{"id":3034,"date":"2022-02-20T22:04:17","date_gmt":"2022-02-20T14:04:17","guid":{"rendered":"https:\/\/egonlin.com\/?p=3034"},"modified":"2022-02-20T22:04:17","modified_gmt":"2022-02-20T14:04:17","slug":"%e7%ac%ac%e4%ba%8c%e8%8a%82%ef%bc%9akd%e6%a0%91","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3034","title":{"rendered":"\u7b2c\u4e8c\u8282\uff1akd\u6811"},"content":{"rendered":"

kd\u6811<\/h1>\n

  k\u8fd1\u90bb\u7b97\u6cd5\u4e2d\u8bb2\u5230\u5b83\u6709\u4e00\u4e2a\u8f83\u4e3a\u81f4\u547d\u7684\u7f3a\u70b9\u5c31\u662f\u6bcf\u4e2a\u5b9e\u4f8b\u5230\u672a\u6765\u65b0\u6570\u636e\u4e4b\u95f4\u90fd\u9700\u8981\u8ba1\u7b97\u4e00\u6b21\u8ddd\u79bb\uff0c\u5982\u679c\u5b9e\u4f8b\u6570\u8d8b\u4e8e\u65e0\u7a77\uff0c\u90a3\u4e48\u8ba1\u7b97\u91cf\u662f\u5f88\u5e9e\u5927\u7684\u3002\u4f46\u662f\u6211\u4eec\u8981\u77e5\u9053\u7684\u662f\u8ba1\u7b97\u8ddd\u79bb\u662f\u4e3a\u4e86\u627e\u5230\u8ddd\u79bb\u76ee\u6807\u70b9\u6700\u8fd1\u7684$k$\u4e2a\u5b9e\u4f8b\uff0c\u90a3\u4e48\u662f\u4e0d\u662f\u6709\u53e6\u5916\u4e00\u79cd\u66f4\u597d\u7684\u65b9\u6cd5\uff0c\u80fd\u591f\u66f4\u5feb\u901f\u627e\u5230\u8fd9$k$\u4e2a\u6700\u8fd1\u7684\u5b9e\u4f8b\u5462\uff1f\u7531\u6b64kd\u6811\u88ab\u53d1\u660e\u4e86\u51fa\u6765\u3002<\/p>\n

  kd\u6811(k-dimensional tree)\u7b80\u5355\u800c\u8a00\u5c31\u662f$k$\u4e2a\u7279\u5f81\u7ef4\u5ea6\u7684\u4e8c\u53c9\u6811\uff0c\u8981\u6ce8\u610f\u8fd9\u91cc\u7684$k$\u503c\u548ck\u8fd1\u90bb\u7b97\u6cd5\u4e2d\u7684$k$\u503c\u4e0d\u540c\u3002<\/p>\n

\"\"<\/div><\/p>\n

kd\u6811\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. kd\u6811\u7684\u6784\u9020\u4e0e\u641c\u7d22<\/li>\n
  2. kd\u6811\u6d41\u7a0b<\/li>\n
  3. kd\u6811\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n

    kd\u6811\u5f15\u5165<\/h1>\n
    # kd\u6811\u5f15\u5165\u56fe\u4f8b\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\n# \u6d4b\u8bd5\u70b9\nplt.scatter(5, 6, marker='s', c='k', s=50)\nplt.text(5, 5, s='\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b(5,6)', fontproperties=font, ha='center')\n\n# \u751f\u6210\u52a8\u4f5c\u7247\nnp.random.seed(1)\naction_x1 = np.random.randint(1, 7, 15)\naction_x2 = np.random.randint(8, 17, 15)\nplt.scatter(action_x1, action_x2, marker='o', s=30, c='r', label='\u52a8\u4f5c\u7247')\n\n# \u751f\u6210\u7231\u60c5\u7247\nromance_x1 = np.random.randint(8, 17, 15)\nromance_x2 = np.random.randint(1, 7, 15)\nplt.scatter(romance_x1, romance_x2, marker='x', s=30, c='g', label='\u7231\u60c5\u7247')\n\n# \u6d4b\u8bd5\u6587\u672c\u6807\u8bb0\nplt.text(4, 11, s='A', ha='center')\nplt.text(5, 7, s='B', ha='center')\nplt.text(1, 14, s='C', ha='center')\n\nplt.xlim(0, 18)\nplt.ylim(0, 18)\nplt.xlabel('\u63a5\u543b\u955c\u5934(\u6b21)', fontproperties=font)\nplt.ylabel('\u6253\u6597\u573a\u666f(\u6b21)', fontproperties=font)\nplt.title('kd\u6811\u5f15\u5165\u56fe\u4f8b', fontproperties=font, fontsize=20)\nplt.legend(prop=font)\nplt.show()<\/code><\/pre>\n
    \"\"<\/div><\/p>\n
      \u8fd9\u91cc\u5c06\u7ee7\u7eed\u6cbf\u7528k\u8fd1\u90bb\u7b97\u6cd5\u7684\u4f8b\u5b50\u3002<\/p>\n
      \u5982\u4e0a\u56fe\u6240\u793a\uff0c\u5047\u8bbe\u73b0\u6709\u4e00\u90e8\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\uff0ck\u8fd1\u90bb\u7684\u601d\u60f3\u662f\u8ba1\u7b97\u51fa\u6570\u636e\u96c6\u4e2d\u6bcf\u4e00\u90e8\u7535\u5f71\u5230\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u7684\u8ddd\u79bb\uff0c\u4e4b\u540e\u627e\u5230$k$\u4e2a\u8fd1\u90bb\u5bf9\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u5206\u7c7b\u3002\u4f46\u662f\u53ef\u4ee5\u53d1\u73b0\u5982\u7535\u5f71C\u8fd9\u6837\u504f\u50fb\u4f4d\u7f6e\u7684\u7535\u5f71\u660e\u663e\u662f\u53ef\u4ee5\u4e0d\u7528\u8ba1\u7b97\u5b83\u4eec\u4e0e\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u7684\u8ddd\u79bb\u7684\u3002<\/p>\n
