\n

                        func<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
                        \nnums :=<\/span> [<\/span>]<\/span>int<\/span>{<\/span>2<\/span>,<\/span> 3<\/span>,<\/span> 5<\/span>}<\/span>
                        \nresult :=<\/span> maxPairStrength<\/span>(<\/span>nums)<\/span>
                        \nfmt.<\/span>Println<\/span>(<\/span>result)<\/span>
                        \n}<\/span><\/p>\n

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

                        Python\u5b8c\u6574\u4ee3\u7801\u5982\u4e0b：<\/h2>\n

                        # -*-coding:utf-8-*-<\/span><\/p>\n

                        from<\/span> math import<\/span> gcd<\/p>\n

                        def<\/span> max_pair_strength<\/span>(<\/span>nums)<\/span>:<\/span>
                        \n # \u6309\u4ece\u5927\u5230\u5c0f\u6392\u5e8f<\/span>
                        \n nums.<\/span>sort(<\/span>reverse=<\/span>True<\/span>)<\/span><\/p>\n

                        # \u8ba1\u7b97\u6240\u6709\u5143\u7d20\u7684\u6574\u4f53 gcd<\/span>
                        \n all_gcd =<\/span> 0<\/span>
                        \n for<\/span> x in<\/span> nums:<\/span>
                        \n all_gcd =<\/span> gcd(<\/span>all_gcd,<\/span> x)<\/span><\/p>\n

                        all_gcd2 =<\/span> all_gcd *<\/span> all_gcd<\/p>\n

                        ans =<\/span> 0<\/span>
                        \n for<\/span> i,<\/span> x in<\/span> enumerate<\/span>(<\/span>nums)<\/span>:<\/span>
                        \n for<\/span> y in<\/span> nums[<\/span>:<\/span>i]<\/span>:<\/span>
                        \n mul =<\/span> x *<\/span> y<\/p>\n

                        if<\/span> mul \/\/<\/span> all_gcd2 <=<\/span> ans:<\/span>
                        \n break<\/span><\/p>\n

                        g =<\/span> gcd(<\/span>x,<\/span> y)<\/span>
                        \n ans =<\/span> max<\/span>(<\/span>ans,<\/span> mul \/\/<\/span> (<\/span>g *<\/span> g)<\/span>)<\/span><\/p>\n

                        return<\/span> ans<\/p>\n

                        def<\/span> main<\/span>(<\/span>)<\/span>:<\/span>
                        \n nums =<\/span> [<\/span>2<\/span>,<\/span> 3<\/span>,<\/span> 5<\/span>]<\/span>
                        \n result =<\/span> max_pair_strength(<\/span>nums)<\/span>
                        \n print<\/span>(<\/span>result)<\/span><\/p>\n

                        if<\/span> __name__ ==<\/span> "__main__"<\/span>:<\/span>
                        \n main(<\/span>)<\/span><\/p>\n

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

                        C++\u5b8c\u6574\u4ee3\u7801\u5982\u4e0b：<\/h2>\n

                        #<\/span>include<\/span> <bits\/stdc++.h><\/span><\/span>
                        \nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

                        int<\/span> gcd_int<\/span>(<\/span>int<\/span> a,<\/span> int<\/span> b)<\/span> {<\/span>
                        \n while<\/span> (<\/span>a !=<\/span> 0<\/span>)<\/span> {<\/span>
                        \n int<\/span> t =<\/span> b %<\/span> a;<\/span>
                        \n b =<\/span> a;<\/span>
                        \n a =<\/span> t;<\/span>
                        \n }<\/span>
                        \n return<\/span> b;<\/span>
                        \n}<\/span><\/p>\n

                        long<\/span> long<\/span> maxPairStrength<\/span>(<\/span>vector<<\/span>int<\/span>><\/span> nums)<\/span> {<\/span>
                        \n sort<\/span>(<\/span>nums.<\/span>begin<\/span>(<\/span>)<\/span>,<\/span> nums.<\/span>end<\/span>(<\/span>)<\/span>,<\/span> greater<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>)<\/span>)<\/span>;<\/span><\/p>\n

                        int<\/span> allGcd =<\/span> 0<\/span>;<\/span>
                        \n for<\/span> (<\/span>int<\/span> x :<\/span> nums)<\/span> {<\/span>
                        \n allGcd =<\/span> gcd_int<\/span>(<\/span>allGcd,<\/span> x)<\/span>;<\/span>
                        \n }<\/span>
                        \n long<\/span> long<\/span> allGcd2 =<\/span> 1LL<\/span> *<\/span> allGcd *<\/span> allGcd;<\/span><\/p>\n

                        long<\/span> long<\/span> ans =<\/span> 0<\/span>;<\/span>
                        \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> (<\/span>int<\/span>)<\/span>nums.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
                        \n int<\/span> x =<\/span> nums[<\/span>i]<\/span>;<\/span>
                        \n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> i;<\/span> ++<\/span>j)<\/span> {<\/span>
                        \n int<\/span> y =<\/span> nums[<\/span>j]<\/span>;<\/span>
                        \n long<\/span> long<\/span> mul =<\/span> 1LL<\/span> *<\/span> x *<\/span> y;<\/span><\/p>\n

                        if<\/span> (<\/span>mul \/<\/span> allGcd2 <=<\/span> ans)<\/span> {<\/span>
                        \n break<\/span>;<\/span>
                        \n }<\/span><\/p>\n

                        int<\/span> g =<\/span> gcd_int<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
                        \n ans =<\/span> max<\/span>(<\/span>ans,<\/span> mul \/<\/span> (<\/span>1LL<\/span> *<\/span> g *<\/span> g)<\/span>)<\/span>;<\/span>
                        \n }<\/span>
                        \n }<\/span>
                        \n return<\/span> ans;<\/span>
                        \n}<\/span><\/p>\n

