{"id":109076,"date":"2026-09-23T09:17:28","date_gmt":"2026-09-23T01:17:28","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/109076.html"},"modified":"2026-09-23T09:17:28","modified_gmt":"2026-09-23T01:17:28","slug":"%e3%80%90%e5%ae%9e%e4%b9%a0%e8%b8%a9%e5%9d%91%e5%ae%9e%e5%bd%95%e3%80%91%e4%bb%8e%e4%b8%80%e4%b8%87%e8%a1%8c%e7%9a%84%e5%87%bd%e6%95%b0%e5%88%b0%e4%b8%80%e5%bc%a0%e5%9b%be%ef%bc%9a%e6%88%91%e7%94%a8","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/109076.html","title":{"rendered":"\u3010\u5b9e\u4e60\u8e29\u5751\u5b9e\u5f55\u3011\u4ece\u4e00\u4e07\u884c\u7684\u51fd\u6570\u5230\u4e00\u5f20\u56fe\uff1a\u6211\u7528\u56fe\u7b97\u6cd5\u5408\u5e76\u77ed\u7ebf\u6bb5"},"content":{"rendered":"

\"\u8bf7\u6dfb\u52a0\u56fe\u7247\u63cf\u8ff0\"<\/p>\n<\/p>\n

🫧 \u52b1\u5fd7\u4e0d\u6389\u5934\u53d1\u7684\u5185\u5411\u7a0b\u5e8f\u5458：\u4e2a\u4eba\u4e3b\u9875<\/font><\/p>\n

\u00a0\u2728\ufe0f \u4e2a\u4eba\u4e13\u680f: \u300aC++\u8bed\u8a00\u300b\u300aLinux\u5b66\u4e60\u300b<\/font><\/p>\n

🌅\u5076\u5c14\u60b2\u4f24，\u5076\u5c14\u88ab\u5e78\u798f\u6240\u5b8c\u5584 <\/font><\/p>\n

\n

👓\ufe0f\u535a\u4e3b\u7b80\u4ecb:<\/p>\n

\"\u8bf7\u6dfb\u52a0\u56fe\u7247\u63cf\u8ff0\"<\/p>\n<\/p>\n

\u6587\u7ae0\u76ee\u5f55<\/h4>\n
    \n
  • \u524d\u8a00<\/li>\n
  • \u4e00\u3001\u95ee\u9898\u7684\u4ea7\u751f<\/li>\n
  • \u4e8c\u3001\u95ee\u9898\u7684\u601d\u8003<\/li>\n
  • \n
      \n
    • 2.1\u3001\u5148\u7ed9"\u77ed"\u5b9a\u4e00\u4e2a\u6807\u51c6<\/li>\n
    • 2.2\u3001\u53ea\u628a\u77ed\u7ebf\u6bb5\u8bb0\u4e0b\u6765，\u591f\u5417？<\/li>\n
    • 2.3\u3001\u5efa\u6a21：\u7ed9\u70b9\u7f16\u53f7，\u7528\u90bb\u63a5\u8868\u5b58<\/li>\n
    • 2.4\u3001\u6700\u5173\u952e\u7684\u4e00\u6b65：\u77ed\u8fb9\u8fde\u6210\u7684\u6574\u5757，\u8981\u4e00\u8d77\u584c\u7f29<\/li>\n
    • 2.5\u3001\u5408\u5e76\u4e00\u4e2a\u8fde\u901a\u5206\u91cf：\u4e09\u4ef6\u4e8b<\/li>\n
    • 2.6\u3001\u4e3a\u4ec0\u4e48\u5916\u9762\u8fd8\u8981\u5957\u4e00\u4e2a while？<\/li>\n<\/ul>\n<\/li>\n
    • \u4e09\u3001\u5b8c\u6574\u4ee3\u7801<\/li>\n
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    • \u603b\u7ed3<\/li>\n<\/ul>\n
      \n

      \u524d\u8a00<\/h2>\n

      \u5728\u65e5\u5e38\u7684\u5de5\u4f5c\u4e2d，\u6211\u4eec\u603b\u4f1a\u78b0\u5230\u5404\u79cd\u5404\u6837\u7684\u95ee\u9898\u3002\u5728\u75db\u82e6\u7684\u540c\u65f6，\u4e5f\u95f4\u63a5\u7684\u63d0\u9ad8\u4e86\u5bf9\u95ee\u9898\u7684\u89e3\u6790\u80fd\u529b，\u4f46\u662f\u6709\u4e00\u4e9b\u5c0f\u4f19\u4f34\u4eec\u8fd8\u6ca1\u6709\u5f00\u59cb\u5b9e\u4e60，\u5374\u4e5f\u60f3\u953b\u70bc\u953b\u70bc\u6211\u4eec\u7528\u4ee3\u7801\u89e3\u51b3\u95ee\u9898\u7684\u80fd\u529b，\u6216\u8005\u7591\u60d1\u5b66\u7684\u4e00\u4e9b\u7b97\u6cd5\u3001STL \u5e93\u7b49，\u662f\u600e\u4e48\u6765\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u7684，\u6240\u4ee5\u5728\u8fd9\u91cc\u535a\u4e3b\u6253\u7b97\u6765\u4e00\u4e2a\u4e13\u8f91，\u6765\u804a\u804a\u6211\u5728\u5199\u4ee3\u7801\u65f6\u78b0\u5230\u7684\u4e00\u4e9b\u95ee\u9898，\u4ee5\u53ca\u6700\u540e\u662f\u600e\u4e48\u89e3\u51b3\u7684，\u7528\u5230\u4e86\u4ec0\u4e48\u7b97\u6cd5\u7b49，\u8ba9\u5927\u5bb6\u4ee5\u540e\u78b0\u5230\u4e00\u6837\u7684\u95ee\u9898\u65f6\u80fd\u5f88\u5feb\u7684\u60f3\u5230\u65b9\u6cd5\u3002<\/p>\n

      \u8fd9\u4e00\u7bc7，\u6211\u60f3\u804a\u804a\u6211\u5728\u5b9e\u73b0\u4e00\u4e2a CAM \u7684"\u627e\u4e2d\u8f74\u7ebf"\u529f\u80fd\u65f6，\u78b0\u5230\u7684\u4e00\u4e2a\u5408\u5e76\u77ed\u7ebf\u6bb5\u7684\u95ee\u9898\u3002\u5b83\u770b\u8d77\u6765\u5f88\u5c0f，\u4f46\u6700\u540e\u662f\u7528\u4e00\u5f20\u56fe\u89e3\u51b3\u7684\u3002<\/p>\n

