{"id":99224,"date":"2026-09-02T07:01:09","date_gmt":"2026-09-01T23:01:09","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/99224.html"},"modified":"2026-09-02T07:01:09","modified_gmt":"2026-09-01T23:01:09","slug":"%e3%80%90%e8%ae%a1%e7%ae%97%e5%87%a0%e4%bd%95-%e5%8d%81%e4%ba%8c%e7%ab%a0%e3%80%91%e7%a9%ba%e9%97%b4%e4%ba%8c%e5%88%86%ef%bc%9a%e7%94%bb%e5%ae%b6%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/99224.html","title":{"rendered":"\u3010\u8ba1\u7b97\u51e0\u4f55 \u5341\u4e8c\u7ae0\u3011\u7a7a\u95f4\u4e8c\u5206\uff1a\u753b\u5bb6\u7b97\u6cd5"},"content":{"rendered":"

\u672c\u6587\u6d89\u53ca\u77e5\u8bc6\u70b9<\/h2>\n

\u6570\u5b66 \u51e0\u4f55<\/p>\n

\u9884\u5907\u77e5\u8bc6<\/h2>\n

O (Big O)：\u8868\u793a\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6，\u63cf\u8ff0\u7684\u662f\u7b97\u6cd5\u7684\u4e0a\u9650\u6216\u6700\u5dee\u8868\u73b0\u3002 \u03a9 (Big Omega)：\u8868\u793a\u6700\u597d\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6，\u63cf\u8ff0\u7684\u662f\u7b97\u6cd5\u7684\u4e0b\u9650\u6216\u6700\u4f73\u8868\u73b0\u3002 \u0398(1) \u2014 \u786e\u754c（\u7d27\u786e\u754c）\u5b83\u8868\u793a\u7b97\u6cd5\u7684\u8fd0\u884c\u65f6\u95f4\u65e2\u4e0d\u4f1a\u8d85\u8fc7\u67d0\u4e2a\u5e38\u6570，\u4e5f\u4e0d\u4f1a\u4f4e\u4e8e\u53e6\u4e00\u4e2a\u5e38\u6570\u3002 \u5706\u76d8：\u5706\u4e0a\u7684\u70b9\u548c\u5706\u5185\u7684\u70b9，\u662f\u4e00\u4e2a\u533a\u57df\u800c\u4e0d\u662f\u66f2\u7ebf\u3002 \u5947\u6570x，x\/2+x\/2+1=x；\u5076\u6570x,x\/2+x\/2=x\u3002<\/p>\n

\u77e9\u5f62\u4e0d\u8d85\u8fc72k\u4e2a\u70b9<\/h3>\n

\u4e00\u5b9a\u5b58\u5728\u5408\u7406\u5212\u5206，\u4f7f\u5f97\u56db\u4e2a\u8c61\u9650\u7684\u70b9\u90fd\u4e0d\u8d85\u8fc7k\u3002 \u4efb\u610f\u6c34\u5e73\u76f4\u7ebfl\u4e0a\u6709c2\u4e2a\u70b9，\u76f4\u7ebf\u4e0a\u6709c1\u4e2a\u70b9，\u76f4\u7ebf\u4e0b\u6709c3\u4e2a\u70b9\u3002\u4f7fmax(c1,c3)\u5c3d\u5feb\u7684\u5927，\u4e14max(c1,c3) <\/p>\n

\u2264<\/p>\n

\\\\le<\/p>\n

<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span> c2+Min(c1,c3)\u3002 \u4e0d\u5931\u4e00\u822c\u6027，\u4ee4<\/p>\n

c<\/p>\n

1<\/p>\n

\u2264<\/p>\n

c<\/p>\n

3<\/p>\n

c1 \\\\le c3<\/p>\n

<\/span><\/span>c<\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>c<\/span>3<\/span><\/span><\/span><\/span><\/span>\u4e14c1\u5728\u4e0a\u65b9，c3\u5728\u4e0b\u65b9\u3002c1\u53cac2\u4e00\u4e2a\u533a\u5206，c3\u4e00\u4e2a\u533a\u57df\u3002\u7531\u4e8ec3\u6240\u5728\u533a\u57df\u70b9\u6570<\/p>\n

\u2264<\/p>\n

k<\/p>\n

\\\\le k<\/p>\n

<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>，\u6545\u53ea\u9700\u8981\u8003\u8651\u4e0a\u534a\u533a\u57df，\u5373c1\u548cc2\u6240\u5728\u533a\u57df\u3002 \u4e00，c2\u662f\u5076\u6570，\u5219<\/p>\n

c<\/p>\n

1<\/p>\n

\u2265<\/p>\n

c<\/p>\n

3<\/p>\n

c1 \\\\ge c3<\/p>\n

<\/span><\/span>c<\/span>1<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>c<\/span>3<\/span><\/span><\/span><\/span><\/span>\u3002\u9009\u62e9\u4efb\u610f\u5782\u7ebf，\u5c06c2\u4e0a\u7684\u70b9\u5e73\u5206\u3002\u5047\u5b9ac1\u7684\u70b9\u5168\u90e8\u5206\u5230\u5de6\u4e0a，\u5219\u5de6\u4e0a\u7684\u70b9\u6570：<\/p>\n

c<\/p>\n

1<\/p>\n

+<\/p>\n

c<\/p>\n

2<\/p>\n

\/<\/p>\n

2<\/p>\n

\u2264<\/p>\n

c<\/p>\n

3<\/p>\n

+<\/p>\n

c<\/p>\n

2<\/p>\n

\/<\/p>\n

2<\/p>\n

c1+c2\/2 \\\\le c3+c2\/2<\/p>\n

<\/span><\/span>c<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>c<\/span>2\/2<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>c<\/span>3<\/span><\/span>+<\/span><\/span><\/span><\/span>c<\/span>2\/2<\/span><\/span><\/span><\/span><\/span>\u3002\u4e24\u8005\u76f8\u52a0\u662f<\/p>\n

2<\/p>\n

k<\/p>\n

，\u6545<\/p>\n

c<\/p>\n

1<\/p>\n

+<\/p>\n

c<\/p>\n

2<\/p>\n

\/<\/p>\n

2<\/p>\n

\u2264<\/p>\n

k<\/p>\n

2k，\u6545c1+c2\/2 \\\\le k<\/p>\n

<\/span><\/span>2<\/span>k<\/span>，\u6545<\/span>c<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>c<\/span>2\/2<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u3002 \u4e8c,c2\u662f\u5947\u6570，\u5219<\/p>\n

c<\/p>\n

1<\/p>\n

+<\/p>\n

1<\/p>\n

\u2264<\/p>\n

c<\/p>\n

3<\/p>\n

c1+1 \\\\le c3<\/p>\n

<\/span><\/span>c<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>c<\/span>3<\/span><\/span><\/span><\/span><\/span>\u9009\u62e9\u4efb\u610f\u5782\u7ebf，\u5c06c2\u4e0a\u7684\u70b9\u5e73\u5206\u3002\u6211\u4eec\u5047\u8bbec1\u7684\u70b9\u5168\u90e8\u843d\u5728c2\u70b9\u591a\u7684\u533a\u57df，\u5373\u5171\u6709<\/p>\n

c<\/p>\n

1<\/p>\n

+<\/p>\n

c<\/p>\n

2<\/p>\n

\/<\/p>\n

2<\/p>\n

+<\/p>\n

1<\/p>\n

\u2264<\/p>\n

c<\/p>\n

3<\/p>\n

+<\/p>\n

c<\/p>\n

2<\/p>\n

\/<\/p>\n

2<\/p>\n

c_1+c_2\/2+1 \\\\le c_3+c_2\/2<\/p>\n

<\/span><\/span>c<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>c<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/2<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>c<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>c<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/2<\/span><\/span><\/span><\/span><\/span>，\u4e24\u8005\u4e4b\u548c<\/p>\n