      \u90a3\u73b0\u5728\u5047\u8bbe\u6709\u6ca1\u6709\u8fd9\u4e48\u4e00\u79cd\u53ef\u80fd\uff1f\u6211\u4eec\u4e0d\u518d\u8ba1\u7b97\u6bcf\u90e8\u7535\u5f71\u5230\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u7684\u8ddd\u79bb\uff0c\u800c\u662f\u76f4\u63a5\u5f97\u5230\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u6700\u8fd1\u7684$k$\u90e8\u7535\u5f71\uff1f\u9996\u5148\u8fd9\u79cd\u5047\u8bbe\u5e94\u8be5\u4e0d\u53ef\u80fd\uff0c\u5176\u6b21\u771f\u7684\u6709\uff0c\u90a3\u8fd8\u8981\u5176\u4ed6\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u4f5c\u751a\uff1f\u90a3\u4e48\u518d\u60f3\u60f3\u80fd\u4e0d\u80fd\u901a\u8fc7\u67d0\u79cd\u65b9\u6cd5\u627e\u5230\u79bb\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u8f83\u8fd1\u7684\u7535\u5f71\u5462\uff1f\u6211\u4eec\u5047\u8bbe\u6709\u8fd9\u79cd\u65b9\u6cd5\uff0c\u5e76\u4e14\u8fd9\u79cd\u65b9\u6cd5\u88ab\u79f0\u4f5ckd\u6811\uff0c\u6211\u4eec\u770b\u770b\u5b83\u662f\u5982\u4f55\u5b9e\u73b0\u7684\u3002<\/p>\n
      \n
    1. \u6bd4\u5982kd\u6811\u627e\u5230\u7535\u5f71A\u5373\u79bb\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u8f83\u8fd1\u7684\u67d0\u90e8\u7535\u5f71\uff0c\u7136\u540e\u628a\u8ddd\u79bb\u5927\u4e8e\u7535\u5f71A\u5230\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u4e4b\u95f4\u7684\u7535\u5f71\u6392\u9664\u6389\uff0c\u6216\u8005\u662f\u7ee7\u7eed\u627e\u627e\u770b\u6709\u6ca1\u6709\u54ea\u90e8\u7535\u5f71\u5230\u300a\u672a\u77e5\u7c7b\u578b\u7684\u7535\u5f71\u300b\u7684\u8ddd\u79bb\u66f4\u8fd1\uff1f<\/li>\n
    2. \u5982\u679c\u53ef\u4ee5\u627e\u5230\u7535\u5f71A\uff0c\u5219\u4e5f\u53ef\u4ee5kd\u6811\u627e\u5230\u7535\u5f71B<\/li>\n
    3. \u9012\u5f52\u4f7f\u7528kd\u6811\u641c\u7d22\u76f4\u5230\u627e\u5230\u6700\u8fd1\u7684\u67d0\u51e0\u90e8\u7535\u5f71\uff0c\u505c\u6b62\u641c\u7d22<\/li>\n<\/ol>\n
        \u4e0a\u8ff0\u6574\u4e2a\u8fc7\u7a0b\u5176\u5b9e\u5c31\u662fkd\u6811\u5b9e\u73b0\u7684\u4e00\u4e2a\u8fc7\u7a0b\uff0c\u63a5\u4e0b\u6765\u5c06\u4ece\u7406\u8bba\u5c42\u9762\u62bd\u8c61\u7684\u8bb2\u89e3kd\u6811\u3002<\/p>\n
      kd\u6811\u8be6\u89e3<\/h1>\n
      \u6784\u9020kd\u6811<\/h2>\n
        kd\u6811\u4e3b\u8981\u662f\u4e0d\u65ad\u5730\u5212\u5206$k$\u7ef4\u7a7a\u95f4\u3002<\/p>\n
        \u5728\u4e00\u4e2a\u4e8c\u7ef4\u7a7a\u95f4\u5e73\u9762\u4e2d\uff0ckd\u6811\u5219\u662f\u4e0d\u65ad\u5730\u4f7f\u7528\u5782\u76f4\u4e8e$x$\u8f74\u6216$y$\u8f74\u7684\u76f4\u7ebf\u628a\u5e73\u9762\u5212\u5206\u6210\u4e00\u7cfb\u5217\u8f83\u5c0f\u7684\u77e9\u5f62\u3002\u5728$k$\u7ef4\u7a7a\u95f4\u4e2d\uff0ckd\u6811\u5219\u662f\u4e0d\u65ad\u5730\u7528\u5782\u76f4\u4e8e\u5750\u6807\u8f74\u7684\u8d85\u5e73\u9762\u5c06$k$\u7ef4\u7a7a\u95f4\u5207\u5206\u6210\u4e00\u7cfb\u5217\u7684$k$\u7ef4\u8d85\u77e9\u5f62\u533a\u57df\u3002<\/p>\n
        \u5047\u8bbe\u6709$m$\u4e2a\u5b9e\u4f8b$n$\u7ef4\u7279\u5f81\u7684\u6570\u636e\u96c6
      \n$$
      \nT={(x_1,y_1),(x_2,y_2),\\cdots,(x_m,y_m)}
      \n$$
      \n\u5176\u4e2d$x_i$\u662f\u5b9e\u4f8b\u7684\u7279\u5f81\u5411\u91cf\u5373$({x_i}^{(1)},{x_i}^{(2)},\\cdots,{x_i}^{(n)})$\uff0c$y_i$\u662f\u5b9e\u4f8b\u7684\u7c7b\u522b\uff0c\u6570\u636e\u96c6\u6709${c_1,c_2,\\cdots,c_j}$\u5171$j$\u4e2a\u7c7b\u522b\u3002<\/p>\n
        \n
      1. \u6784\u9020k\u7ef4\u7a7a\u95f4\u7684\u8d85\u77e9\u5f62\u533a\u57df\u3002\u5982\u679c\u662f\u6709\u4e24\u4e2a\u7279\u5f81$x_1$\u548c$x2$\u7684\u4e8c\u7ef4\u7a7a\u95f4\uff0c\u5219\u662f\u7531$(x1<\/em>{min},x1{max},x2<\/em>{min},x2_{max})$\u6784\u6210\u7684\u77e9\u5f62\u533a\u57df<\/li>\n