      \"\u8bf7\u6dfb\u52a0\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

      \n

      \u4e00\u3001\u95ee\u9898\u7684\u4ea7\u751f<\/h2>\n

      \u6709\u4e00\u5929，\u8001\u677f\u5bf9\u535a\u4e3b\u8bf4，\u4f60\u63a5\u4e0b\u6765\u7684\u4efb\u52a1\u662f\u89e3\u51b3\u4e00\u4e2a\u51fd\u6570\u7684 bug，\u535a\u4e3b\u5f97\u77e5\u4efb\u52a1\u540e\u6b23\u559c\u82e5\u72c2，\u8fd9\u7b80\u76f4\u5c31\u662f\u6478\u9c7c\u7684\u7f8e\u5dee，\u4e00\u4e2a\u51fd\u6570\u80fd\u6709\u591a\u96be，\u770b\u6211\u901f\u901f\u6574\u5b8c\u540e\u6478\u51e0\u5929\u9c7c\u5148\u2570(\u00b0\u25bd\u00b0)\u256f\u3002 \"\u8bf7\u6dfb\u52a0\u56fe\u7247\u63cf\u8ff0\" \u7136\u540e\u5c31\u770b\u5230\u4e86\u8fd9\u4e2a\u51fd\u6570\u7684\u771f\u9762\u76ee\u0ca5_\u0ca5\u3002\u4ec0\u4e48\u53eb\u505a\u4e00\u4e2a\u51fd\u6570\u6709\u4e00\u4e07\u884c\u554a\u3002\u535a\u4e3b\u867d\u7136\u6b32\u54ed\u65e0\u6cea，\u4f46\u662f\u8fd8\u662f\u60f3\u7ec6\u7ec6\u54c1\u54c1\u8fd9\u5768\u5c4e\u5c71，\u7ed3\u679c\u8d8a\u54c1\u8d8a\u5fc3\u60ca，\u4e3a\u4ec0\u4e48\u4e00\u4e2a\u5faa\u73af\u4f53\u91cc\u9762\u6709 9000 \u884c\u4ee3\u7801\u554a，\u8fd9\u4e2a\u4e09\u91cd for \u5faa\u73af\u52a0\u5d4c\u5957lambda \u662f\u4ec0\u4e48\u4e1c\u897f\u554a，\u800c\u4e14\u5168\u662f\u6d6e\u70b9\u6570\u8fd0\u7b97\u662f\u4ec0\u4e48\u9b3c\u554a\u3002\u5c31\u8fd9\u6837，\u535a\u4e3b\u5014\u5f3a\u4e86 1 \u5468\u540e\u5b9e\u5728\u662f\u6ca1\u62db\u4e86，\u53ea\u80fd\u91cd\u5199\u4e86，\u56e0\u4e3a\u662f\u8fb9\u7f18\u7684\u529f\u80fd，\u6ca1\u6709\u592a\u590d\u6742\u7684\u8c03\u7528，\u6240\u4ee5\u91cd\u5199\u4e0d\u9700\u8981\u6539\u592a\u591a\u522b\u7684\u5730\u65b9，\u53ea\u8981\u4fdd\u6301\u8fd9\u4e2a\u51fd\u6570\u540d\u4e0d\u53d8\u5c31\u884c\u4e86\u3002<\/p>\n

      \u95f2\u8bdd\u5c11\u8bf4，\u63a5\u4e0b\u6765\u535a\u4e3b\u5728\u5b9e\u73b0\u529f\u80fd\u7684\u65f6\u5019\u5c31\u9047\u5230\u4e86\u4e00\u4e2a\u95ee\u9898，\u751f\u6210\u4e86\u4e00\u4e2a\u9aa8\u67b6，\u8fd9\u4e2a\u9aa8\u67b6\u662f\u7528\u4e00\u4e2a\u6570\u7ec4\u4fdd\u5b58\u7684，\u8fd9\u4e2a\u6570\u7ec4\u91cc\u9762\u4fdd\u5b58\u4e86\u5f88\u591a\u7ebf\u6bb5，\u7ebf\u6bb5\u662f\u7528\u4e24\u4e2a\u70b9\u8bb0\u5f55\u4e0b\u6765\u7684\u3002<\/p>\n

      struct<\/span> Point<\/span>
      \n{<\/span>
      \ndouble<\/span> x;<\/span>
      \ndouble<\/span> y;<\/span>
      \n}<\/span>;<\/span>
      \nvector<<\/span>pair<<\/span>Point,<\/span> Point>><\/span> segments;<\/span><\/p>\n

      \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u4fdd\u5b58\u7684\u662f\u9aa8\u67b6\u7684\u7ebf\u6bb5，\u4f46\u662f\u6b64\u65f6\u7684\u95ee\u9898\u5c31\u662f，\u8fd9\u91cc\u9762\u6709\u5f88\u591a\u9519\u8bef\u7684\u975e\u5e38\u77ed\u7684\u7ebf\u6bb5，\u5f97\u53bb\u6389，\u6700\u597d\u662f\u5408\u5e76\u8d77\u6765，\u4f46\u662f\u6539\u600e\u4e48\u505a\u5462？<\/p>\n

      \n

      \u4e8c\u3001\u95ee\u9898\u7684\u601d\u8003<\/h2>\n

      \u6211\u4eec\u7684\u76ee\u6807\u662f：\u8ba9\u8fd9\u4e9b\u975e\u5e38\u77ed\u7684\u7ebf\u6bb5\u5408\u5e76\u5728\u4e00\u8d77，\u53ea\u7559\u4e0b\u4e00\u4e2a\u5173\u952e\u7684\u3001\u5e72\u51c0\u7684\u9aa8\u67b6\u3002<\/p>\n

      2.1\u3001\u5148\u7ed9"\u77ed"\u5b9a\u4e00\u4e2a\u6807\u51c6<\/h3>\n

      \u60f3\u8981\u5408\u5e76"\u975e\u5e38\u77ed\u7684\u7ebf\u6bb5"，\u7b2c\u4e00\u6b65\u5c31\u5f97\u56de\u7b54：\u591a\u77ed\u624d\u7b97\u77ed？<\/p>\n

      \u6240\u4ee5\u8981\u5f15\u5165\u4e00\u4e2a\u9608\u503c，\u6765\u5224\u65ad\u4e00\u6761\u7ebf\u6bb5\u662f\u4e0d\u662f\u77ed\u7ebf\u6bb5：<\/p>\n

      double<\/span> tol;<\/span><\/p>\n

      \u6709\u4e86\u6807\u51c6，\u63a5\u4e0b\u6765\u5c31\u5f97\u7b97\u51fa\u6bcf\u6761\u7ebf\u6bb5\u7684\u957f\u5ea6，\u624d\u80fd\u62ff\u53bb\u548c\u9608\u503c\u6bd4\u8f83\u3002\u4e3a\u6b64\u9700\u8981\u4e00\u4e2a\u6c42\u4e24\u70b9\u8ddd\u79bb\u7684\u51fd\u6570：<\/p>\n

      double<\/span> distance<\/span>(<\/span>const<\/span> Point&<\/span> a,<\/span> const<\/span> Point&<\/span> b)<\/span> {<\/span>
      \n double<\/span> dx =<\/span> a.<\/span>x –<\/span> b.<\/span>x;<\/span>
      \n double<\/span> dy =<\/span> a.<\/span>y –<\/span> b.<\/span>y;<\/span>
      \n return<\/span> std::<\/span>sqrt<\/span>(<\/span>dx *<\/span> dx +<\/span> dy *<\/span> dy)<\/span>;<\/span>
      \n}<\/span><\/p>\n

      \u5f88\u7b80\u5355，\u5c31\u662f\u521d\u4e2d\u5c31\u5b66\u8fc7\u7684\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\u3002\u6709\u4e86\u5b83，\u6211\u4eec\u5c31\u80fd\u904d\u5386 segments，\u628a\u77ed\u7ebf\u6bb5\u5168\u90e8\u6311\u51fa\u6765\u3002<\/p>\n

      2.2\u3001\u53ea\u628a\u77ed\u7ebf\u6bb5\u8bb0\u4e0b\u6765，\u591f\u5417？<\/h3>\n

      \u6311\u51fa\u77ed\u7ebf\u6bb5\u4e4b\u540e，\u600e\u4e48\u8bb0\u5f55\u5462？\u6709\u7684\u5c0f\u4f19\u4f34\u53ef\u80fd\u60f3\u5f53\u7136\u5730\u89c9\u5f97：\u8fd9\u4e0d\u662f\u5f88\u7b80\u5355，\u8ddf segments \u4e00\u6837\u4e0d\u5c31\u884c\u4e86：<\/p>\n

      std::<\/span>vector<<\/span>std::<\/span>pair<<\/span>Point,<\/span> Point>><\/span> shortSegments;<\/span><\/p>\n