\u2264<\/p>\n

2<\/p>\n

k<\/p>\n

，\u6545<\/p>\n

c<\/p>\n

1<\/p>\n

+<\/p>\n

c<\/p>\n

2<\/p>\n

\/<\/p>\n

2<\/p>\n

+<\/p>\n

1<\/p>\n

\u2264<\/p>\n

k<\/p>\n

\\\\le 2k，\u6545c1+c2\/2+1 \\\\le k<\/p>\n

<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>2<\/span>k<\/span>，\u6545<\/span>c<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>c<\/span>2\/2<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u524d\u8a00<\/h2>\n

z-\u7f13\u51b2\u7b97\u6cd5(z-buffer algorithm)\u5c31\u662f\u4e00\u79cd\u975e\u5e38\u7b80\u660e\u7684\u9690\u85cf\u9762\u6d88\u9664\u6cd5，\u5176\u8fc7\u7a0b\u5982\u4e0b\u3002\u9996\u5148，\u5bf9\u573a\u666f\u8fdb\u884c\u53d8\u6362，\u4f7f\u5f97\u89c6\u7ebf\u65b9\u5411\u4e3a\u6b63\u7684z-\u65b9\u5411\u3002\u63a5\u4e0b\u6765，\u5b89\u88c5\u4efb\u610f\u6b21\u5e8f\u5bf9\u573a\u666f\u4e2d\u7684\u7269\u4f53\u8fdb\u884c\u626b\u63cf\u8f6c\u6362\u3002\u6240\u8c13\u7684\u626b\u63cf\u8f6c\u6362，\u5c31\u662f\u786e\u5b9a\u88ab\u6539\u7269\u4f53\u7684\u6295\u5f71\u6240\u8986\u76d6\u7684\u90a3\u4e9b\u50cf\u7d20\u2013\u53ea\u6709\u5728\u8fd9\u4e9b\u4f4d\u7f6e，\u8be5\u7269\u4f53\u624d\u6709\u53ef\u80fd\u662f\u53ef\u89c1\u7684\u3002\u5df2\u7ecf\u7ecf\u8fc7\u5904\u7406\u5f97\u5230\u7684\u53f3\u5404\u7269\u4f53\u7684\u4fe1\u606f，\u88ab\u6539\u7b97\u6cd5\u5b58\u653e\u5728\u4e24\u4e2a\u7f13\u51b2\u4e2d\u2013\u4e00\u4e2a\u79f0\u4e3a\u5e27\u7f13\u51b2，\u53e6\u4e00\u4e2a\u79f0\u4e3a\u6df1\u5ea6\u7f13\u51b2\u3002\u5e27\u7f13\u51b2\u4e2d\u5b58\u50a8\u4e86\u4e0e\u6bcf\u4e2a\u50cf\u7d20\u5f53\u524d\u53ef\u89c1\u7684\u7269\u4f53\u7684（\u5149）\u5f3a\u5ea6\u3002\u6240\u8c13\u201c\u5f53\u524d\u53ef\u89c1\u7684\u7269\u4f53\u201d，\u5c31\u662f\u5728\u5f53\u524d\u5df2\u7ecf\u5904\u7406\u8fc7\u7684\u5404\u7269\u4f53\u4e2d，\u4e0e\u67d0\u50cf\u7d20\u53ef\u89c1\u7684\u7269\u4f53\u3002\u6df1\u5ea6\u7f13\u51b2\u4e2d\u5b58\u50a8\u4e86\u5f53\u524d\u4e0e\u5404\u4e2a\u50cf\u7d20\u53ef\u89c1\u7269\u4f53\u7684z-\u5750\u6807（\u66f4\u51c6\u786e\u5730，\u5b58\u50a8\u7684\u662f\u7269\u4f53\u4e0a\u4e0e\u50cf\u7d20\u53ef\u89c1\u7684\u90a3\u4e00\u70b9\u51fa\u7684z-\u5750\u6807）\u3002\u73b0\u5728，\u5047\u5b9a\u5728\u5bf9\u67d0\u63d0\u8fdb\u884c\u626b\u63cf\u8f6c\u6362\u7684\u8fc7\u7a0b\u4e2d，\u6b63\u5728\u5904\u7406\u67d0\u4e00\u50cf\u7d20\u3002\u82e5\u6b64\u7269\u4f53\u5728\u6539\u50cf\u7d20\u5904\u7684z-\u5750\u6807\u6bd4\u5f53\u524d\u5b58\u50a8\u5728\u6df1\u5ea6\u7f13\u51b2\u4e2d\u7684z-\u5750\u6807\u66f4\u5c0f，\u5219\u8bf4\u660e\u8be5\u7269\u4f53\u4f4d\u4e8e\u5f53\u524d\u53ef\u89c1\u7269\u4f53\u7684\u524d\u65b9\u3002\u4e8e\u662f，\u5c31\u9700\u8981\u5c06\u8fd9\u4e00\u65b0\u7269\u4f53\u7684（\u5149）\u5f3a\u5ea6\u503c\u5b58\u5165\u5e27\u7f13\u51b2，\u540c\u65f6\u7528\u65b0\u7684z-\u5750\u6807\u66f4\u65b0\u6df1\u5ea6\u7f13\u51b2\u3002\u53cd\u4e4b，\u82e5\u7269\u4f53\u5728\u8be5\u50cf\u7d20\u5904\u7684z-\u5750\u6807\u6bd4\u6df1\u5ea6\u7f13\u51b2\u4e2d\u5f53\u524d\u7684z-\u5750\u6807\u66f4\u591a，\u5219\u65b0\u7684\u8fd9\u4e00\u7269\u4f53（\u5728\u6b64\u50cf\u7d20\u5904）\u5c06\u4e0d\u53ef\u89c1，\u56e0\u6b64\u5e27\u7f13\u51b2\u548c\u6df1\u5ea6\u7f13\u51b2\u90fd\u5e94\u8be5\u4fdd\u6301\u539f\u6837，z-\u7f13\u51b2\u7b97\u6cd5\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u501f\u52a9\u786c\u4ef6\u76f4\u63a5\u5b9e\u73b0，\u56e0\u800c\u5b9e\u9645\u7684\u8fd0\u884c\u901f\u5ea6\u5f88\u5feb\u3002\u6b63\u56e0\u4e3a\u6b64，\u5b83\u79f0\u4e3a\u6700\u5e38\u7528\u7684\u9690\u85cf\u9762\u6d88\u9664\u65b9\u6cd5\u3002\u8be5\u7b97\u6cd5\u4e0d\u8db3\u4e4b\u5904：\u6df1\u5ea6\u7f13\u51b2\u9700\u8981\u989d\u5916\u5360\u7528\u5927\u91cf\u7684\u5b58\u50a8\u7a7a\u95f4\u3002\u800c\u4e14，\u5bf9\u4e8e\u6bcf\u4e2a\u7269\u4f53，\u88ab\u5176\u8986\u76d6\u7684\u6bcf\u4e00\u4e2a\u50cf\u7d20\u90fd\u9700\u8981\u8fdb\u884cz-\u5750\u6807\u7684\u6d4b\u8bd5\u6bd4\u8f83\u3002 \u6ce8\u91ca：\u53ef\u4ee5\u60f3\u8c61\u81ea\u5df1\u7ad9\u5728<\/p>\n