      2. \u9009\u62e9\u7279\u5f81$x^{(1)}$\u4e3a\u5750\u6807\u8f74\uff0c\u4ee5$T$\u4e2d\u6240\u6709\u5b9e\u4f8b\u7684$x^{(1)}$\u5750\u6807\u7684\u4e2d\u4f4d\u6570\u4f5c\u4e3a\u5207\u5206\u70b9\uff0c\u5c06\u6839\u7ed3\u70b9\u5bf9\u5e94\u7684\u8d85\u77e9\u5f62\u533a\u57df\u5207\u5206\u6210\u5de6\u53f3\u4e24\u4e2a\u5b50\u533a\u57df\u3002\u5c06$x^{(1)}$\u5bf9\u5e94\u503c\u5c0f\u4e8e\u5207\u5206\u70b9\u7684\u5b9e\u4f8b\u5212\u5165\u5de6\u5b50\u533a\u57df\uff1b\u5c06$x^{(1)}$\u5bf9\u5e94\u503c\u5927\u4e8e\u5207\u5206\u70b9\u7684\u5b9e\u4f8b\u5212\u5165\u53f3\u5b50\u533a\u57df\uff1b\u5c06\u5207\u5206\u70b9\u4fdd\u7559\u5728\u6839\u7ed3\u70b9<\/li>\n
      3. \u91cd\u590d2\u6b65\u9aa4\uff0c\u5373\u9009\u62e9$x^{(l)}, \\quad (l=1,2,\\cdots,n)$\u4e3a\u5207\u5206\u7684\u5750\u6807\u8f74\uff0c\u4ee5\u8be5\u7ed3\u70b9\u4e2d\u8fd8\u5269\u4e0b\u7684$k$\u4e2a\u5b9e\u4f8b\u7684$x^{(l)}$\u5750\u6807\u7684\u4e2d\u4f4d\u6570\u4f5c\u4e3a\u5207\u5206\u70b9\uff0c\u5c06\u8be5\u7ed3\u70b9\u5bf9\u5e94\u7684\u8d85\u77e9\u5f62\u533a\u57df\u5207\u5206\u6210\u5de6\u53f3\u4e24\u4e2a\u5b50\u533a\u57df\u3002\u5c06$x^{(l)}$\u5bf9\u5e94\u503c\u5c0f\u4e8e\u5207\u5206\u70b9\u7684\u5b9e\u4f8b\u5212\u5165\u5de6\u5b50\u533a\u57df\uff1b\u5c06$x^{(l)}$\u5bf9\u5e94\u503c\u5927\u4e8e\u5207\u5206\u70b9\u7684\u5b9e\u4f8b\u5212\u5165\u53f3\u5b50\u533a\u57df\uff1b\u5c06\u5207\u5206\u70b9\u4fdd\u7559\u5728\u8be5\u7ed3\u70b9<\/li>\n
      4. \u5207\u5272\u540e\u7684\u5b50\u533a\u57df\u6ca1\u6709\u5b9e\u4f8b\u65f6\uff0c\u5373\u65e0\u6cd5\u5212\u5206\u65f6\u7ed3\u675f<\/li>\n<\/ol>\n
          \u6784\u9020kd\u6811\u65f6\u9700\u8981\u6ce8\u610f\u5de6\u5b50\u7ed3\u70b9\u5bf9\u5e94\u5750\u6807$x^{(l)}$\u5c0f\u4e0e\u5207\u5206\u70b9\u7684$x^{(l)}$\u5750\u6807\uff0c\u53f3\u5b50\u7ed3\u70b9\u5bf9\u5e94\u5750\u6807$x^{(l)}$\u5927\u4e8e\u5207\u5206\u70b9\u7684$x^{(l)}$\u5750\u6807\u3002<\/p>\n
        \"\"<\/div><\/p>\n
        \u793a\u4f8b<\/h3>\n
          \u5047\u8bbe\u6709\u4e00\u4e2a\u4e8c\u7ef4\u7a7a\u95f4$(x_1,x_2)$\u7684\u6570\u636e\u96c6
        \n$$
        \nT = {(2,3)^T,(5,4)^T,(9,6)^T,(4,7)^T,(8,1)^T,(7,2)^T}
        \n$$
        \n  \u9996\u5148$x$\u8f74\u4e0a\u7684\u6570\u636e\u6709$(2\u30014\u30015\u30017\u30018\u30019)$\uff0c\u4e2d\u4f4d\u6570\u4e3a$7$(\u6ce8\uff1a\u5982\u679c\u4ee5$5$\u5212\u5206\u4e5f\u884c\uff0c\u4f46\u662f\u672c\u6587\u90fd\u662f\u4ee5\u8f83\u5927\u7684\u4f5c\u4e3a\u5207\u5206\u70b9\uff0c\u4f46\u662f\u4e0d\u80fd\u4ee5${\\frac{5+7}{2}}$\u5212\u5206\uff0c\u603b\u4e4b\u5212\u5206\u70b9\u7b26\u5408kd\u6811\u7684\u6784\u9020\u8981\u6c42\u5373\u53ef)\uff0c\u5219\u4ee5$x=7$\u5212\u5206\u4e00\u6b21\u77e9\u5f62\u533a\u57df\uff1b\u5de6\u5b50\u533a\u57df$y$\u8f74\u4e0a\u7684\u6570\u636e\u6709$(3\u30014\u30017)$\uff0c\u4e2d\u4f4d\u6570\u4e3a$4$\uff0c\u5219\u4ee5$y=4$\u5212\u5206\u4e00\u6b21\u6570\u636e\uff0c\u63a5\u7740\u4ee5$x$\u8f74\u4e0a\u7684\u6570\u636e\u5212\u5206\uff0c\u800c$x$\u8f74\u6570\u636e\u53ea\u5269\u4e0b$(2,4)$\uff0c\u76f4\u63a5\u4ee5$x=4$\u5212\u5206\u5de6\u5b50\u533a\u57df\u7684\u53f3\u5b50\u533a\u57df\uff0c\u4ee5$x=2$\u5212\u5206\u5de6\u5b50\u533a\u57df\u7684\u5de6\u5b50\u533a\u57df\uff1b\u53f3\u5b50\u533a\u57df$y$\u8f74\u4e0a\u6570\u636e\u6709$(1\u30016)$\uff0c\u7531\u4e8e\u5212\u5206\u70b9\u9700\u8981\u5927\u4e8e\u5de6\u5b50\u7ed3\u70b9\u7684\uff0c\u56e0\u6b64\u53f3\u5b50\u7ed3\u70b9\u4e3a$(9,6)$\uff0c\u5373\u4ee5$y=6$\u5212\u5206\u5de6\u5b50\u533a\u57df\uff0c\u63a5\u7740\u53ea\u5269\u4e0b\u4e00\u4e2a\u70b9$(8,1)$\uff0c\u53c8\u4ee5$x$\u8f74\u5212\u5206\uff0c\u5219\u4ee5$x=8$\u5212\u5206\u3002<\/p>\n
          \u901a\u8fc7\u4ee5\u4e0a\u5212\u5206\uff0c\u5373\u53ef\u5f97\u4ee5\u4e0b\u7279\u5f81\u7a7a\u95f4\u5212\u5206\u56fe\u3002<\/p>\n