      \u4ece"\u8bb0\u5f55\u4e0b\u6765"\u8fd9\u4e2a\u5c42\u9762\u770b，\u5012\u4e5f\u6ca1\u9519\u3002\u4f46\u6211\u4eec\u5f97\u56de\u5230\u6700\u521d\u7684\u95ee\u9898：\u6211\u4eec\u8981\u505a\u7684\u662f\u5408\u5e76\u3002 \u6240\u8c13\u5408\u5e76，\u5c31\u662f\u628a\u539f\u6765\u77ed\u7ebf\u6bb5\u6240\u5728\u7684\u4f4d\u7f6e，\u6536\u7f29\u6210\u4e00\u4e2a\u70b9\u3002\u5047\u5982\u73b0\u5728\u6709\u4e00\u6761\u77ed\u7ebf\u6bb5 ab：<\/p>\n

      c —- a — b ——- d<\/p>\n

      \u5982\u679c\u5408\u5e76\u65f6\u4fdd\u7559 a \u70b9\u3001\u4e22\u6389 b \u70b9，\u90a3\u4e48\u95ee\u9898\u6765\u4e86：\u539f\u6765\u8fde\u5728 b \u4e0a\u7684\u90a3\u4e9b\u7ebf\u6bb5\u600e\u4e48\u529e？<\/p>\n

      \u5b83\u4eec\u73b0\u5728\u662f\u8fde\u5728 b \u4e0a\u7684，\u800c b \u9a6c\u4e0a\u5c31\u8981\u88ab\u4e22\u6389\u4e86，\u6240\u4ee5\u5fc5\u987b\u628a\u5b83\u4eec\u5168\u90e8\u6539\u63a5\u5230 a \u4e0a\u2014\u2014\u4e5f\u5c31\u662f c\u2014a \u548c a\u2014d\u3002\u90a3\u5982\u679c\u6211\u4eec\u53ea\u7528\u4e00\u4e2a vector \u8bb0\u5f55\u77ed\u7ebf\u6bb5，\u4f1a\u53d1\u751f\u4ec0\u4e48？\u4e3a\u4e86\u627e\u5230"\u8c01\u539f\u672c\u8fde\u5728 b \u4e0a"，\u6211\u4eec\u53ea\u80fd\u56de\u5934\u53bb\u904d\u5386\u6574\u4e2a segments\u3002\u800c\u6bcf\u5904\u7406\u4e00\u6761\u77ed\u7ebf\u6bb5\u90fd\u8981\u904d\u5386\u4e00\u6b21，\u77ed\u7ebf\u6bb5\u4e00\u591a，\u65f6\u95f4\u590d\u6742\u5ea6\u76f4\u63a5\u62c9\u6ee1\u3002<\/p>\n

      \u6240\u4ee5\u771f\u6b63\u7684\u96be\u70b9\u4e0d\u662f"\u8bb0\u4e0b\u77ed\u7ebf\u6bb5"，\u800c\u662f"\u8bb0\u4e0b\u6bcf\u4e2a\u70b9\u548c\u8c01\u76f8\u8fde"\u3002 \u6211\u5de6\u601d\u53f3\u60f3，\u6700\u540e\u60f3\u5230\u4e86\u56fe\u3002<\/p>\n

      \u662f\u554a\u2014\u2014\u56fe\u7b80\u76f4\u662f\u4e3a\u8fd9\u4e2a\u95ee\u9898\u91cf\u8eab\u5b9a\u505a\u7684\u7ed3\u6784：\u5b83\u65e2\u80fd\u8bb0\u5f55\u77ed\u7ebf\u6bb5（\u54ea\u4e24\u4e2a\u70b9\u4e4b\u95f4\u6709\u4e00\u6761\u77ed\u8fb9），\u53c8\u80fd\u8bb0\u5f55\u6bcf\u4e2a\u70b9\u63a5\u4e86\u54ea\u4e9b\u90bb\u5c45\u3002\u8fd9\u6837\u5728\u5408\u5e76\u65f6，\u6211\u4eec\u5c31\u53ef\u4ee5\u5f88\u5feb\u5730\u628a b \u7684\u90bb\u5c45\u5168\u90e8\u6539\u63a5\u5230 a \u4e0a，\u540c\u65f6\u628a b \u4ece\u56fe\u91cc\u6458\u6389\u3002<\/p>\n

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

      2.3\u3001\u5efa\u6a21：\u7ed9\u70b9\u7f16\u53f7，\u7528\u90bb\u63a5\u8868\u5b58<\/h3>\n

      \u4e0d\u8fc7\u5728\u771f\u6b63\u753b\u56fe\u4e4b\u524d，\u8fd8\u6709\u4e00\u4e2a\u5c34\u5c2c\u7684\u95ee\u9898：Point \u91cc\u88c5\u7684\u662f\u6d6e\u70b9\u6570，\u6d6e\u70b9\u6570\u662f\u4e0d\u80fd\u76f4\u63a5\u62ff\u6765\u5f53\u4e0b\u6807\u7684\u3002 \u6240\u4ee5\u6211\u4eec\u8981\u7ed9\u6bcf\u4e2a\u70b9\u5206\u914d\u4e00\u4e2a\u552f\u4e00\u7684\u6574\u6570 ID，\u7528 ID \u8868\u793a\u56fe\u4e2d\u7684\u8282\u70b9：<\/p>\n

      \/\/ \u5f53\u524d\u5de5\u4f5c\u6570\u636e：\u6240\u6709\u7aef\u70b9，\u4ee5\u53ca\u6bcf\u6761\u7ebf\u6bb5\u4e24\u7aef\u70b9\u7684 ID<\/span>
      \nstd::<\/span>vector<<\/span>Point><\/span> pts;<\/span>
      \nstd::<\/span>vector<<\/span>int<\/span>><\/span> startIds,<\/span> endIds;<\/span><\/p>\n

      auto<\/span> getOrCreate =<\/span> [<\/span>&<\/span>]<\/span>(<\/span>const<\/span> Point&<\/span> p)<\/span> -><\/span> int<\/span> {<\/span>
      \n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> pts.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n if<\/span> (<\/span>distance<\/span>(<\/span>pts[<\/span>i]<\/span>,<\/span> p)<\/span> <<\/span> eps)<\/span> {<\/span> \/\/ \u6d6e\u70b9\u6570\u6bd4\u8f83，\u7528 eps \u800c\u4e0d\u662f ==<\/span>
      \n return<\/span> static_cast<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>i)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span>
      \n pts.<\/span>push_back<\/span>(<\/span>p)<\/span>;<\/span>
      \n return<\/span> static_cast<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>pts.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> –<\/span> 1<\/span>;<\/span>
      \n}<\/span>;<\/span><\/p>\n

      \/\/ \u521d\u59cb\u5316：\u7ed9\u6240\u6709\u7aef\u70b9\u5206\u914d\u552f\u4e00 ID<\/span>
      \nfor<\/span> (<\/span>const<\/span> auto<\/span>&<\/span> seg :<\/span> segments)<\/span> {<\/span>
      \n int<\/span> sid =<\/span> getOrCreate<\/span>(<\/span>seg.<\/span>first)<\/span>;<\/span>
      \n int<\/span> eid =<\/span> getOrCreate<\/span>(<\/span>seg.<\/span>second)<\/span>;<\/span>
      \n if<\/span> (<\/span>sid ==<\/span> eid)<\/span> continue<\/span>;<\/span> \/\/ \u9000\u5316\u7ebf\u6bb5，\u76f4\u63a5\u4e22\u6389<\/span>
      \n startIds.<\/span>push_back<\/span>(<\/span>sid)<\/span>;<\/span>
      \n endIds.<\/span>push_back<\/span>(<\/span>eid)<\/span>;<\/span>
      \n}<\/span><\/p>\n