(<\/p>\n

0<\/p>\n

,<\/p>\n

0<\/p>\n

,<\/p>\n

\u2212<\/p>\n

\u221e<\/p>\n

)<\/p>\n

(0,0,-\\\\infty)<\/p>\n

<\/span><\/span>(<\/span>0<\/span>,<\/span><\/span>0<\/span>,<\/span><\/span>\u2212<\/span>\u221e<\/span>)<\/span><\/span><\/span><\/span><\/span> \u753b\u5bb6\u7b97\u6cd5\u5219\u53ef\u4ee5\u907f\u514d\u8fd9\u4e9b\u8ba1\u7b97\u3002\u8be5\u7b97\u6cd5\u9996\u5148\u6309\u7167\u5404\u7269\u4f53\u5230\u89c6\u70b9\u7684\u8ddd\u79bb，\u5bf9\u5176\u8fdb\u884c\u6392\u5e8f\u3002\u7136\u540e，\u4ece\u8ddd\u79bb\u89c6\u70b9\u6700\u8fdc\u7684\u7269\u4f53\u5f00\u53d1，\u5b89\u88c5\u6240\u8c13\u7684\u201c\u6df1\u5ea6\u987a\u5e8f\u201d，\u5bf9\u7269\u4f53\u8fdb\u884c\u626b\u63cf\u8f6c\u6362\u3002\u5728\u5bf9\u7269\u4f53\u8fdb\u884c\u626b\u63cf\u8f6c\u6362\u7684\u8fc7\u7a0b\u4e2d，\u6211\u4eec\u4e0d\u9700\u8981\u5bf9\u5176z-\u5750\u6807\u505a\u4efb\u4f55\u7684\u6d4b\u8bd5\u6bd4\u8f83，\u5373\u53ef\u5176(\u5149)\u5f3a\u5ea6\u503c\u76f4\u63a5\u5b58\u5165\u5e27\u7f13\u51b2\u3002\u5373\u4f7f\u539f\u5148\u5e27\u7f13\u51b2\u4e2d\u8be5\u4f4d\u7f6e\u5df2\u7ecf\u5b58\u6709\u6570\u5b57，\u4e5f\u53ef\u4ee5\u5c3d\u7ba1\u8986\u76d6\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u4e3a\u4e86\u987a\u5229\u5730\u5e94\u7528\u8fd9\u4e00\u65b9\u6cd5，\u5fc5\u987b\u80fd\u591f\u5feb\u901f\u5730\u5bf9\u6240\u6709\u7269\u4f53\u8fdb\u884c\u6392\u5e8f\u3002\u8fd9\u6837\u5e76\u4e0d\u5bb9\u6613\u3002\u6309z\u5e8f\u4f1a\u4ea7\u751f\u5faa\u73af\u3002<\/p>\n

\u4ee5\u4e09\u4e2a\u4e09\u89d2\u5f62\u4e3a\u4f8b，\u65e0\u8bba\u5b83\u4eec\u5982\u4f55\u6784\u6210\u4e00\u4e2a\u5faa\u73af，\u6211\u4eec\u603b\u662f\u80fd\u591f\u5c06\u5176\u4e2d\u7684\u4e00\u4e2a\u5207\u5206\u4e3a\u4e00\u4e2a\u4e09\u89d2\u5f62\u548c\u4e00\u4e2a\u56db\u8fb9\u5f62，\u4ece\u800c\u4fdd\u8bc1\u5728\u8fd9\u6837\u7684\u56db\u4e2a\u7269\u4f53\u4e4b\u95f4\u5b58\u5728\u4e00\u4e2a\u6b63\u786e\u7684\u663e\u793a\u6b21\u5e8f\u3002\u7531\u4e8e\u6df1\u5ea6\u6b21\u5e8f\u53d6\u51b3\u4e8e\u89c6\u70b9\u7684\u4f4d\u7f6e，\u6240\u4ee5\u5728\u6bcf\u6b21\u89c6\u70b9\u79fb\u52a8\u4e4b\u540e，\u90fd\u5fc5\u987b\u91cd\u65b0\u8fdb\u884c\u8ba1\u7b97\u3002\u5982\u679c\u5411\u98de\u884c\u6a21\u62df\u5668\u8fd9\u6837\u7684\u73af\u5883，\u8981\u6c42\u4ee5\u5b9e\u65f6\u7684\u901f\u5ea6\u8fd0\u884c\u753b\u5bb6\u7b97\u6cd5，\u6211\u4eec\u5c31\u9700\u8981\u5bf9\u573a\u666f\u8fdb\u884c\u67d0\u79cd\u9884\u5904\u7406，\u4ece\u800c\u4f7f\u5f97\u5bf9\u4efb\u4f55\u4e00\u4e2a\u89c6\u70b9，\u90fd\u80fd\u591f\u5feb\u901f\u8ba1\u7b97\u51fa\u6b63\u786e\u7684\u663e\u793a\u987a\u5e8f\u3002\u8fd9\u79cd\u4f18\u96c5\u7684\u6570\u636e\u7ed3\u6784\u5c31\u662f \u7a7a\u95f4\u4e8c\u5206\u6811(binary space partition tree BSPT)，\u7b80\u79f0BSP\u6811\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

BSP\u6811\u7684\u5b9a\u4e49<\/h2>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u4efb\u4e00\u8d85\u5e73\u9762<\/p>\n

h<\/p>\n

:<\/p>\n

a<\/p>\n

1<\/p>\n

x<\/p>\n

1<\/p>\n

+<\/p>\n

a<\/p>\n

2<\/p>\n

x<\/p>\n

2<\/p>\n

+<\/p>\n

\u22ef<\/p>\n

+<\/p>\n

a<\/p>\n

d<\/p>\n

x<\/p>\n

d<\/p>\n

+<\/p>\n

a<\/p>\n

d<\/p>\n

+<\/p>\n

1<\/p>\n

=<\/p>\n

0<\/p>\n

h:a_1x_1+a_2x_2+\\\\cdots + a_dx_d+a_{d+1}=0<\/p>\n

<\/span><\/span>h<\/span><\/span>:<\/span><\/span><\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>d<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u90fd\u786e\u5b9a\u4e86\u4e24\u4e2a\u5f00\u7684\u534a\u7a7a\u95f4，\u6211\u4eec\u7528<\/p>\n

h<\/p>\n

+<\/p>\n

\u548c<\/p>\n

h<\/p>\n

\u2212<\/p>\n

\u6765\u8868\u793a\u6b63\u3001\u8d1f\u534a\u7a7a\u95f4\u3002\u5373<\/p>\n

h^+\u548ch^-\u6765\u8868\u793a\u6b63\u3001\u8d1f\u534a\u7a7a\u95f4\u3002\u5373<\/p>\n

<\/span><\/span>h<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<\/span>h<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6765\u8868\u793a\u6b63\u3001\u8d1f\u534a\u7a7a\u95f4\u3002\u5373<\/span><\/span><\/span><\/span><\/span>\u3002 <\/p>\n

h<\/p>\n

+<\/p>\n

:<\/p>\n

=<\/p>\n

{<\/p>\n

(<\/p>\n

x<\/p>\n

1<\/p>\n

,<\/p>\n

x<\/p>\n

2<\/p>\n

,<\/p>\n

\u22ef
\n \u2009<\/p>\n

,<\/p>\n

x<\/p>\n

d<\/p>\n

)<\/p>\n

\u2223<\/p>\n

a<\/p>\n

1<\/p>\n

x<\/p>\n

1<\/p>\n

+<\/p>\n

a<\/p>\n

2<\/p>\n

x<\/p>\n

2<\/p>\n

+<\/p>\n

\u22ef<\/p>\n

a<\/p>\n

d<\/p>\n

x<\/p>\n

d<\/p>\n

+<\/p>\n

a<\/p>\n

d<\/p>\n

+<\/p>\n

1<\/p>\n

><\/p>\n

0<\/p>\n

}<\/p>\n

h^+ :=\\\\{(x_1,x_2,\\\\cdots ,x_d)|a_1x_1+a_2x_2+\\\\cdots a_dx_d + a_{d+1}>0\\\\}<\/p>\n