        # kd\u6811\u7684\u6784\u9020\u793a\u7279\u5f81\u7a7a\u95f4\u5212\u5206\u56fe\u4f8b\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\nplt.scatter(2, 3, c='r', s=30)\nplt.text(2, 3.5, s='$(2,3)$', ha='center')\nplt.scatter(5, 4, c='r', s=30)\nplt.text(5, 4.5, s='$(5,4)$', ha='center')\nplt.scatter(9, 6, c='r', s=30)\nplt.text(9, 6.5, s='$(9,6)$', ha='center')\nplt.scatter(4, 7, c='r', s=30)\nplt.text(4, 7.5, s='$(4,7)$', ha='center')\nplt.scatter(8, 1, c='r', s=30)\nplt.text(8, 1.5, s='$(8,1)$', ha='center')\nplt.scatter(7, 2, c='r', s=30)\nplt.text(7, 2.5, s='$(7,2)$', ha='center')\n\nplt.hlines(4, 0, 7, linestyle='-', color='k')\nplt.hlines(6, 7, 10, linestyle='-', color='k')\n\nplt.vlines(2, 0, 4, linestyle='-', color='k')\nplt.vlines(4, 4, 10, linestyle='-', color='k')\nplt.vlines(7, 0, 10, linestyle='-', color='k')\nplt.vlines(8, 0, 6, linestyle='-', color='k')\n\nplt.xlim(0, 10)\nplt.ylim(0, 10)\nplt.title('kd\u6811\u6784\u9020-\u793a\u4f8b\u56fe\u4f8b1', fontproperties=font, fontsize=20)\nplt.show()<\/code><\/pre>\n
        \"\"<\/div><\/p>\n
          \u540c\u8d85\u77e9\u5f62\u533a\u57df\u5212\u5206\u4e00\u6837\u53ef\u4ee5\u6784\u9020\u5982\u4e0b\u56fe\u6240\u793a\u7684kd\u4e8c\u53c9\u6811<\/p>\n
          \u9996\u5148\u4ee5$x$\u8f74\u4f5c\u4e3a\u5212\u5206\u8f74\uff0c$x$\u8f74\u4e0a\u7684\u6570\u636e\u6709$(2\u30014\u30015\u30017\u30018\u30019)$\uff0c\u4e2d\u4f4d\u6570\u4e3a$7$\uff0c\u6839\u7ed3\u70b9\u4e3a$(7,2)$\uff0c\u5de6\u5b50\u7ed3\u70b9$(2,3)\u3001(4,7)\u3001(5,4)$\uff0c\u53f3\u5b50\u7ed3\u70b9$(8,1)\u3001(9,6)$\uff1b\u4e4b\u540e\u4ee5$y$\u8f74\u4f5c\u4e3a\u5212\u5206\u8f74\uff0c\u5de6\u5b50\u7ed3\u70b9$y$\u8f74\u6709\u6570\u636e$(3\u30014\u30017)$\uff0c\u5219\u5de6\u5b50\u7ed3\u70b9\u7684\u4e2d\u4f4d\u6570\u4e3a$4$\uff0c\u5219\u5de6\u5b50\u7ed3\u70b9$(5,4)$\uff0c\u5de6\u5b50\u7ed3\u70b9\u7684\u5de6\u5b59\u5b50\u7ed3\u70b9$(2,3)$\uff0c\u5de6\u5b50\u7ed3\u70b9\u7684\u53f3\u5b59\u5b50\u7ed3\u70b9$(4,7)$\uff1b\u53f3\u5b50\u7ed3\u70b9$y$\u8f74\u6709\u6570\u636e$(1\u30016)$\uff0c\u5219\u6709\u53f3\u5b50\u7ed3\u70b9$(9,6)$\uff0c\u53f3\u5b50\u7ed3\u70b9\u7684\u5de6\u5b59\u5b50\u7ed3\u70b9$(8,1)$\u3002<\/p>\n
        # kd\u6811\u7684\u6784\u9020kd\u4e8c\u53c9\u6811\u5f62\u6210\u56fe\u4f8b\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\nplt.scatter(20, 15, c='white', edgecolor='k', s=2000)\nplt.text(20, 14.5, s='$(7,2)$', ha='center',\n         fontsize=15, color='k', fontweight='bold')\nplt.annotate(s='', xytext=(18.5, 13.5), xy=(13.5, 11.5),\n             arrowprops=dict(arrowstyle="-", color='b'))\n\nplt.scatter(12, 10, c='white', edgecolor='k', s=2000)\nplt.text(12, 9.5, s='$(5,4)$', ha='center',\n         fontsize=15, color='k', fontweight='bold')\nplt.annotate(s='', xytext=(12, 8), xy=(9, 5),\n             arrowprops=dict(arrowstyle="-", color='b'))\n\nplt.scatter(8, 3, c='white', edgecolor='k', s=2000)\nplt.text(8, 2.5, s='$(2,3)$', ha='center',\n         fontsize=15, color='k', fontweight='bold')\n\nplt.scatter(16, 3, c='white', edgecolor='k', s=2000)\nplt.text(16, 2.5, s='$(4,7)$', ha='center',\n         fontsize=15, color='k', fontweight='bold')\nplt.annotate(s='', xytext=(12, 8), xy=(16, 5),\n             arrowprops=dict(arrowstyle="-", color='b'))\n\nplt.scatter(28, 10, c='white', edgecolor='k', s=2000)\nplt.text(28, 9.5, s='$(9,6)$', ha='center',\n         fontsize=15, color='k', fontweight='bold')\nplt.annotate(s='', xytext=(21.5, 13.5), xy=(26, 11),\n             arrowprops=dict(arrowstyle="-", color='b'))\n\nplt.scatter(24, 3, c='white', edgecolor='k', s=2000)\nplt.text(24, 2.5, s='$(8,1)$', ha='center',\n         