      \u8fd9\u91cc\u6709\u4e24\u4e2a\u7ec6\u8282\u503c\u5f97\u8bf4\u4e00\u4e0b\u3002<\/p>\n

      \u7b2c\u4e00，\u4e3a\u4ec0\u4e48\u628a\u8d77\u70b9\u548c\u7ec8\u70b9\u5206\u6210\u4e24\u4e2a\u6570\u7ec4？ \u56e0\u4e3a\u540e\u9762\u64cd\u4f5c\u7ebf\u6bb5\u65f6\u57fa\u672c\u90fd\u662f"\u6210\u5bf9"\u64cd\u4f5c\u7684，\u5982\u679c\u628a\u5b83\u4eec\u6df7\u5728\u4e00\u4e2a\u5bb9\u5668\u91cc，\u5220\u9664\u548c\u66ff\u6362\u65f6\u5c31\u5f97\u5904\u7406\u4e0b\u6807\u5947\u5076\u6027，\u975e\u5e38\u5bb9\u6613\u51fa\u9519\u3002\u5206\u5f00\u5b58\u4e4b\u540e，\u4e00\u6761\u7ebf\u6bb5\u5c31\u662f"startIds[i] \u8fde\u5230 endIds[i]\u201c，\u589e\u5220\u90fd\u5e72\u51c0\u3002 \u7b2c\u4e8c，\u4e3a\u4ec0\u4e48\u4e0d\u7528 pts[i] == p \u5224\u65ad\u4e24\u4e2a\u70b9\u662f\u5426\u76f8\u540c？ \u56e0\u4e3a Point \u91cc\u662f double\u3002\u4e24\u4e2a\u7406\u8bba\u4e0a\u76f8\u540c\u7684\u70b9，\u7ecf\u8fc7\u4e00\u8fde\u4e32\u8fd0\u7b97\u540e\u53ef\u80fd\u5dee\u51fa 1e-16，\u7528 == \u4e00\u5b9a\u4f1a\u6709\u6f0f\u7f51\u7684\u3002\u6240\u4ee5\u8fd9\u91cc\u7528 distance(…) < eps \u6765\u5224\u5b9a"\u662f\u540c\u4e00\u4e2a\u70b9\u201d\u3002<\/p>\n

      \u6709\u4e86 ID \u4e4b\u540e，\u56fe\u5c31\u53ef\u4ee5\u76f4\u63a5\u5efa\u51fa\u6765\u4e86：<\/p>\n

      int<\/span> n =<\/span> static_cast<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>pts.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
      \nstd::<\/span>vector<<\/span>std::<\/span>set<<\/span>int<\/span>>><\/span> adj<\/span>(<\/span>n)<\/span>;<\/span> \/\/ \u8bb0\u5f55\u6240\u6709\u8fb9<\/span>
      \nstd::<\/span>vector<<\/span>std::<\/span>set<<\/span>int<\/span>>><\/span> shortAdj<\/span>(<\/span>n)<\/span>;<\/span> \/\/ \u8bb0\u5f55\u6240\u6709\u77ed\u8fb9<\/span><\/p>\n

      \u7528 std::set \u800c\u4e0d\u662f vector \u5b58\u90bb\u5c45，\u662f\u4e3a\u4e86\u81ea\u52a8\u53bb\u91cd\u2014\u2014\u540c\u4e00\u4e2a\u70b9\u53ef\u80fd\u88ab\u591a\u6761\u7ebf\u6bb5\u8fde\u5230，\u91cd\u590d\u7684\u90bb\u5c45\u4f1a\u8ba9\u540e\u9762\u7684\u5408\u5e76\u903b\u8f91\u51fa\u9519\u3002<\/p>\n

      2.4\u3001\u6700\u5173\u952e\u7684\u4e00\u6b65：\u77ed\u8fb9\u8fde\u6210\u7684\u6574\u5757，\u8981\u4e00\u8d77\u584c\u7f29<\/h3>\n

      \u5199\u5230\u8fd9\u91cc，\u6211\u4e00\u5f00\u59cb\u7684\u601d\u8def\u662f"\u9010\u6761\u5408\u5e76\u77ed\u8fb9"：\u627e\u5230\u4e00\u6761\u77ed\u8fb9 ab，\u5c31\u628a b \u5e76\u5230 a \u4e0a\u3002\u4f46\u5f88\u5feb\u5c31\u53d1\u73b0\u8fd9\u6837\u4e0d\u5bf9\u3002\u770b\u8fd9\u79cd\u60c5\u51b5：<\/p>\n

      a — b — c — d<\/p>\n

      \u56db\u6761\u77ed\u8fb9\u9996\u5c3e\u76f8\u63a5，\u5982\u679c\u53ea\u6309"\u4e24\u4e24\u5408\u5e76"\u6765\u505a，\u5904\u7406 A-B \u65f6\u628a B \u5e76\u5230 A，\u518d\u5904\u7406 B-C \u65f6 B \u5df2\u7ecf\u4e0d\u5b58\u5728\u4e86\u2026\u2026\u4e00\u8f6e\u4e0b\u6765\u8981\u4e48\u6f0f\u6389，\u8981\u4e48\u9677\u5165\u53cd\u590d\u4fee\u6539\u3002\u6b63\u786e\u7684\u770b\u6cd5\u662f：\u77ed\u8fb9\u5728\u56fe\u4e0a\u8fde\u6210\u7684\u6574\u5757\u533a\u57df，\u5e94\u8be5\u6574\u4f53\u584c\u7f29\u6210\u4e00\u4e2a\u70b9\u3002 \u8fd9\u5728\u56fe\u8bba\u91cc\u6709\u73b0\u6210\u7684\u540d\u5b57\u2014\u2014\u8fde\u901a\u5206\u91cf\u3002\u628a\u77ed\u8fb9\u6784\u6210\u7684\u5b50\u56fe\u5355\u72ec\u62ff\u51fa\u6765，\u6bcf\u4e2a\u8fde\u901a\u5206\u91cf\u91cc\u7684\u6240\u6709\u70b9，\u6700\u7ec8\u90fd\u8981\u5408\u5e76\u6210\u540c\u4e00\u4e2a\u70b9\u3002<\/p>\n

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

      \u8fd9\u5c31\u662f\u6574\u5957\u7b97\u6cd5\u7684\u6838\u5fc3\u3002\u60f3\u6e05\u695a\u8fd9\u4e00\u70b9\u4e4b\u540e，\u5269\u4e0b\u7684\u90fd\u662f\u5de5\u7a0b\u6d3b\u513f\u3002<\/p>\n

      2.5\u3001\u5408\u5e76\u4e00\u4e2a\u8fde\u901a\u5206\u91cf：\u4e09\u4ef6\u4e8b<\/h3>\n

      \u5bf9\u6bcf\u4e2a\u5305\u542b\u4e24\u4e2a\u4ee5\u4e0a\u70b9\u7684\u8fde\u901a\u5206\u91cf，\u8981\u505a\u4e09\u4ef6\u4e8b\u3002<\/p>\n

      \u7b2c\u4e00\u4ef6，\u7b97\u51fa\u8fd9\u4e2a\u5206\u91cf\u5408\u5e76\u540e\u7684\u4f4d\u7f6e\u3002<\/p>\n

      \u4fdd\u7559\u54ea\u4e00\u4e2a\u70b9\u5462？\u5982\u679c\u76f4\u63a5\u53d6\u5176\u4e2d\u4e00\u4e2a\u70b9，\u6574\u4e2a\u9aa8\u67b6\u4f1a\u671d\u90a3\u4e2a\u70b9"\u6b6a\u8fc7\u53bb"；\u53d6\u5e73\u5747\u4f4d\u7f6e（\u8d28\u5fc3）\u66f4\u7a33：<\/p>\n