<\/span><\/span>h<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:=<\/span><\/span><\/span><\/span>{(<\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u22ef<\/span><\/span><\/span>,<\/span><\/span>x<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\u2223<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span>a<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>d<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span>}<\/span><\/span><\/span><\/span><\/span> <\/p>\n

h<\/p>\n

\u2212<\/p>\n

:<\/p>\n

=<\/p>\n

{<\/p>\n

(<\/p>\n

x<\/p>\n

1<\/p>\n

,<\/p>\n

x<\/p>\n

2<\/p>\n

,<\/p>\n

\u22ef
\n \u2009<\/p>\n

,<\/p>\n

x<\/p>\n

d<\/p>\n

)<\/p>\n

\u2223<\/p>\n

a<\/p>\n

1<\/p>\n

x<\/p>\n

1<\/p>\n

+<\/p>\n

a<\/p>\n

2<\/p>\n

x<\/p>\n

2<\/p>\n

+<\/p>\n

\u22ef<\/p>\n

a<\/p>\n

d<\/p>\n

x<\/p>\n

d<\/p>\n

+<\/p>\n

a<\/p>\n

d<\/p>\n

+<\/p>\n

1<\/p>\n

<<\/p>\n

0<\/p>\n

}<\/p>\n

h^- :=\\\\{(x_1,x_2,\\\\cdots ,x_d)|a_1x_1+a_2x_2+\\\\cdots a_dx_d + a_{d+1}<0\\\\}<\/p>\n

<\/span><\/span>h<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:=<\/span><\/span><\/span><\/span>{(<\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u22ef<\/span><\/span><\/span>,<\/span><\/span>x<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\u2223<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span>a<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>d<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>0<\/span>}<\/span><\/span><\/span><\/span><\/span> \u8fd9\u6837，\u5bf9\u4e8ed\u7ef4\u7a7a\u95f4\u4efb\u610fn\u4e2a\u7269\u4f53\u6240\u7ec4\u6210\u7684\u96c6\u5408S，\u4e0e\u4e4b\u5bf9\u5e94\u7684BSP\u6811\u53ef\u4ee5\u5b9a\u4e49\u4e00\u68f5\u5177\u6709\u5982\u4e0b\u6027\u8d28\u7684\u4e8c\u53c9\u6811T: \u82e5card(S) <\/p>\n

\u2264<\/p>\n

1<\/p>\n

\\\\le 1<\/p>\n

<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u5219T\u662f\u4e00\u7247\u53f6\u5b50；S\u4e2d\u7684\u7269\u4f53\u788e\u7247（\u5982\u679c\u5b58\u5728\u7684\u8bdd）\u88ab\u663e\u793a\u5730\u5b58\u50a8\u5728\u8fd9\u5339\u53f6\u5b50\u4e2d\u3002\u82e5\u5c06\u8fd9\u5339\u53f6\u5b50\u8bb0\u4f5cv，\u5219\u5b58\u50a8\u4e8e\u8fd9\u7247\u53f6\u5904\u7684\u96c6\u5408（\u53ef\u80fd\u662f\u7a7a\u96c6）\u88ab\u8bb0\u4f5cS(v)\u3002 \u82e5card(S)>1，\u5219T\u7684\u6839\u8282\u70b9v\u5b58\u50a8\u7684\u662f\u4e00\u5f20\u8d85\u5e73\u9762<\/p>\n

h<\/p>\n

v<\/p>\n

h_v<\/p>\n

<\/span><\/span>h<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u4ee5\u53ca\u54ea\u4e9b\u5b8c\u5168\u843d\u5728<\/p>\n

h<\/p>\n

v<\/p>\n

h_v<\/p>\n

<\/span><\/span>h<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0a\u7684\u7269\u4f53\u6240\u7ec4\u6210\u7684\u96c6\u5408S(v)\u3002v\u7684\u5de6\u5b69\u5b50\u662f\u4e00\u68f5BSP\u5b50\u6811<\/p>\n

T<\/p>\n

\u2212<\/p>\n

T^-<\/p>\n

<\/span><\/span>T<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u6839，\u8fd9\u68f5\u6811\u5bf9\u5e94\u4e8e<\/p>\n

S<\/p>\n

\u2212<\/p>\n

:<\/p>\n

=<\/p>\n

{<\/p>\n

h<\/p>\n

v<\/p>\n

\u2212<\/p>\n

\u2229<\/p>\n

s<\/p>\n

\u2223<\/p>\n

s<\/p>\n

\u2208<\/p>\n

S<\/p>\n

}<\/p>\n

S^-:=\\\\{h_v^- \\\\cap s| s \\\\in S\\\\}<\/p>\n

<\/span><\/span>S<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:=<\/span><\/span><\/span><\/span>{<\/span>h<\/span><\/span>v<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2229<\/span><\/span><\/span><\/span>s<\/span>\u2223<\/span>s<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span>}<\/span><\/span><\/span><\/span><\/span>;v\u7684\u53f3\u5b69\u5b50\u4e3a\u53e6\u4e00\u68f5BSP\u5b50\u6811<\/p>\n

T<\/p>\n

+<\/p>\n

T^+<\/p>\n

<\/span><\/span>T<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u6839，\u8fd9\u68f5\u6811\u5bf9\u5e94\u4e8e\u96c6\u5408<\/p>\n

S<\/p>\n

+<\/p>\n

:<\/p>\n

=<\/p>\n

{<\/p>\n

h<\/p>\n

v<\/p>\n

+<\/p>\n

\u2229<\/p>\n

s<\/p>\n

\u2223<\/p>\n

s<\/p>\n

\u2208<\/p>\n

S<\/p>\n

}<\/p>\n

S^+ :=\\\\{ h_v^+ \\\\cap s| s\\\\in S\\\\}<\/p>\n

<\/span><\/span>S<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:=<\/span><\/span><\/span><\/span>{<\/span>h<\/span><\/span>v<\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2229<\/span><\/span><\/span><\/span>s<\/span>\u2223<\/span>s<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span>}<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" BSP\u6811\u7684\u89c4\u6a21，\u5b9a\u4e49\u4e3a\u6811\u4e2d\u6240\u6709\u8282\u70b9v\u6240\u5bf9\u5e94\u96c6\u5408S(v)\u7684\u603b\u4f53\u89c4\u6a21\u3002\u6362\u800c\u8a00\u4e4b，\u4e00\u68f5BSP\u6811\u7684\u89c4\u6a21\u5c31\u662f\u6240\u751f\u6210\u7269\u4f53\u7684\u788e\u7247\u603b\u6570\u3002\u82e5BSP\u4e2d\u6ca1\u6709\u65e0\u7528\u7684\u5206\u5272\u7ebf\u2013\u5373\u5206\u5272\u7a7a\u5b50\u7a7a\u95f4\u7684\u5206\u5272\u7ebf-\u5219\u76f8\u5bf9\u4e8eBSP\u6811\u7684\u89c4\u6a21，\u6811\u4e2d\u8282\u70b9\u7684\u6570\u76ee\u81f3\u591a\u6210\u7ebf\u6027\u6b63\u6bd4\u5173\u7cfb\u3002\u6839\u636eBSP\u7684\u89c4\u6a21，\u5e76\u4e0d\u80fd\u786e\u5b9a\u6240\u9700\u5b58\u50a8\u7a7a\u95f4\u5927\u5c0f\u3002 BSP\u5c06\u5bfc\u51fa\u4e00\u4e2a\u5b50\u533a\u57df\u5212\u5206,\u800cBSP\u6811\u4e2d\u7684\u53f6\u5b50\u5219\u5206\u522b\u8868\u793a\u5176\u4e2d\u7684\u5404\u5f20\u9762\u3002\u66f4\u4e00\u822c\u5730\u8bf4，\u5bf9\u4e8eBSP\u6811T\u4e2d\u7684\u6bcf\u4e00\u4e2a\u8282\u70b9，\u6211\u4eec\u90fd\u53ef\u4ee5\u627e\u51fa\u4e00\u4e2a\u4e0e\u4e4b\u5bf9\u5e94\u7684\u51f8\u5b50\u533a\u57df\u2013\u8fd9\u4e2a\u5b50\u533a\u57df，\u5c31\u662f\u534a\u7a7a\u95f4<\/p>\n