fontsize=15, color='k', fontweight='bold')\nplt.annotate(s='', xytext=(27, 8), xy=(24.5, 5),\n             arrowprops=dict(arrowstyle="-", color='b'))\n\nplt.hlines(15, 24, 38, linestyle='--', color='r')\nplt.text(39, 14.5, ha='center', color='r', s='X', fontsize=15)\nplt.hlines(10, 32, 38, linestyle='--', color='b')\nplt.text(39, 9.5, ha='center', color='b', s='Y', fontsize=15)\nplt.hlines(3, 28, 38, linestyle='--', color='r')\nplt.text(39, 2.5, ha='center', color='r', s='X', fontsize=15)\n\nplt.xlim(-1, 40)\nplt.ylim(-1, 20)\nplt.title('kd\u6811\u6784\u9020-\u793a\u4f8b\u56fe\u4f8b2', fontproperties=font, fontsize=20)\nplt.show()<\/code><\/pre>\n
        \"\"<\/div><\/p>\n
        kd\u6811\u641c\u7d22<\/h2>\n
          \u4ece\u6839\u7ed3\u70b9\u51fa\u53d1\uff0c\u9012\u5f52\u7684\u5411\u4e0b\u8bbf\u95eekd\u6811\uff0c\u5982\u679c\u76ee\u6807\u70b9$x$\u7684$x^{(l)}$\u7ef4\u7684\u5750\u6807\u5c0f\u4e8e\u5207\u5206\u70b9\u7684\u5750\u6807\uff0c\u5219\u79fb\u52a8\u5230\u5de6\u5b50\u7ed3\u70b9\uff0c\u5426\u5219\u79fb\u52a8\u5230\u53f3\u5b50\u7ed3\u70b9\uff0c\u76f4\u5230\u5b50\u7ed3\u70b9\u4e3a\u53f6\u5b50\u7ed3\u70b9\u4e3a\u6b62\uff0c\u5e76\u5047\u8bbe\u8be5\u53f6\u5b50\u7ed3\u70b9\u4e3a\u76ee\u6807\u70b9\u7684\u5f53\u524d\u6700\u8fd1\u70b9\u3002<\/p>\n
          \u9012\u5f52\u7684\u4ece\u8be5\u53f6\u5b50\u7ed3\u70b9\u5411\u4e0a\u56de\u9000\uff0c\u5bf9\u6bcf\u4e2a\u7ed3\u70b9\u4e0a\u7684\u5b9e\u4f8b\u90fd\u8fdb\u884c\u5982\u4e0b\u64cd\u4f5c\uff1a<\/p>\n
          \n
        1. \u5982\u679c\u8be5\u5b9e\u4f8b\u5230\u76ee\u6807\u70b9\u7684\u8ddd\u79bb\u66f4\u8fd1\uff0c\u5219\u4ee5\u8be5\u5b9e\u4f8b\u70b9\u4e3a\u5f53\u524d\u6700\u8fd1\u70b9<\/li>\n
        2. \u68c0\u67e5\u5f53\u524d\u6700\u8fd1\u70b9\u7236\u7ed3\u70b9\u7684\u53e6\u4e00\u5b50\u7ed3\u70b9\u5bf9\u5e94\u7684\u533a\u57df\u662f\u5426\u6709\u66f4\u8fd1\u7684\u70b9\uff0c\u5373\u53e6\u4e00\u5b50\u7ed3\u70b9\u7684\u8d85\u77e9\u5f62\u533a\u57df\u662f\u5426\u4e0e\u4ee5\u76ee\u6807\u70b9\u4e3a\u7403\u5fc3\u3001\u4ee5\u76ee\u6807\u70b9\u5230\u5f53\u524d\u6700\u8fd1\u70b9\u7684\u534a\u5f84\u5f62\u6210\u7684\u8d85\u7403\u4f53\u662f\u5426\u76f8\u4ea4\n
            \n
          1. \u5982\u679c\u76f8\u4ea4\uff0c\u5219\u53e6\u4e00\u5b50\u7ed3\u70b9\u5bf9\u5e94\u7684\u8d85\u77e9\u5f62\u533a\u57df\u5185\u5b58\u5728\u79bb\u76ee\u6807\u70b9\u66f4\u8fd1\u7684\u70b9\uff0c\u79fb\u5230\u53e6\u4e00\u5b50\u7ed3\u70b9\u7ee7\u7eed\u9012\u5f52\u641c\u7d22<\/li>\n
          2. \u5982\u679c\u4e0d\u76f8\u4ea4\uff0c\u5219\u5411\u4e0a\u56de\u9000<\/li>\n<\/ol>\n<\/li>\n
          3. \u5f53\u56de\u9000\u5230\u6839\u7ed3\u70b9\u65f6\u7ed3\u675f\uff0c\u76ee\u6807\u70b9\u7684\u6700\u8fd1\u90bb\u70b9\u4e3a\u5f53\u524d\u6700\u8fd1\u70b9<\/li>\n<\/ol>\n
              \u4e0a\u8ff0kd\u6811\u641c\u7d22\u7684\u8fc7\u7a0b\u53ef\u4ee5\u770b\u51fa\uff0c\u7531\u4e8e\u5f88\u591a\u5b9e\u4f8b\u70b9\u6240\u5728\u7684\u8d85\u77e9\u5f62\u533a\u57df\u548c\u8d85\u7403\u4f53\u4e0d\u76f8\u4ea4\uff0c\u538b\u6839\u4e0d\u9700\u8981\u8ba1\u7b97\u8ddd\u79bb\uff0c\u6253\u6253\u8282\u7701\u4e86\u8ba1\u7b97\u65f6\u95f4\u3002<\/p>\n
              \u4f46\u662f\u503c\u5f97\u6ce8\u610f\u7684\u662fkd\u6811\u7684\u5e73\u5747\u8ba1\u7b97\u590d\u6742\u5ea6\u4e3a$O(\\log{N})$\uff0c\u5f53\u7279\u5f81\u7ef4\u6570\u63a5\u8fd1\u8bad\u7ec3\u96c6\u5b9e\u4f8b\u6570\u65f6\uff0ckd\u6811\u7684\u641c\u7d22\u6548\u7387\u5219\u4f1a\u8fc5\u901f\u4e0b\u964d\uff0c\u51e0\u4e4e\u63a5\u8fd1\u7ebf\u6027\u626b\u63cf\u3002<\/p>\n
            \u793a\u4f8b<\/h3>\n
              \u63a5\u4e0b\u6765\u5c06\u62ff\u4e0a\u4e00\u8282\u6784\u9020\u7684kd\u6811\u4e3e\u4f8bkd\u6811\u641c\u7d22\u7684\u6574\u4e2a\u8fc7\u7a0b\uff0c\u5047\u8bbe\u76ee\u6807\u70b9\u4e3a$(2,4.5)$\u3002<\/p>\n