      Point center{<\/span>0.0<\/span>,<\/span> 0.0<\/span>}<\/span>;<\/span>
      \nfor<\/span> (<\/span>int<\/span> idx :<\/span> comp)<\/span> {<\/span>
      \n center.<\/span>x +=<\/span> pts[<\/span>idx]<\/span>.<\/span>x;<\/span>
      \n center.<\/span>y +=<\/span> pts[<\/span>idx]<\/span>.<\/span>y;<\/span>
      \n}<\/span>
      \ncenter.<\/span>x \/=<\/span> static_cast<\/span><<\/span>double<\/span>><\/span><\/span><\/span>(<\/span>comp.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
      \ncenter.<\/span>y \/=<\/span> static_cast<\/span><<\/span>double<\/span>><\/span><\/span><\/span>(<\/span>comp.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span><\/p>\n

      \u7b2c\u4e8c\u4ef6，\u628a\u5206\u91cf\u5916\u7684\u90bb\u5c45\u6539\u63a5\u5230\u4ee3\u8868\u70b9\u4e0a\u3002<\/p>\n

      \u5206\u91cf\u91cc\u6211\u4eec\u53ea\u7559\u4e00\u4e2a\u4ee3\u8868\u70b9 rep，\u5176\u4f59\u5168\u90e8\u6807\u8bb0\u4e3a"\u5df2\u79fb\u9664"\u3002\u7136\u540e\u904d\u5386\u5b83\u4eec\u539f\u6765\u7684\u90bb\u5c45，\u51e1\u662f\u4e0d\u5728\u672c\u5206\u91cf\u5185\u7684（\u4e5f\u5c31\u662f\u8fde\u5411\u5916\u9762\u7684\u957f\u8fb9），\u4e00\u5f8b\u6539\u63a5\u5230 rep \u4e0a：<\/p>\n

      const<\/span> int<\/span> rep =<\/span> comp.<\/span>front<\/span>(<\/span>)<\/span>;<\/span>
      \npts[<\/span>rep]<\/span> =<\/span> center;<\/span>
      \nfor<\/span> (<\/span>size_t k =<\/span> 1<\/span>;<\/span> k <<\/span> comp.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>k)<\/span> removed[<\/span>comp[<\/span>k]<\/span>]<\/span> =<\/span> true<\/span>;<\/span><\/p>\n

      for<\/span> (<\/span>int<\/span> idx :<\/span> comp)<\/span> {<\/span>
      \n if<\/span> (<\/span>idx ==<\/span> rep)<\/span> continue<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> nb :<\/span> adj[<\/span>idx]<\/span>)<\/span> {<\/span>
      \n if<\/span> (<\/span>removed[<\/span>nb]<\/span> ||<\/span> nb ==<\/span> rep)<\/span> continue<\/span>;<\/span> \/\/ \u5206\u91cf\u5185\u90e8\u7684\u8fb9，\u76f4\u63a5\u4e22\u6389<\/span>
      \n adj[<\/span>rep]<\/span>.<\/span>insert<\/span>(<\/span>nb)<\/span>;<\/span>
      \n adj[<\/span>nb]<\/span>.<\/span>erase<\/span>(<\/span>idx)<\/span>;<\/span> \/\/ \u5bf9\u9762\u4e5f\u522b\u5fd8\u4e86\u6539<\/span>
      \n adj[<\/span>nb]<\/span>.<\/span>insert<\/span>(<\/span>rep)<\/span>;<\/span>
      \n }<\/span>
      \n adj[<\/span>idx]<\/span>.<\/span>clear<\/span>(<\/span>)<\/span>;<\/span>
      \n}<\/span><\/p>\n

      \u6ce8\u610f\u8fd9\u91cc\u6700\u5173\u952e\u7684\u4e00\u70b9：\u6539\u90bb\u63a5\u8868\u662f\u53cc\u5411\u7684\u3002 \u4f60\u4e0d\u4ec5\u8981\u628a nb \u6302\u5230 rep \u4e0a，\u8fd8\u5f97\u628a nb \u539f\u6765\u8bb0\u5f55\u7684 idx \u5220\u6389\u3001\u6362\u6210 rep，\u5426\u5219\u4e0b\u4e00\u6b21\u904d\u5386\u7684\u65f6\u5019，\u5b83\u4f1a\u53bb\u627e\u4e00\u4e2a\u5df2\u7ecf\u4e0d\u5b58\u5728\u7684\u70b9\u3002<\/p>\n

      \u7b2c\u4e09\u4ef6，\u6309\u90bb\u63a5\u8868\u91cd\u5efa\u70b9\u8868\u548c\u8fb9\u8868\u3002<\/p>\n

      \u56e0\u4e3a\u70b9\u5df2\u7ecf\u88ab\u79fb\u9664\u4e86，\u4e0b\u6807\u5168\u4e71\u4e86，\u6240\u4ee5\u5e72\u8106\u6574\u4e2a\u91cd\u5efa\u4e00\u904d：\u5148\u7ed9\u5269\u4e0b\u7684\u70b9\u91cd\u65b0\u7f16\u53f7，\u518d\u7528\u4e00\u4e2a set<pair<int,int>> \u6536\u96c6\u53bb\u91cd\u540e\u7684\u8fb9\u3002\u8fd9\u91cc\u7528 edgeSet \u800c\u4e0d\u662f\u76f4\u63a5\u585e\u8fdb vector，\u662f\u4e3a\u4e86\u9632\u6b62\u540c\u4e00\u6761\u8fb9\u88ab\u5b58\u4e24\u6b21\u2014\u2014\u6bd5\u7adf\u90bb\u63a5\u8868\u91cc u \u6709 v\u3001v \u4e5f\u6709 u，\u904d\u5386\u4e24\u904d\u5c31\u4f1a\u91cd\u590d\u3002\u81f3\u4e8e BFS \u627e\u8fde\u901a\u5206\u91cf\u7684\u90e8\u5206，\u5c31\u662f\u6700\u57fa\u7840\u7684\u5e7f\u641c，\u8fd9\u91cc\u5c31\u4e0d\u5c55\u5f00\u8bb2\u4e86\u3002<\/p>\n

      2.6\u3001\u4e3a\u4ec0\u4e48\u5916\u9762\u8fd8\u8981\u5957\u4e00\u4e2a while？<\/h3>\n

      \u8fd8\u6709\u4e00\u4e2a\u5f88\u5bb9\u6613\u88ab\u5ffd\u7565\u7684\u70b9：\u5408\u5e76\u4f1a\u8ba9\u4ee3\u8868\u70b9\u79fb\u52a8\u4f4d\u7f6e，\u800c\u79fb\u52a8\u4e4b\u540e，\u53ef\u80fd\u53c8\u51fa\u73b0\u4e86\u65b0\u7684\u77ed\u8fb9\u3002 \u6bd4\u5982 A \u548c B \u5408\u5e76\u540e，\u65b0\u7684\u70b9\u66f4\u9760\u8fd1 C \u4e86，\u539f\u672c\u4e0d\u7b97\u77ed\u7684 A-C \u53d8\u6210\u4e86\u77ed\u8def\u3002\u6240\u4ee5\u6574\u4e2a\u8fc7\u7a0b\u5fc5\u987b\u5faa\u73af\u6267\u884c，\u76f4\u5230\u67d0\u4e00\u8f6e\u91cc\u4e00\u6761\u77ed\u8fb9\u90fd\u627e\u4e0d\u5230\u4e3a\u6b62：<\/p>\n

      while<\/span> (<\/span>true<\/span>)<\/span> {<\/span>
      \n \/\/ 1. \u91cd\u5efa\u90bb\u63a5\u8868<\/span>
      \n \/\/ 2. \u627e\u51fa\u6240\u6709\u77ed\u8fb9，\u4e00\u6761\u90fd\u6ca1\u6709\u5c31 break<\/span>
      \n \/\/ 3. BFS \u627e\u8fde\u901a\u5206\u91cf<\/span>
      \n \/\/ 4. \u9010\u4e2a\u5206\u91cf\u584c\u7f29<\/span>
      \n \/\/ 5. \u91cd\u5efa\u70b9\u8868\u4e0e\u8fb9\u8868<\/span>
      \n}<\/span><\/p>\n