h<\/p>\n

u<\/p>\n

t<\/p>\n

\u7684\u4ea4\u96c6，\u5176\u4e2d<\/p>\n

u<\/p>\n

\u4e3a<\/p>\n

v<\/p>\n

\u7684\u7956\u5148\u3002\u82e5<\/p>\n

v<\/p>\n

\u6765\u81ea<\/p>\n

u<\/p>\n

\u7684\u5de6\u5b50\u6811，\u5219<\/p>\n

t<\/p>\n

=<\/p>\n

\u2212<\/p>\n

；\u82e5\u6765\u81ea\u53f3\u5b50\u6811，\u5219<\/p>\n

t<\/p>\n

=<\/p>\n

+<\/p>\n

h_u^t\u7684\u4ea4\u96c6，\u5176\u4e2du\u4e3av\u7684\u7956\u5148\u3002\u82e5v\u6765\u81eau\u7684\u5de6\u5b50\u6811，\u5219t=-；\u82e5\u6765\u81ea\u53f3\u5b50\u6811，\u5219t=+<\/p>\n

<\/span><\/span>h<\/span><\/span>u<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u4ea4\u96c6，\u5176\u4e2d<\/span>u<\/span>\u4e3a<\/span>v<\/span>\u7684\u7956\u5148\u3002\u82e5<\/span>v<\/span>\u6765\u81ea<\/span>u<\/span>\u7684\u5de6\u5b50\u6811，\u5219<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>；\u82e5\u6765\u81ea\u53f3\u5b50\u6811，\u5219<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span> BSP\u53ef\u7528\u4efb\u610f\u8d85\u5e73\u9762\u8fdb\u884c\u5206\u5272\u3002\u5047\u8bbe\u6211\u4eec\u5e0c\u671b\u9488\u5bf9\u5e73\u9762\u4e0a\u7684\u4e00\u7ec4\u7ebf\u6bb5，\u6784\u9020\u51fa\u4e0e\u4e4b\u5bf9\u5e94\u7684BSP\u3002\u5229\u7528\u7ebf\u6bb5\u6240\u5728\u76f4\u7ebf\u4f5c\u4e3a\u5206\u5272\u7ebf，\u79f0\u4e3a\u4e00\u4e2a\u81ea\u52a8\u5212\u5206\u3002\u5982\u679c\u4e09\u7ef4\u7a7a\u95f4\u7684\u4e00\u7ec4\u5e73\u9762\u591a\u8fb9\u5f62，\u90a3\u4e48\u6b64\u65f6\u7684\u81ea\u52a8\u5212\u5206\u7684\u5206\u5272\u7ebf\u5c31\u662f\u5e73\u9762\u591a\u8fb9\u5f62\u6240\u5728\u5e73\u9762\u3002<\/p>\n

2 BSP\u6811\u53ca\u753b\u5bb6\u7b97\u6cd5<\/h2>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u5047\u5b9a\u5df2\u7ecf\u9488\u5bf9\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u7ec4\u7269\u4f53S,\u5df2\u7ecf\u6784\u9020\u4e86\u4e00\u68f5BST\u6811T\u3002\u5e94\u8be5\u5982\u4f55\u5229\u7528T\u6765\u5f97\u5230\u6211\u4eec\u6240\u9700\u8981\u7684\u6df1\u5ea6\u6b21\u5e8f\u3002\u8bbe\u89c6\u70b9<\/p>\n

P<\/p>\n

v<\/p>\n

i<\/p>\n

e<\/p>\n

w<\/p>\n

P_{view}<\/p>\n

<\/span><\/span>P<\/span><\/span>v<\/span>i<\/span>e<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5e76\u5047\u8bbe\u76f8\u5bf9\u4e8eT\u6839\u8282\u70b9\u6240\u5728\u5b58\u50a8\u7684\u90a3\u5f20\u8d85\u5e73\u9762，<\/p>\n

p<\/p>\n

v<\/p>\n

i<\/p>\n

e<\/p>\n

w<\/p>\n

p_{view}<\/p>\n

<\/span><\/span>p<\/span><\/span>v<\/span>i<\/span>e<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4f4d\u4e8e\u5176\u4e0a\u65b9\u3002\u663e\u7136，\u4f4d\u4e8e\u5206\u5272\u5e73\u9762\u4e0b\u65b9\u7684\u4efb\u4f55\u7269\u54c1，\u90fd\u4e0d\u53ef\u80fd\u906e\u6321\u4f4f\u4f4d\u4e8e\u4e0a\u65b9\u7684\u4efb\u4f55\u7269\u4f53\u3002\u5148\u663e\u793a<\/p>\n

T<\/p>\n

\u2212<\/p>\n

，\u5728\u663e\u793a<\/p>\n

T<\/p>\n

+<\/p>\n

T^-，\u5728\u663e\u793aT^+<\/p>\n

<\/span><\/span>T<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5728\u663e\u793a<\/span>T<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u4e0d\u4f1a\u6709\u95ee\u9898\u3002\u5404\u5b50\u6811\u5185\u90e8\u4e5f\u662f\u5982\u6b64\u3002 \u5982\u679c<\/p>\n

P<\/p>\n

v<\/p>\n

i<\/p>\n

e<\/p>\n

w<\/p>\n

P_{view}<\/p>\n

<\/span><\/span>P<\/span><\/span>v<\/span>i<\/span>e<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6b63\u597d\u843d\u5728\u5206\u5272\u5e73\u9762<\/p>\n

h<\/p>\n

v<\/p>\n

h_v<\/p>\n

<\/span><\/span>h<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0a\u65f6，\u6211\u4eec\u5e76\u4e0d\u753b\u51faS(v)\u4e2d\u7684\u4efb\u4f55\u591a\u8fb9\u5f62\u2013\u56e0\u4e3a\u591a\u8fb9\u5f62\u90fd\u4e8c\u7ef4\u5e73\u9762\u7269\u4f53，\u6240\u4ee5\u4ece\u4e0e\u5171\u9762\u7684\u4efb\u4f55\u4e00\u4e2a\u70b9\u6765\u770b，\u5b83\u4eec\u90fd\u662f\u4e0d\u53ef\u89c1\u7684\u3002 \u5047\u5b9a，\u591a\u9762\u4f53\u7684\u6bcf\u4e2a\u5c0f\u5e73\u9762\u90fd\u5df2\u7ecf\u8fdb\u884c\u4e09\u89d2\u5256\u5206\u3002\u56e0\u6b64，\u6211\u4eec\u7684\u4efb\u52a1\u5c31\u662f：\u9488\u5bf9\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7ed9\u5b9a\u7684\u4e00\u7ec4\u4e09\u89d2\u5f62，\u6784\u9020\u51fa\u4e00\u68f5\u89c4\u6a21\u5c3d\u5feb\u5c0f\u7684BSP\u6811\u3002<\/p>\n