              \n
            1. \u641c\u7d22\u76ee\u6807\u70b9\u5bf9\u5e94\u7684\u53f6\u5b50\u7ed3\u70b9\n
                \n
              1. \u4ece\u6839\u7ed3\u70b9$(7,2)$\u5f00\u59cb\u67e5\u627e\uff0c\u7531\u4e8e$(7,2)$\u662f\u7531$x=7$\u5212\u5206\u7684\uff0c\u5e76\u4e14\u76ee\u6807\u70b9\u7684$x$\u503c\u4e3a$2$\uff0c\u7531\u4e8e$2<7$\u5219\u5230\u5de6\u5b50$(5,4)$\u7ed3\u70b9<\/li>\n
              2. \u7531\u4e8e$(5,4)$\u662f\u7531$y=4$\u5206\u9694\u8d85\u5e73\u9762\u7684\uff0c\u5e76\u4e14\u76ee\u6807\u70b9\u7684$y$\u503c\u4e3a$4.5$\uff0c\u7531\u4e8e$4.5>4$\u5219\u5230\u53f3\u5b50$(4,7)$\u53f6\u5b50\u7ed3\u70b9<\/li>\n
              3. \u5047\u8bbe$(4,7)$\u53f6\u5b50\u7ed3\u70b9\u4e3a\u5f53\u524d\u6700\u8fd1\u7ed3\u70b9<\/li>\n
              4. \u76ee\u6807\u6389\u641c\u7d22\u5230\u53f6\u5b50\u7ed3\u70b9\u7684\u8def\u5f84\u4e3a$(7,2)\\rightarrow(5,4)\\rightarrow(4,7)$<\/li>\n<\/ol>\n<\/li>\n
              5. \u641c\u7d22\u76ee\u6807\u70b9\u5bf9\u5e94\u7684\u5f53\u524d\u6700\u8fd1\u70b9\n
                  \n
                1. \u5f53\u524d\u6700\u8fd1\u7ed3\u70b9$(4,7)$\u5230\u76ee\u6807\u70b9\u7684\u8ddd\u79bb\u4e3a$3.2$\uff0c\u800c\u5f53\u524d\u6700\u8fd1\u7ed3\u70b9\u7684\u7236\u8282\u70b9$(5,4)$\u5230\u76ee\u6807\u70b9\u7684\u8ddd\u79bb\u4e3a$3.0$\uff0c\u5219\u5f53\u524d\u6700\u8fd1\u7ed3\u70b9\u66f4\u65b0\u4e3a$(5,4)$<\/li>\n
                2. \u4ee5\u4e0b\u56fe\u84dd\u8272\u4e94\u89d2\u661f\u76ee\u6807\u70b9$(2,4.5)$\u4e3a\u5706\u5fc3\uff0c\u4ee5\u5f53\u524d\u6700\u8fd1\u7ed3\u70b9$(5\uff0c4)$\u5230\u76ee\u6807\u70b9\u7684\u8ddd\u79bb$3.0$\u4e3a\u534a\u5f84\u505a\u4e00\u4e2a\u8d85\u7403\u4f53\uff0c\u5373\u4e0b\u56fe\u7684\u7ea2\u8272\u5706\u5708<\/li>\n
                3. \u53ef\u4ee5\u53d1\u73b0\u7ea2\u8272\u5706\u5708\u548c$y=4$\u8d85\u5e73\u9762\u76f8\u4ea4\uff0c\u56e0\u6b64\u8fdb\u5165$(5,4)$\u7684\u5de6\u5b50\u7ed3\u70b9\u67e5\u627e\uff0c\u5373\u627e\u5230$(2,3)$<\/li>\n
                4. \u8ba1\u7b97$(2,3)$\u5230\u76ee\u6807\u70b9\u7684\u8ddd\u79bb\u4e3a$1.5$\uff0c\u5219\u5f53\u524d\u6700\u8fd1\u7ed3\u70b9\u66f4\u65b0\u4e3a$(2,3)$<\/li>\n
                5. \u4ee5\u4e0b\u56fe\u84dd\u8272\u4e94\u89d2\u661f\u76ee\u6807\u70b9$(2,4.5)$\u4e3a\u5706\u5fc3\uff0c\u4ee5\u5f53\u524d\u6700\u8fd1\u7ed3\u70b9$(2\uff0c3)$\u5230\u76ee\u6807\u70b9\u7684\u8ddd\u79bb$1.5$\u4e3a\u534a\u5f84\u505a\u4e00\u4e2a\u8d85\u7403\u4f53\uff0c\u5373\u4e0b\u56fe\u7684\u7eff\u8272\u5706\u5708<\/li>\n
                6. \u7531\u4e8e\u7ed3\u70b9$(2,3)$\u4e3a\u53f6\u5b50\u7ed3\u70b9\uff0c\u5f00\u59cb\u6cbf\u7236\u7ed3\u70b9\u56de\u6eaf\uff0c\u7236\u7ed3\u70b9$(5,4)$\u5df2\u7ecf\u8003\u8651\u8fc7\uff0c\u7ee7\u7eed\u5f80\u4e0a\u56de\u6eaf\u5230$(7,2)$<\/li>\n
                7. \u7eff\u8272\u5706\u5708\u548c$x=7$\u6ca1\u6709\u76f8\u4ea4\uff0c\u53c8\u7531\u4e8e$(7,2)$\u4e3a\u6839\u8282\u70b9\uff0c\u641c\u7d22\u7ed3\u675f<\/li>\n
                8. \u901a\u8fc7\u4e0a\u8ff0\u641c\u7d22\u76ee\u6807\u70b9\u6700\u8fd1\u70b9\u4e3a$(2,3)$\uff0c\u6700\u8fd1\u8ddd\u79bb\u4e3a$1.5$<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
                    \u503c\u5f97\u6ce8\u610f\u7684\u662f\u4e0a\u8ff0\u90fd\u662f\u4ee5\u6700\u8fd1\u90bb\u5c55\u5f00\u8ba8\u8bbakd\u6811\u7684\uff0c\u5982\u679c\u60f3\u5f97\u5230$k$\u4e2a\u8fd1\u90bb\uff0c\u53ea\u9700\u8981\u6700\u540e\u4fdd\u7559$k$\u4e2a\u6700\u8fd1\u90bb\u7684\u7ed3\u70b9\u4e0a\u7684\u5b9e\u4f8b\u70b9\u5373\u53ef\uff0c\u4e4b\u540e\u4f9d\u636e\u591a\u6570\u8868\u51b3\u6cd5\u5373\u53ef\u83b7\u5f97\u76ee\u6807\u70b9\u7684\u7c7b\u522b\uff1b\u5982\u679c\u662f\u56de\u5f52\u95ee\u9898\uff0c\u53d6$k$\u4e2a\u8fd1\u90bb\u70b9\u7684\u6807\u8bb0\u503c\u7684\u5e73\u5747\u6570\u6216\u4e2d\u4f4d\u6570\u5373\u53ef\u3002<\/p>\n