      \u6bcf\u4e00\u8f6e\u81f3\u5c11\u4f1a\u6d88\u6389\u4e00\u4e2a\u70b9，\u6240\u4ee5\u8fd9\u4e2a\u5faa\u73af\u4e00\u5b9a\u4f1a\u5728\u6709\u9650\u8f6e\u5185\u7ed3\u675f\u3002<\/p>\n

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

      \n

      \u4e09\u3001\u5b8c\u6574\u4ee3\u7801<\/h2>\n

      \u628a\u4e0a\u9762\u7684\u601d\u8def\u62fc\u8d77\u6765，\u5c31\u662f\u6700\u7ec8\u7684\u5b9e\u73b0（\u4e3a\u4e86\u65b9\u4fbf\u9605\u8bfb，\u6211\u505a\u4e86\u4e00\u70b9\u70b9\u6574\u7406\u548c\u52a0\u56fa）：<\/p>\n

      #<\/span>include<\/span> <cmath><\/span><\/span>
      \n#<\/span>include<\/span> <queue><\/span><\/span>
      \n#<\/span>include<\/span> <set><\/span><\/span>
      \n#<\/span>include<\/span> <utility><\/span><\/span>
      \n#<\/span>include<\/span> <vector><\/span><\/span><\/p>\n

      struct<\/span> Point<\/span>
      \n{<\/span>
      \n double<\/span> x =<\/span> 0.0<\/span>;<\/span>
      \n double<\/span> y =<\/span> 0.0<\/span>;<\/span>
      \n}<\/span>;<\/span><\/p>\n

      using<\/span> Segment =<\/span> std::<\/span>pair<<\/span>Point,<\/span> Point><\/span>;<\/span><\/p>\n

      \/\/ \u4e24\u70b9\u95f4\u8ddd\u79bb<\/span>
      \ninline<\/span> double<\/span> distance<\/span>(<\/span>const<\/span> Point&<\/span> a,<\/span> const<\/span> Point&<\/span> b)<\/span> {<\/span>
      \n const<\/span> double<\/span> dx =<\/span> a.<\/span>x –<\/span> b.<\/span>x;<\/span>
      \n const<\/span> double<\/span> dy =<\/span> a.<\/span>y –<\/span> b.<\/span>y;<\/span>
      \n return<\/span> std::<\/span>sqrt<\/span>(<\/span>dx *<\/span> dx +<\/span> dy *<\/span> dy)<\/span>;<\/span>
      \n}<\/span><\/p>\n

      std::<\/span>vector<<\/span>Segment><\/span> mergeShortSegments<\/span>(<\/span>const<\/span> std::<\/span>vector<<\/span>Segment><\/span>&<\/span> segments,<\/span>
      \n double<\/span> tol,<\/span> double<\/span> eps =<\/span> 1e-9<\/span>)<\/span>
      \n{<\/span>
      \n std::<\/span>vector<<\/span>Segment><\/span> result;<\/span>
      \n if<\/span> (<\/span>segments.<\/span>empty<\/span>(<\/span>)<\/span>)<\/span> return<\/span> result;<\/span><\/p>\n

      \/\/ ———- 1. \u7ed9\u6bcf\u4e2a\u7aef\u70b9\u5206\u914d\u552f\u4e00 ID ———-<\/span>
      \n std::<\/span>vector<<\/span>Point><\/span> pts;<\/span>
      \n std::<\/span>vector<<\/span>int<\/span>><\/span> startIds,<\/span> endIds;<\/span><\/p>\n

      auto<\/span> getOrCreate =<\/span> [<\/span>&<\/span>]<\/span>(<\/span>const<\/span> Point&<\/span> p)<\/span> -><\/span> int<\/span> {<\/span>
      \n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> pts.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n if<\/span> (<\/span>distance<\/span>(<\/span>pts[<\/span>i]<\/span>,<\/span> p)<\/span> <<\/span> eps)<\/span> {<\/span>
      \n return<\/span> static_cast<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>i)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span>
      \n pts.<\/span>push_back<\/span>(<\/span>p)<\/span>;<\/span>
      \n return<\/span> static_cast<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>pts.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> –<\/span> 1<\/span>;<\/span>
      \n }<\/span>;<\/span><\/p>\n

      for<\/span> (<\/span>const<\/span> auto<\/span>&<\/span> seg :<\/span> segments)<\/span> {<\/span>
      \n int<\/span> sid =<\/span> getOrCreate<\/span>(<\/span>seg.<\/span>first)<\/span>;<\/span>
      \n int<\/span> eid =<\/span> getOrCreate<\/span>(<\/span>seg.<\/span>second)<\/span>;<\/span>
      \n if<\/span> (<\/span>sid ==<\/span> eid)<\/span> continue<\/span>;<\/span> \/\/ \u9000\u5316\u7ebf\u6bb5，\u4e22\u5f03<\/span>
      \n startIds.<\/span>push_back<\/span>(<\/span>sid)<\/span>;<\/span>
      \n endIds.<\/span>push_back<\/span>(<\/span>eid)<\/span>;<\/span>
      \n }<\/span><\/p>\n

      \/\/ ———- 2. \u53cd\u590d\u5408\u5e76，\u76f4\u5230\u6ca1\u6709\u77ed\u8fb9 ———-<\/span>
      \n while<\/span> (<\/span>true<\/span>)<\/span> {<\/span>
      \n const<\/span> int<\/span> n =<\/span> static_cast<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>pts.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span><\/p>\n

      \/\/ 2.1 \u6240\u6709\u8fb9\u6784\u6210\u7684\u90bb\u63a5\u8868<\/span>
      \n std::<\/span>vector<<\/span>std::<\/span>set<<\/span>int<\/span>>><\/span> adj<\/span>(<\/span>n)<\/span>;<\/span>
      \n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> startIds.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n int<\/span> u =<\/span> startIds[<\/span>i]<\/span>,<\/span> v =<\/span> endIds[<\/span>i]<\/span>;<\/span>
      \n if<\/span> (<\/span>u ==<\/span> v ||<\/span> distance<\/span>(<\/span>pts[<\/span>u]<\/span>,<\/span> pts[<\/span>v]<\/span>)<\/span> <<\/span> eps)<\/span> continue<\/span>;<\/span>
      \n adj[<\/span>u]<\/span>.<\/span>insert<\/span>(<\/span>v)<\/span>;<\/span>
      \n adj[<\/span>v]<\/span>.<\/span>insert<\/span>(<\/span>u)<\/span>;<\/span>
      \n }<\/span><\/p>\n