\u6784\u9020BSP\u6811<\/h2>\n

\u5e73\u9762BSP\u6811<\/h3>\n

\u8bbeS\u4e3a\u5e73\u9762\u4e0a\u4e00\u7ec4\u5171n\u6761\u4e92\u4e0d\u76f8\u4ea4\u7684\u7ebf\u6bb5\u3002\u6211\u4eec\u6682\u4e14\u8981\u6c42：\u53ea\u6709S\u4e2d\u5404\u7ebf\u6bb5\u6240\u5728\u7684\u76f4\u7ebf，\u624d\u80fd\u505a\u5206\u5272\u7ebf\u3002\u4e0b\u9762\u8fd9\u4e2a\u6784\u9020BSP\u7684\u9012\u5f52\u7b97\u6cd5，\u662f\u4e0d\u8bc1\u81ea\u660e\u7684\u3002\u4efb\u4e00\u7ebf\u6bb5s\u6240\u5728\u76f4\u7ebf，\u8bb0\u4f5cl(s)\u3002 \u7b97\u6cd5：2DBsp(S) \u8f93\u5165：\u4e00\u7ec4\u7ebf\u6bb5S={<\/p>\n

s<\/p>\n

1<\/p>\n

,<\/p>\n

s<\/p>\n

2<\/p>\n

,<\/p>\n

\u22ef
\n \u2009<\/p>\n

,<\/p>\n

s<\/p>\n

n<\/p>\n

s_1,s_2,\\\\cdots ,s_n<\/p>\n

<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u22ef<\/span><\/span><\/span>,<\/span><\/span>s<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>} \u8f93\u51fa：S\u7684\u4e00\u68f5BSP\u6811 1 \u5982\u679c(card(S) <\/p>\n

\u2264<\/p>\n

1<\/p>\n

\\\\le 1<\/p>\n

<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>) 2. then \u76f4\u63a5\u751f\u6210\u4e00\u68f5\u53ea\u542b\u6709\u4e00\u7247\u53f6\u5b50\u7684\u6811T,\u96c6\u5408S\u663e\u793a\u5b58\u50a8\u4e8e\u5176\u4e2d 3. return T 4. else (<\/p>\n

\u2217<\/p>\n

\u5c06<\/p>\n

l<\/p>\n

(<\/p>\n

s<\/p>\n

1<\/p>\n

)<\/p>\n

\u4f5c\u4e3a\u4e00\u6761\u5206\u5272\u7ebf<\/p>\n

\u2217<\/p>\n

* \u5c06l(s_1)\u4f5c\u4e3a\u4e00\u6761\u5206\u5272\u7ebf*<\/p>\n

<\/span><\/span>\u2217<\/span>\u5c06<\/span>l<\/span>(<\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\u4f5c\u4e3a\u4e00\u6761\u5206\u5272\u7ebf<\/span>\u2217<\/span><\/span><\/span><\/span><\/span>) 5. <\/p>\n

S<\/p>\n

+<\/p>\n

\u2190<\/p>\n

{<\/p>\n

s<\/p>\n

\u2229<\/p>\n

\u2223<\/p>\n

(<\/p>\n

s<\/p>\n

1<\/p>\n

)<\/p>\n

+<\/p>\n

\u2223<\/p>\n

s<\/p>\n

\u2208<\/p>\n

S<\/p>\n

}<\/p>\n

;<\/p>\n

T<\/p>\n

+<\/p>\n

\u2190<\/p>\n

2<\/p>\n

D<\/p>\n

B<\/p>\n

s<\/p>\n

p<\/p>\n

(<\/p>\n

S<\/p>\n

+<\/p>\n

)<\/p>\n

S^+ \\\\leftarrow\\\\{ s \\\\cap |(s_1)^+| s \\\\in S\\\\};T^+ \\\\leftarrow 2DBsp(S^+)<\/p>\n

<\/span><\/span>S<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2190<\/span><\/span><\/span><\/span>{<\/span>s<\/span><\/span>\u2229<\/span><\/span><\/span><\/span>\u2223<\/span>(<\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span>}<\/span>;<\/span><\/span>T<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2190<\/span><\/span><\/span><\/span>2<\/span>D<\/span>B<\/span>s<\/span>p<\/span>(<\/span>S<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> 6. <\/p>\n

S<\/p>\n

\u2212<\/p>\n

\u2190<\/p>\n

s<\/p>\n

\u2229<\/p>\n

\u2223<\/p>\n

(<\/p>\n

s<\/p>\n

1<\/p>\n

)<\/p>\n

\u2212<\/p>\n

\u2223<\/p>\n

s<\/p>\n

\u2208<\/p>\n

S<\/p>\n

;<\/p>\n

T<\/p>\n

\u2212<\/p>\n

\u2190<\/p>\n

2<\/p>\n

D<\/p>\n

B<\/p>\n

s<\/p>\n

p<\/p>\n

(<\/p>\n

S<\/p>\n

\u2212<\/p>\n

)<\/p>\n

S^- \\\\leftarrow { s\\\\cap |(s_1)^-|s \\\\in S};T^- \\\\leftarrow 2DBsp(S^-)<\/p>\n

<\/span><\/span>S<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2190<\/span><\/span><\/span><\/span>s<\/span><\/span>\u2229<\/span><\/span>\u2223<\/span>(<\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>s<\/span><\/span>\u2208<\/span><\/span>S<\/span><\/span>;<\/span><\/span>T<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2190<\/span><\/span><\/span><\/span>2<\/span>D<\/span>B<\/span>s<\/span>p<\/span>(<\/span>S<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> 7. \u5347\u6210\u4e00\u68f5BSP\u6811T <\/p>\n

(<\/p>\n

\u5176\u6839\u8282\u70b9\u4e3a<\/p>\n

v<\/p>\n

，\u5de6\u5b50\u6811\u4e3a<\/p>\n

T<\/p>\n

\u2212<\/p>\n

,<\/p>\n

\u53f3\u5b50\u6811\u4e3a<\/p>\n

T<\/p>\n

+<\/p>\n

)<\/p>\n

,<\/p>\n

\u800c\u4e14<\/p>\n

S<\/p>\n

(<\/p>\n

v<\/p>\n

)<\/p>\n

=<\/p>\n

{<\/p>\n

s<\/p>\n

\u2208<\/p>\n

S<\/p>\n

\u2223<\/p>\n

s<\/p>\n

\u2282<\/p>\n

\u2223<\/p>\n

(<\/p>\n

s<\/p>\n

1<\/p>\n

)<\/p>\n

}<\/p>\n

)<\/p>\n

(\u5176\u6839\u8282\u70b9\u4e3av，\u5de6\u5b50\u6811\u4e3aT^-,\u53f3\u5b50\u6811\u4e3aT^+),\u800c\u4e14S(v)=\\\\{ s \\\\in S | s \\\\sub |(s_1)\\\\})<\/p>\n