                  <\/p>\n
                  # kd\u6811\u7684\u6784\u9020\u793a\u7279\u5f81\u7a7a\u95f4\u5212\u5206\u56fe\u4f8b\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\nplt.scatter(2, 3, c='r', s=30)\nplt.text(2, 3.5, s='$(2,3)$', ha='center')\nplt.scatter(5, 4, c='r', s=30)\nplt.text(5, 4.5, s='$(5,4)$', ha='center')\nplt.scatter(9, 6, c='r', s=30)\nplt.text(9, 6.5, s='$(9,6)$', ha='center')\nplt.scatter(4, 7, c='r', s=30)\nplt.text(4, 7.5, s='$(4,7)$', ha='center')\nplt.scatter(8, 1, c='r', s=30)\nplt.text(8, 1.5, s='$(8,1)$', ha='center')\nplt.scatter(7, 2, c='r', s=30)\nplt.text(7, 2.5, s='$(7,2)$', ha='center')\n\nplt.hlines(4, 0, 7, linestyle='-', color='k')\nplt.hlines(6, 7, 10, linestyle='-', color='k')\n\nplt.vlines(2, 0, 4, linestyle='-', color='k')\nplt.vlines(4, 4, 10, linestyle='-', color='k')\nplt.vlines(7, 0, 10, linestyle='-', color='k')\nplt.vlines(8, 0, 6, linestyle='-', color='k')\n\nplt.scatter(2, 4.5, s=30410, c='white', edgecolor='r')\nplt.scatter(2, 4.5, s=15000, c='white', edgecolor='g')\nplt.scatter(2, 4.5, s=50, c='b', marker='*')\nplt.text(2, 5, s='\u76ee\u6807\u70b9$(2,4.5)$', ha='center',fontproperties=font)\nplt.scatter(2, 3, c='r', s=30)\nplt.scatter(4, 7, c='r', s=30)\n\nplt.xlim(0, 10)\nplt.ylim(0, 10)\nplt.title('kd\u6811\u641c\u7d22-\u793a\u4f8b\u56fe\u4f8b', fontproperties=font, fontsize=20)\nplt.show()<\/code><\/pre>\n
                  \"\"<\/div><\/p>\n
                  kd\u6811\u6d41\u7a0b<\/h1>\n
                  \u8f93\u5165<\/h2>\n
                    \u6709$m$\u4e2a\u5b9e\u4f8b$n$\u7ef4\u7279\u5f81\u7684\u6570\u636e\u96c6
                  \n$$
                  \nT={(x_1,y_1),(x_2,y_2),\\cdots,(x_m,y_m)}
                  \n$$
                  \n\u5176\u4e2d$x_i$\u662f\u5b9e\u4f8b\u7684\u7279\u5f81\u5411\u91cf\u5373$({x_i}^{(1)},{x_i}^{(2)},\\cdots,{x_i}^{(n)})$\u3002<\/p>\n
                  \u8f93\u51fa<\/h2>\n
                    \u8ddd\u79bb\u76ee\u6807\u70b9\u6700\u8fd1\u7684$k$\u4e2a\u5b9e\u4f8b\u53ca$k$\u4e2a\u5b9e\u4f8b\u5230\u76ee\u6807\u70b9\u7684\u8ddd\u79bb\u3002<\/p>\n
                  \u6d41\u7a0b<\/h2>\n
                    \n
                  1. \u6784\u9020kd\u6811<\/li>\n
                  2. \u641c\u7d22\u79bb\u76ee\u6807\u70b9\u6700\u8fd1\u7684$k$\u4e2a\u5b9e\u4f8b\u70b9<\/li>\n
                  3. \u5206\u7c7b\u95ee\u9898\u4f9d\u636e\u591a\u6570\u8868\u51b3\u6cd5\u5373\u53ef\u83b7\u5f97\u76ee\u6807\u70b9\u7684\u7c7b\u522b\uff1b\u5982\u679c\u662f\u56de\u5f52\u95ee\u9898\uff0c\u53d6 ? \u4e2a\u8fd1\u90bb\u70b9\u7684\u6807\u8bb0\u503c\u7684\u5e73\u5747\u6570\u6216\u4e2d\u4f4d\u6570\u5373\u53ef\u3002<\/li>\n<\/ol>\n
                    kd\u6811\u4f18\u7f3a\u70b9<\/h1>\n
                    \u4f18\u70b9<\/h2>\n
                      \n
                    1. \u7b80\u5355\u6613\u61c2\uff0c\u5bb9\u6613\u5b9e\u73b0\uff0c\u53ef\u4ee5\u505a\u5206\u7c7b\u4e5f\u53ef\u4ee5\u505a\u56de\u5f52<\/li>\n
                    2. \u57fa\u4e8e\u5b9e\u4f8b\u5b66\u4e60\uff0c\u5bf9\u6570\u636e\u6ca1\u6709\u5047\u8bbe\uff0c\u4e0d\u9700\u8981\u901a\u8fc7\u6a21\u578b\u8bad\u7ec3\u83b7\u5f97\u53c2\u6570<\/li>\n
                    3. \u8f83\u4e8ek\u8fd1\u90bb\u7b97\u6cd5\u8ba1\u7b97\u91cf\u51cf\u5c11\u4e86<\/li>\n<\/ol>\n
                      \u7f3a\u70b9<\/h2>\n
                        \n
                      1. \u65e0\u8bba\u54ea\u4e00\u79cd\u8ddd\u79bb\u5ea6\u91cf\u65b9\u5f0f\u90fd\u9700\u8981\u4f7f\u7528\u5230\u7279\u5f81\u503c\u4e4b\u95f4\u7684\u5dee\u503c\uff0c\u5982\u679c\u67d0\u4e9b\u7279\u5f81\u503c\u4e4b\u95f4\u7684\u5dee\u503c\u8fc7\u5927\u4f1a\u63a9\u76d6\u5dee\u503c\u8f83\u5c0f\u7279\u5f81\u5bf9\u9884\u6d4b\u503c\u7684\u5f71\u54cd(\u4e00\u822c\u4f7f\u7528\u6570\u636e\u9884\u5904\u7406\u4e2d\u7684\u5f52\u4e00\u5316\u65b9\u6cd5\u5904\u7406\u7279\u5f81\u503c)<\/li>\n