      \/\/ 2.2 \u77ed\u8fb9\u6784\u6210\u7684\u90bb\u63a5\u8868<\/span>
      \n bool<\/span> hasShort =<\/span> false<\/span>;<\/span>
      \n std::<\/span>vector<<\/span>std::<\/span>set<<\/span>int<\/span>>><\/span> shortAdj<\/span>(<\/span>n)<\/span>;<\/span>
      \n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> startIds.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n int<\/span> u =<\/span> startIds[<\/span>i]<\/span>,<\/span> v =<\/span> endIds[<\/span>i]<\/span>;<\/span>
      \n if<\/span> (<\/span>u ==<\/span> v)<\/span> continue<\/span>;<\/span>
      \n const<\/span> double<\/span> d =<\/span> distance<\/span>(<\/span>pts[<\/span>u]<\/span>,<\/span> pts[<\/span>v]<\/span>)<\/span>;<\/span>
      \n if<\/span> (<\/span>d <<\/span> tol &&<\/span> d >=<\/span> eps)<\/span> {<\/span>
      \n shortAdj[<\/span>u]<\/span>.<\/span>insert<\/span>(<\/span>v)<\/span>;<\/span>
      \n shortAdj[<\/span>v]<\/span>.<\/span>insert<\/span>(<\/span>u)<\/span>;<\/span>
      \n hasShort =<\/span> true<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span>
      \n if<\/span> (<\/span>!<\/span>hasShort)<\/span> break<\/span>;<\/span> \/\/ \u6ca1\u6709\u77ed\u8fb9\u4e86，\u6536\u5de5<\/span><\/p>\n

      \/\/ 2.3 BFS \u627e\u51fa\u77ed\u8fb9\u56fe\u7684\u8fde\u901a\u5206\u91cf<\/span>
      \n std::<\/span>vector<<\/span>char<\/span>><\/span> visited<\/span>(<\/span>n,<\/span> 0<\/span>)<\/span>;<\/span>
      \n std::<\/span>vector<<\/span>std::<\/span>vector<<\/span>int<\/span>>><\/span> comps;<\/span>
      \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n if<\/span> (<\/span>visited[<\/span>i]<\/span> ||<\/span> shortAdj[<\/span>i]<\/span>.<\/span>empty<\/span>(<\/span>)<\/span>)<\/span> continue<\/span>;<\/span>
      \n std::<\/span>vector<<\/span>int<\/span>><\/span> comp;<\/span>
      \n std::<\/span>queue<<\/span>int<\/span>><\/span> q;<\/span>
      \n q.<\/span>push<\/span>(<\/span>i)<\/span>;<\/span>
      \n visited[<\/span>i]<\/span> =<\/span> 1<\/span>;<\/span>
      \n while<\/span> (<\/span>!<\/span>q.<\/span>empty<\/span>(<\/span>)<\/span>)<\/span> {<\/span>
      \n const<\/span> int<\/span> u =<\/span> q.<\/span>front<\/span>(<\/span>)<\/span>;<\/span>
      \n q.<\/span>pop<\/span>(<\/span>)<\/span>;<\/span>
      \n comp.<\/span>push_back<\/span>(<\/span>u)<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> nb :<\/span> shortAdj[<\/span>u]<\/span>)<\/span> {<\/span>
      \n if<\/span> (<\/span>!<\/span>visited[<\/span>nb]<\/span>)<\/span> {<\/span>
      \n visited[<\/span>nb]<\/span> =<\/span> 1<\/span>;<\/span>
      \n q.<\/span>push<\/span>(<\/span>nb)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span>
      \n }<\/span>
      \n comps.<\/span>push_back<\/span>(<\/span>std::<\/span>move<\/span>(<\/span>comp)<\/span>)<\/span>;<\/span>
      \n }<\/span><\/p>\n

      \/\/ 2.4 \u6bcf\u4e2a\u8fde\u901a\u5206\u91cf\u584c\u7f29\u6210\u4e00\u4e2a\u70b9<\/span>
      \n std::<\/span>vector<<\/span>char<\/span>><\/span> removed<\/span>(<\/span>n,<\/span> 0<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>const<\/span> auto<\/span>&<\/span> comp :<\/span> comps)<\/span> {<\/span>
      \n if<\/span> (<\/span>comp.<\/span>size<\/span>(<\/span>)<\/span> <=<\/span> 1<\/span>)<\/span> continue<\/span>;<\/span><\/p>\n

      \/\/ \u7528\u8d28\u5fc3\u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u4f4d\u7f6e<\/span>
      \n Point center{<\/span>0.0<\/span>,<\/span> 0.0<\/span>}<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> idx :<\/span> comp)<\/span> {<\/span>
      \n center.<\/span>x +=<\/span> pts[<\/span>idx]<\/span>.<\/span>x;<\/span>
      \n center.<\/span>y +=<\/span> pts[<\/span>idx]<\/span>.<\/span>y;<\/span>
      \n }<\/span>
      \n center.<\/span>x \/=<\/span> static_cast<\/span><<\/span>double<\/span>><\/span><\/span><\/span>(<\/span>comp.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
      \n center.<\/span>y \/=<\/span> static_cast<\/span><<\/span>double<\/span>><\/span><\/span><\/span>(<\/span>comp.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span><\/p>\n

      const<\/span> int<\/span> rep =<\/span> comp.<\/span>front<\/span>(<\/span>)<\/span>;<\/span>
      \n pts[<\/span>rep]<\/span> =<\/span> center;<\/span>
      \n for<\/span> (<\/span>size_t k =<\/span> 1<\/span>;<\/span> k <<\/span> comp.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>k)<\/span> {<\/span>
      \n removed[<\/span>comp[<\/span>k]<\/span>]<\/span> =<\/span> 1<\/span>;<\/span>
      \n }<\/span><\/p>\n

      \/\/ \u628a\u8fde\u5411\u5916\u90e8\u7684\u8fb9\u6539\u63a5\u5230 rep \u4e0a<\/span>
      \n for<\/span> (<\/span>int<\/span> idx :<\/span> comp)<\/span> {<\/span>
      \n if<\/span> (<\/span>idx ==<\/span> rep)<\/span> continue<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> nb :<\/span> adj[<\/span>idx]<\/span>)<\/span> {<\/span>
      \n if<\/span> (<\/span>removed[<\/span>nb]<\/span> ||<\/span> nb ==<\/span> rep)<\/span> continue<\/span>;<\/span>
      \n adj[<\/span>rep]<\/span>.<\/span>insert<\/span>(<\/span>nb)<\/span>;<\/span>
      \n adj[<\/span>nb]<\/span>.<\/span>erase<\/span>(<\/span>idx)<\/span>;<\/span>
      \n adj[<\/span>nb]<\/span>.<\/span>insert<\/span>(<\/span>rep)<\/span>;<\/span>
      \n }<\/span>
      \n adj[<\/span>idx]<\/span>.<\/span>clear<\/span>(<\/span>)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span><\/p>\n