<\/span><\/span>(<\/span>\u5176\u6839\u8282\u70b9\u4e3a<\/span>v<\/span>，\u5de6\u5b50\u6811\u4e3a<\/span>T<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u53f3\u5b50\u6811\u4e3a<\/span>T<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span>\u800c\u4e14<\/span>S<\/span>(<\/span>v<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span>s<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span>\u2223<\/span>s<\/span><\/span>\u2282<\/span><\/span><\/span><\/span>\u2223<\/span>(<\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)})<\/span><\/span><\/span><\/span><\/span> 8 return T<\/p>\n

\u9009\u62e9\u5206\u5272\u7ebf\u65f6，\u53ea\u7528\u7b2c\u4e00\u6761\u7ebf\u6bb5<\/p>\n

s<\/p>\n

1<\/p>\n

s_1<\/p>\n

<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u80fd\u5426\u9009\u7528\u4f7f\u5f97l(s)\u4e0e\u5c3d\u53ef\u80fd\u5c11\u7684\u7ebf\u6bb5\u76f8\u4ea4\u7684\u90a3\u6761\u7ebf\u6bb5<\/p>\n

s<\/p>\n

\u2208<\/p>\n

S<\/p>\n

s \\\\in S<\/p>\n

<\/span><\/span>s<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span><\/span><\/span><\/span><\/span>？\u4e0d\u884c，\u627e\u51fa\u8fd9\u6837\u7684\u7ebf\u6bb5，\u9700\u8981\u5927\u91cf\u65f6\u95f4\u3002\u8f83\u597d\u7684\u529e\u6cd5\u662f\u968f\u673a\u9009\u62e9\u3002 \u7b97\u6cd5 2DRandomBsp(S) 1 \u751f\u6210\u96c6\u5408S\u4e2d\u5404\u7ebf\u6bb5\u7684\u4e00\u4e2a\u968f\u673a\u6392\u5217S\u2019=<\/p>\n

s<\/p>\n

1<\/p>\n

,<\/p>\n

\u22ef
\n \u2009<\/p>\n

,<\/p>\n

s<\/p>\n

n<\/p>\n

s_1,\\\\cdots,s_n<\/p>\n

<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u22ef<\/span><\/span><\/span>,<\/span><\/span>s<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> 2 <\/p>\n

T<\/p>\n

\u2190<\/p>\n

2<\/p>\n

D<\/p>\n

B<\/p>\n

s<\/p>\n

p<\/p>\n

(<\/p>\n

S<\/p>\n

\u2032<\/p>\n

)<\/p>\n

T \\\\leftarrow 2DBsp(S')<\/p>\n

<\/span><\/span>T<\/span><\/span>\u2190<\/span><\/span><\/span><\/span>2<\/span>D<\/span>B<\/span>s<\/span>p<\/span>(<\/span>S<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> 3 return T<\/p>\n

\u5f15\u740612.1：\u7b97\u6cd52DRandomBsp\u6240\u751f\u6210\u788e\u7247\u7684\u671f\u671b\u6570\u76ee\u4e3aO(nlogn)\u3002 \u5b9a\u740612.2：\u53ef\u4ee5\u5728O(nnlogn)\u671f\u671b\u65f6\u95f4\u5185，\u6784\u9020\u51fa\u4e00\u4e2a\u89c4\u6a21\u4e3aO(nlogn)\u7684BSP\u3002<\/p>\n

4 \u4e09\u7ef4 BSP \u6811\u7684\u89c4\u6a21<\/h2>\n

\u9009\u4fee\u5185\u5bb9，\u7565\u3002 \u5b9a\u740612.5：\u5bf9\u4e8e<\/p>\n

R<\/p>\n

3<\/p>\n

R^3<\/p>\n

<\/span><\/span>R<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u4efb\u610f\u4e00\u7ec4\u5171n\u4e2a\u4e92\u4e0d\u76f8\u4ea4\u7684\u4e09\u89d2\u5f62，\u90fd\u5b58\u5728\u4e00\u68f5\u89c4\u6a21\u4e3aO(n^2)\u7684BSP\u6811\u3002\u6b64\u5916，\u7684\u786e\u5b58\u5728\u67d0\u4e9b\u6784\u5f62，\u5176\u4efb\u4f55BSP\u7684\u89c4\u6a21\u81f3\u5c11\u662fO(nn)\u3002<\/p>\n

5 \u4f4e\u5bc6\u5ea6\u573a\u666f\u7684BSP\u6811<\/h2>\n

\u5c06\u7269\u4f53o\u7684\u76f4\u5f84\u8bb0\u4f5cdiam(o)\u3002\u5bf9<\/p>\n

R<\/p>\n

d<\/p>\n

R^d<\/p>\n

<\/span><\/span>R<\/span><\/span>d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684\u4efb\u610f\u4e00\u7ec4\u7269\u4f53S，\u5176\u5bc6\u5ea6\u4e3a\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\u7684\u6700\u5c0f<\/p>\n

\u03bb<\/p>\n

\\\\lambda<\/p>\n

<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u3002\u4efb\u610f\u7403\u4f53B\u6700\u591a\u4e0eS\u4e2d\u6ee1\u8db3daim(o)<\/p>\n

\u2265<\/p>\n

\\\\ge<\/p>\n

<\/span><\/span>\u2265<\/span><\/span><\/span><\/span><\/span>diam(B)\u7684<\/p>\n

\u03bb<\/p>\n

\\\\lambda<\/p>\n

<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u4e2a\u7269\u4f53<\/p>\n

o<\/p>\n

\u2208<\/p>\n

S<\/p>\n

o\\\\in S<\/p>\n

<\/span><\/span>o<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span><\/span><\/span><\/span><\/span>\u76f8\u4ea4\u3002B\u672c\u8eab\u4e0d\u5c5e\u4e8eS，\u4f46\u4e2d\u5fc3\u4f4d\u7f6e\u3001\u534a\u5f84\u53ef\u4ee5\u4efb\u53d6\u3002 \u4efb\u610fn\u4e2a\u4e92\u4e0d\u76f8\u4ea4\u7403\u4f53\u7684\u5bc6\u5ea6\u5747\u4e3a\u0398(1)\u3002 \u8bbeS\u4e3a<\/p>\n

R<\/p>\n

2<\/p>\n

\u4e2d\u7684\u4e00\u7ec4\u7269\u4f53<\/p>\n

(<\/p>\n

\u7ebf\u6bb5\u3001\u5706\u76d8\u3001\u4e09\u89d2\u5f62\u7b49\u7b49<\/p>\n

)<\/p>\n

R^2\u4e2d\u7684\u4e00\u7ec4\u7269\u4f53(\u7ebf\u6bb5\u3001\u5706\u76d8\u3001\u4e09\u89d2\u5f62\u7b49\u7b49)<\/p>\n

<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684\u4e00\u7ec4\u7269\u4f53<\/span>(<\/span>\u7ebf\u6bb5\u3001\u5706\u76d8\u3001\u4e09\u89d2\u5f62\u7b49\u7b49<\/span>)<\/span><\/span><\/span><\/span><\/span>,S\u7684\u5bc6\u5ea6\u4e3a<\/p>\n

\u03bb<\/p>\n

\\\\lambda<\/p>\n

<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u3002\u4e3a\u6bcf\u4e2a\u7269\u4f53<\/p>\n

o<\/p>\n

\u2208<\/p>\n

S<\/p>\n

\u5b9a\u4e49\u5c11\u91cf\u7684\u4e00\u7ec4\u70b9<\/p>\n

\u2212<\/p>\n

\u2212<\/p>\n

\u79f0\u4e3a\u54e8\u5175<\/p>\n

(<\/p>\n

g<\/p>\n

u<\/p>\n

a<\/p>\n

r<\/p>\n

d<\/p>\n

)<\/p>\n

o \\\\in S\u5b9a\u4e49\u5c11\u91cf\u7684\u4e00\u7ec4\u70b9–\u79f0\u4e3a\u54e8\u5175(guard)<\/p>\n