                        int<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
                        \n vector<<\/span>int<\/span>><\/span> nums =<\/span> {<\/span>2<\/span>,<\/span> 3<\/span>,<\/span> 5<\/span>}<\/span>;<\/span>
                        \n long<\/span> long<\/span> result =<\/span> maxPairStrength<\/span>(<\/span>nums)<\/span>;<\/span>
                        \n cout <<<\/span> result <<<\/span> endl;<\/span>
                        \n return<\/span> 0<\/span>;<\/span>
                        \n}<\/span><\/p>\n

                        \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n","protected":false},"excerpt":{"rendered":"

                        2026-10-31：\u6570\u5bf9\u7684\u6700\u5927\u5f3a\u5ea6\u3002\u7528go\u8bed\u8a00，\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums\u3002\u9700\u8981\u4ece\u6570\u7ec4\u4e2d\u9009\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u4e0d\u540c\u7684\u5143\u7d20，\u7ec4\u6210\u4e00\u4e2a\u6570\u5bf9\u3002\u8be5\u6570\u5bf9\u7684\u5f3a\u5ea6\u7b49\u4e8e：\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u4e58\u79ef，\u9664\u4ee5\u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u7684\u5e73\u65b9\u3002\u8bf7\u8ba1\u7b97\u5e76\u8fd4\u56de\u6240\u6709\u53ef\u80fd\u6570\u5bf9\u4e2d\u80fd\u591f\u5f97\u5230\u7684\u6700\u5927\u5f3a\u5ea6\u503c\u3002
                        \n2 < nums.length < 2000\u3002
                        \n1 < nums[i] < 100000\u3002
                        \n\u8f93\u5165： nums [2,3,5]\u3002
                        \n\u8f93\u51fa： 1<\/p>\n","protected":false},"author":2,"featured_media":120412,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11820,746,99,427],"topic":[],"class_list":["post-120415","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-atomgit","tag-golang","tag-java","tag-427"],"yoast_head":"\n2026-10-31\uff1a\u6570\u5bf9\u7684\u6700\u5927\u5f3a\u5ea6\u3002\u7528go\u8bed\u8a00\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums\u3002\u9700\u8981\u4ece\u6570\u7ec4\u4e2d\u9009\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u4e0d\u540c\u7684\u5143\u7d20\uff0c\u7ec4\u6210\u4e00\u4e2a\u6570\u5bf9\u3002\u8be5\u6570\u5bf9\u7684\u5f3a\u5ea6\u7b49\u4e8e\uff1a\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u4e58\u79ef\uff0c\u9664\u4ee5\u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u7684\u5e73\u65b9\u3002\u8bf7\u8ba1\u7b97\u5e76 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/120415.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2026-10-31\uff1a\u6570\u5bf9\u7684\u6700\u5927\u5f3a\u5ea6\u3002\u7528go\u8bed\u8a00\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums\u3002\u9700\u8981\u4ece\u6570\u7ec4\u4e2d\u9009\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u4e0d\u540c\u7684\u5143\u7d20\uff0c\u7ec4\u6210\u4e00\u4e2a\u6570\u5bf9\u3002\u8be5\u6570\u5bf9\u7684\u5f3a\u5ea6\u7b49\u4e8e\uff1a\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u4e58\u79ef\uff0c\u9664\u4ee5\u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u7684\u5e73\u65b9\u3002\u8bf7\u8ba1\u7b97\u5e76 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"2026-10-31：\u6570\u5bf9\u7684\u6700\u5927\u5f3a\u5ea6\u3002\u7528go\u8bed\u8a00，\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums\u3002\u9700\u8981\u4ece\u6570\u7ec4\u4e2d\u9009\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u4e0d\u540c\u7684\u5143\u7d20，\u7ec4\u6210\u4e00\u4e2a\u6570\u5bf9\u3002\u8be5\u6570\u5bf9\u7684\u5f3a\u5ea6\u7b49\u4e8e：\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u4e58\u79ef，\u9664\u4ee5\u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u7684\u5e73\u65b9\u3002\u8bf7\u8ba1\u7b97\u5e76\u8fd4\u56de\u6240\u6709\u53ef\u80fd\u6570\u5bf9\u4e2d\u80fd\u591f\u5f97\u5230\u7684\u6700\u5927\u5f3a\u5ea6\u503c\u3002 2 < nums.length < 2000\u3002 1 < nums[i] < 100000\u3002 \u8f93\u5165： nums [2,3,5]\u3002 \u8f93\u51fa： 1\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/120415.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-31T08:48:50+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261031084847-6ae5ab6fc7caa.png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/120415.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/120415.html\",\"name\":\"2026-10-31\uff1a\u6570\u5bf9\u7684\u6700\u5927\u5f3a\u5ea6\u3002\u7528go\u8bed\u8a00\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums\u3002\u9700\u8981\u4ece\u6570\u7ec4\u4e2d\u9009\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u4e0d\u540c\u7684\u5143\u7d20\uff0c\u7ec4\u6210\u4e00\u4e2a\u6570\u5bf9\u3002\u8be5\u6570\u5bf9\u7684\u5f3a\u5ea6\u7b49\u4e8e\uff1a\u8fd9\u4e24\u4e2a\u5143\u7d20\u7684\u4e58\u79ef\uff0c\u9664\u4ee5\u5b83\u4eec\u7684\u6700\u5927\u516c\u7ea6\u6570\u7684\u5e73\u65b9\u3002\u8bf7\u8ba1\u7b97\u5e76 - 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