      \/\/ 2.5 \u6309\u90bb\u63a5\u8868\u91cd\u5efa\u70b9\u8868\u548c\u8fb9\u8868<\/span>
      \n std::<\/span>vector<<\/span>Point><\/span> newPts;<\/span>
      \n std::<\/span>vector<<\/span>int<\/span>><\/span> oldToNew<\/span>(<\/span>n,<\/span> –<\/span>1<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n if<\/span> (<\/span>!<\/span>removed[<\/span>i]<\/span>)<\/span> {<\/span>
      \n oldToNew[<\/span>i]<\/span> =<\/span> static_cast<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>newPts.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
      \n newPts.<\/span>push_back<\/span>(<\/span>pts[<\/span>i]<\/span>)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span><\/p>\n

      std::<\/span>set<<\/span>std::<\/span>pair<<\/span>int<\/span>,<\/span> int<\/span>>><\/span> edgeSet;<\/span>
      \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n if<\/span> (<\/span>removed[<\/span>i]<\/span>)<\/span> continue<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> nb :<\/span> adj[<\/span>i]<\/span>)<\/span> {<\/span>
      \n if<\/span> (<\/span>removed[<\/span>nb]<\/span> ||<\/span> nb ==<\/span> i)<\/span> continue<\/span>;<\/span>
      \n int<\/span> a =<\/span> oldToNew[<\/span>i]<\/span>,<\/span> b =<\/span> oldToNew[<\/span>nb]<\/span>;<\/span>
      \n if<\/span> (<\/span>a ><\/span> b)<\/span> std::<\/span>swap<\/span>(<\/span>a,<\/span> b)<\/span>;<\/span>
      \n edgeSet.<\/span>insert<\/span>(<\/span>{<\/span>a,<\/span> b}<\/span>)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span><\/p>\n

      pts =<\/span> std::<\/span>move<\/span>(<\/span>newPts)<\/span>;<\/span>
      \n startIds.<\/span>clear<\/span>(<\/span>)<\/span>;<\/span>
      \n endIds.<\/span>clear<\/span>(<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>const<\/span> auto<\/span>&<\/span> e :<\/span> edgeSet)<\/span> {<\/span>
      \n startIds.<\/span>push_back<\/span>(<\/span>e.<\/span>first)<\/span>;<\/span>
      \n endIds.<\/span>push_back<\/span>(<\/span>e.<\/span>second)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span><\/p>\n

      \/\/ ———- 3. \u8fd8\u539f\u6210\u7ebf\u6bb5\u5217\u8868 ———-<\/span>
      \n result.<\/span>reserve<\/span>(<\/span>startIds.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> startIds.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n result.<\/span>push_back<\/span>(<\/span>{<\/span>pts[<\/span>startIds[<\/span>i]<\/span>]<\/span>,<\/span> pts[<\/span>endIds[<\/span>i]<\/span>]<\/span>}<\/span>)<\/span>;<\/span>
      \n }<\/span>
      \n return<\/span> result;<\/span>
      \n}<\/span><\/p>\n

      \n

      \u56db\u3001\u51e0\u4e2a\u5bb9\u6613\u8e29\u7684\u5751<\/h2>\n

      \u4ee3\u7801\u672c\u8eab\u4e0d\u957f，\u4f46\u91cc\u9762\u6709\u51e0\u4e2a\u5730\u65b9\u662f\u6211\u6539\u4e86\u597d\u51e0\u904d\u624d\u5199\u5bf9\u7684，\u5355\u72ec\u5217\u51fa\u6765\u3002 \u7b2c\u4e00\u4e2a，\u6d6e\u70b9\u6570\u6c38\u8fdc\u4e0d\u8981\u7528 == \u6bd4\u8f83\u3002 \u5224\u65ad\u4e24\u4e2a\u70b9\u662f\u4e0d\u662f\u540c\u4e00\u4e2a\u70b9\u3001\u5224\u65ad\u4e00\u6761\u7ebf\u6bb5\u662f\u4e0d\u662f\u96f6\u957f\u5ea6，\u7edf\u7edf\u8981\u7528 eps\u3002\u6211\u4e00\u5f00\u59cb\u5c31\u662f\u5728\u8fd9\u91cc\u683d\u4e86\u8ddf\u5934：\u7406\u8bba\u4e0a\u540c\u4e00\u4e2a\u70b9，\u8fd0\u7b97\u4e4b\u540e\u5dee\u4e86 1e-16，\u7ed3\u679c\u88ab\u5224\u6210\u4e24\u4e2a\u4e0d\u540c\u7684\u70b9，\u56fe\u4e0a\u51ed\u7a7a\u591a\u51fa\u4e00\u5806\u5b64\u7acb\u8282\u70b9\u3002 \u7b2c\u4e8c\u4e2a，\u9000\u5316\u7ebf\u6bb5\u8981\u63d0\u524d\u4e22\u6389\u3002 \u5982\u679c\u4e00\u6761\u7ebf\u6bb5\u7684\u4e24\u7aef\u88ab\u5224\u5b9a\u6210\u540c\u4e00\u4e2a\u70b9（sid == eid），\u5b83\u662f\u4e00\u6761\u96f6\u957f\u5ea6\u7ebf\u6bb5，\u5fc5\u987b\u63d0\u524d\u8df3\u8fc7\u3002\u5426\u5219\u5728"\u7b2c\u4e00\u8f6e\u5c31\u6ca1\u6709\u77ed\u8fb9\u3001\u76f4\u63a5\u9000\u51fa"\u7684\u60c5\u51b5\u4e0b，\u8fd9\u4e9b\u96f6\u957f\u7ebf\u6bb5\u4f1a\u88ab\u539f\u6837\u5e26\u51fa\u53bb\u2014\u2014\u56e0\u4e3a\u5b83\u5efa\u90bb\u63a5\u8868\u65f6\u5c31\u88ab u == v \u8df3\u8fc7\u4e86，\u6839\u672c\u6ca1\u673a\u4f1a\u88ab\u6e05\u7406\u3002\u8fd9\u4e2a\u5c0f bug \u5f88\u9690\u853d，\u6211\u662f\u62ff\u51e0\u7ec4\u8fb9\u754c\u6570\u636e\u6328\u4e2a\u8bd5\u624d\u53d1\u73b0\u7684\u3002 \u7b2c\u4e09\u4e2a，\u6539\u56fe\u7684\u65f6\u5019\u90bb\u63a5\u8868\u8981\u53cc\u5411\u6539\u3002 \u628a nb \u63a5\u5230 rep \u4e0a\u65f6，\u522b\u5fd8\u4e86\u628a nb \u90a3\u8fb9\u8bb0\u5f55\u7684\u65e7\u70b9\u5220\u6389\u3002\u6f0f\u6389\u8fd9\u4e00\u6b65，\u4e0b\u4e00\u6b21\u904d\u5386\u5c31\u4f1a\u8bbf\u95ee\u5230\u4e00\u4e2a\u5df2\u7ecf\u88ab\u79fb\u9664\u7684\u70b9\u3002 \u7b2c\u56db\u4e2a，\u91cd\u5efa\u8fb9\u8868\u8981\u7528 set \u53bb\u91cd\u3002 \u90bb\u63a5\u8868\u662f\u53cc\u5411\u7684，\u76f4\u63a5\u904d\u5386\u4f1a\u5f97\u5230\u4e24\u6761\u76f8\u540c\u7684\u8fb9\u3002 \u7b2c\u4e94\u4e2a，getOrCreate \u7528\u7684\u662f\u7ebf\u6027\u67e5\u627e，\u70b9\u591a\u4e86\u4f1a\u6162\u3002 \u4e0a\u9762\u4e3a\u4e86\u597d\u8bfb，\u6211\u7528\u7684\u662f"\u9010\u4e2a\u6bd4\u8f83"，\u590d\u6742\u5ea6\u662f O(P\u00b2)\u3002\u5982\u679c\u9aa8\u67b6\u91cc\u6709\u51e0\u5341\u4e07\u4e2a\u70b9，\u8fd9\u91cc\u5c31\u4f1a\u6210\u4e3a\u74f6\u9888\u3002\u5b9e\u9645\u9879\u76ee\u91cc\u53ef\u4ee5\u6362\u6210\u4e00\u4e2a\u54c8\u5e0c\u8868（\u628a\u70b9\u5750\u6807\u91cf\u5316\u5230\u7f51\u683c\u518d\u5efa\u7d22\u5f15），\u80fd\u964d\u5230\u63a5\u8fd1 O\u00a7\u3002\u8fd9\u4e00\u70b9\u6211\u5f53\u65f6\u662f\u538b\u6d4b\u4e4b\u540e\u624d\u53d1\u73b0\u8981\u4f18\u5316\u7684\u3002<\/p>\n

      \n

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