                      2. kd\u6811\u7684\u5efa\u7acb\u9700\u8981\u5927\u91cf\u7684\u5185\u5b58\u6d88\u8017(\u6362\u5185\u5b58\u5427\uff01\uff01\uff01)<\/li>\n
                      3. \u76f8\u6bd4\u8f83\u51b3\u7b56\u6811\uff0c\u89e3\u91ca\u578b\u4e0d\u5f3a(\u5ba2\u6237\u771f\u7684\u60f3\u8981\u89e3\u91ca\u6027\u5f3a\u7684\u6a21\u578b\u53ef\u4ee5\u6362\u51b3\u7b56\u6811\u8bd5\u4e00\u8bd5)<\/li>\n<\/ol>\n
                        \u5c0f\u7ed3<\/h1>\n
                          kd\u6811\u66f4\u591a\u7684\u4f7f\u7528\u4e86\u4e8c\u53c9\u6811\u7684\u601d\u8def\uff0c\u5f53\u7136\u5b83\u4e5f\u5f88\u597d\u7684\u5b9e\u73b0\u4e86\u6211\u4eec\u60f3\u8981\u5b9e\u73b0\u7684\uff0c\u8fd9\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n
                          \u5982\u679c\u4f60\u7ec6\u5fc3\u7684\u8bdd\uff0c\u53ef\u4ee5\u53d1\u73b0\u5728\u641c\u7d22\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5982\u679c\u8d85\u7403\u4f53\u78b0\u5230\u4e86\u8d85\u77e9\u5f62\u7684\u4e00\u70b9\u68f1\u89d2\u5c31\u9700\u8981\u53bb\u641c\u7d22\u8d85\u77e9\u5f62\u533a\u57df\u5185\u6709\u6ca1\u6709\u79bb\u76ee\u6807\u70b9\u66f4\u8fd1\u7684\u70b9\uff0c\u5f53\u7136\u6709\u89e3\u51b3\u65b9\u6cd5\uff0c\u53ef\u4ee5\u4f7f\u7528\u7403\u6811(ball tree)\uff0c\u4f46\u662f\u5176\u5b9e\u8f83kd\u6811\u5e76\u6ca1\u6709\u90a3\u4e48\u660e\u663e\u7684\u4f18\u5316\uff0c\u8fd9\u91cc\u5c31\u4e0d\u591a\u53d9\u8ff0\u4e86\u3002\u7b80\u800c\u8a00\u4e4b\u5c31\u662f\u7403\u6811\u76f8\u8f83\u4e8ekd\u6811\u4f7f\u7528\u7684\u662f\u8d85\u7403\u4f53\u5207\u5272\u6570\u636e\u96c6\uff0c\u6709\u5174\u8da3\u7684\u53ef\u4ee5\u81ea\u5df1\u601d\u8003\u601d\u8003(\u5148\u6784\u9020\u4e00\u4e2a\u6700\u5c0f\u7403\u4f53\u5305\u542b\u6240\u6709\u6570\u636e\uff0c\u7136\u540e\u9012\u5f52\u6784\u9020\u5c0f\u7403\u4f53\u2014\u2014\u5148\u9009\u62e9\u4e00\u4e2a\u79bb\u7b2c\u4e00\u4e2a\u7403\u4f53\u4e2d\u5fc3\u6700\u8fdc\u7684\u70b9A\uff0c\u518d\u9009\u62e9\u4e00\u4e2a\u79bb\u70b9A\u6700\u8fdc\u7684\u70b9B\uff0c\u90a3\u4e2a\u6570\u636e\u79bb\u54ea\u4e2a\u70b9\u8fd1\u5219\u5c5e\u4e8e\u54ea\u4e00\u4e2a\u70b9\u7684\u90a3\u4e00\u7c7b\uff0c\u8fd9\u6837\u5c31\u5b8c\u7f8e\u628a\u4e00\u4e2a\u7403\u4f53\u5207\u5206\u6210\u4e24\u4e2a\u7403\u4f53)\u3002<\/p>\n
                          kd\u6811\u8bb2\u5b8c\uff0ck\u8fd1\u90bb\u4e5f\u5c31\u544a\u4e00\u6bb5\u843d\u4e86\u3002\u4e0b\u4e00\u7bc7\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u542c\u8d77\u6765\u53ef\u80fd\u548c\u4f20\u7edf\u7b97\u6cd5\u4e2d\u7684\u6811\u7ed3\u6784\u6709\u5173\uff0c\u4f46\u5b83\u5230\u5e95\u662f\u4e0d\u662f\u4e00\u4e2a\u6811\u7ed3\u6784\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u5462\uff1f\u770b\u5b8c\u4e86\u5c31\u77e5\u9053\u4e86\u2014\u2014\u51b3\u7b56\u6811\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
                        kd\u6811   k\u8fd1\u90bb\u7b97\u6cd5\u4e2d\u8bb2\u5230\u5b83\u6709\u4e00\u4e2a\u8f83\u4e3a\u81f4\u547d\u7684\u7f3a\u70b9\u5c31\u662f\u6bcf\u4e2a\u5b9e\u4f8b\u5230\u672a\u6765\u65b0\u6570\u636e\u4e4b\u95f4\u90fd\u9700\u8981\u8ba1\u7b97\u4e00 […]<\/p>\n","protected":false},"author":3,"featured_media":3038,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,288],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3034"}],"collection":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3034"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3034\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/3038"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}