<\/span><\/span>o<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span>\u5b9a\u4e49\u5c11\u91cf\u7684\u4e00\u7ec4\u70b9<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u2212<\/span>\u79f0\u4e3a\u54e8\u5175<\/span>(<\/span>g<\/span>u<\/span>a<\/span>r<\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u4f7f\u5f97\u54e8\u5175\u7684\u5206\u5e03\u53cd\u5e94\u7269\u4f53\u7684\u5206\u5e03，\u5e76\u8fdb\u800c\u4f9d\u9760\u8fd9\u4e9b\u54e8\u5175\u7684\u8f85\u52a9\u6765\u6784\u9020BSP\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u5c06o\u7684\u5305\u56f4\u6846\u2013\u5373\u5305\u56f4o\u3001\u4e0e\u5750\u6807\u8f74\u5e73\u884c\u7684\u6700\u5c0f\u77e9\u5f62\u2013\u8bb0\u4f5cbb(o)\u3002\u4e8e\u662f，\u53ef\u4ee5\u76f4\u63a5\u9009\u53d6bb(o)\u7684\u56db\u4e2a\u9876\u70b9\u4f5c\u4e3ao\u7684\u54e8\u5175\u3002S\u4e2d\u6240\u6709\u7684\u7269\u4f53\u76844n\u4e2a\u54e8\u5175\u3002\u8fd94n\u4e2a\u54e8\u5175，\u7ec4\u6210\u4e00\u4e2a\u591a\u952e\u96c6\u5408(multiset),\u8bb0\u4f5cJ(S)\u3002\u4f4e\u5bc6\u5ea6S\u7684G(S)\u4e2d\u7684\u54e8\u5175\u7684\u786e\u53ef\u4ee5\u53cd\u6620S\u4e2d\u7269\u4f53\u7684\u5206\u5e03；S\u4e2d\u4e0e\u4efb\u4e00\u6b63\u65b9\u5f62<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u76f8\u4ea4\u7684\u7269\u4f53，\u4e0d\u4f1a\u8d85\u8fc7\u843d\u5728<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u5185\u90e8\u7684\u54e8\u5175\u6570\u3002\u7528\u5706\u76d8\u6765\u5b9a\u4e49\u4e8c\u7ef4\u7a7a\u95f4\u7684\u5bc6\u7801\u3002 \u5f15\u740612.6：\u5e73\u884c\u4e8e\u5750\u6807\u8f74\u3001\u5185\u542bG(S)\u4e2dk\u5404\u54e8\u5175\u7684\u6b63\u65b9\u5f62，\u81f3\u591a\u4e0eS\u4e2d\u7684<\/p>\n

k<\/p>\n

+<\/p>\n

4<\/p>\n

\u03bb<\/p>\n

k+4\\\\lambda<\/p>\n

<\/span><\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>4<\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u4e2a\u7269\u4f53\u76f8\u4ea4\u3002 \u8bc1\u660e：\u4efb\u53d6\u5e73\u884c\u4e8e\u5750\u6807\u8f74，\u5185\u542bG(S)\u4e2dk\u4e2a\u54e8\u5175\u7684\u4e00\u4e2a\u6b63\u65b9\u5f62<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u3002\u663e\u7136，<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u5185\u7684\u54e8\u5175\u81f3\u591a\u6765\u81eak\u4e2a\u7269\u4f53\u3002S\u4e2d\u5176\u4f59\u7684\u7269\u4f53，\u6784\u6210\u96c6\u5408S\u2019\u3002S\u2019\u7684\u5bc6\u5ea6\u4e0d\u8d85\u8fc7<\/p>\n

\u03bb<\/p>\n

\\\\lambda<\/p>\n

<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u3002\u4ee5\u4e0b\u53ea\u9700\u8bc1\u660e，S\u2019\u4e2d\u81f3\u591a<\/p>\n

4<\/p>\n

l<\/p>\n

a<\/p>\n

m<\/p>\n

b<\/p>\n

d<\/p>\n

a<\/p>\n

\u4e2a\u7269\u4f53\u4e0e<\/p>\n

\u03c3<\/p>\n

\u76f8\u4ea4<\/p>\n

4lambda \u4e2a\u7269\u4f53\u4e0e\\\\sigma \u76f8\u4ea4<\/p>\n

<\/span><\/span>4<\/span>l<\/span>amb<\/span>d<\/span>a<\/span>\u4e2a\u7269\u4f53\u4e0e<\/span>\u03c3<\/span>\u76f8\u4ea4<\/span><\/span><\/span><\/span><\/span>\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u82e5\u7269\u4f53<\/p>\n

o<\/p>\n

\u2208<\/p>\n

S<\/p>\n

\u2032<\/p>\n

\u4e0e<\/p>\n

\u03c3<\/p>\n

\u76f8\u4ea4，\u5219\u663e\u7136<\/p>\n

b<\/p>\n

b<\/p>\n

(<\/p>\n

o<\/p>\n

)<\/p>\n

\u4e5f\u5fc5\u7136\u548c<\/p>\n

\u03c3<\/p>\n

o\\\\in S'\u4e0e\\\\sigma\u76f8\u4ea4，\u5219\u663e\u7136bb(o)\u4e5f\u5fc5\u7136\u548c\\\\sigma<\/p>\n

<\/span><\/span>o<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>S<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e<\/span>\u03c3<\/span>\u76f8\u4ea4，\u5219\u663e\u7136<\/span>bb<\/span>(<\/span>o<\/span>)<\/span>\u4e5f\u5fc5\u7136\u548c<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u76f8\u4ea4\u3002\u7531S\u2019\u7684\u5b9a\u4e49，bb(o)\u7684\u9876\u70b9\u5747\u4e0d\u4f1a\u843d\u5728\u6b63\u65b9\u5f62<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u5185\u90e8\u3002\u4e8e\u662f\u5982\u56fe12-21\u6240\u793a，\u8981\u4e48bb(o)\u5230x-\u8f74\u7684\u6295\u5f71\u8986\u76d6<\/p>\n

\u03c3<\/p>\n

\u5230<\/p>\n

x<\/p>\n

\u8f74\u7684\u6295\u5f71<\/p>\n

\\\\sigma \u5230x\u8f74\u7684\u6295\u5f71<\/p>\n

<\/span><\/span>\u03c3<\/span>\u5230<\/span>x<\/span>\u8f74\u7684\u6295\u5f71<\/span><\/span><\/span><\/span><\/span>，\u8981\u4e48bb(o)\u5230y-\u8f74\u7684\u6295\u5f71\u8986\u76d6<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u5230y\u8f74\u7684\u6295\u5f71，\u751a\u81f3\u517c\u800c\u6709\u4e4b\u3002\u8fd9\u5c31\u610f\u5473\u7740，o\u7684\u76f4\u5f84\u4e0d\u4f1a\u5c0f\u4e8e<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u7684\u8fb9\u957f\u3002\u5373<\/p>\n

d<\/p>\n

a<\/p>\n

i<\/p>\n

m<\/p>\n

(<\/p>\n

o<\/p>\n

)<\/p>\n

\u2265<\/p>\n

d<\/p>\n

i<\/p>\n

a<\/p>\n

m<\/p>\n

(<\/p>\n

\u03c3<\/p>\n

)<\/p>\n

\/<\/p>\n

2<\/p>\n

daim(o) \\\\ge diam(\\\\sigma)\/\\\\sqrt 2<\/p>\n

<\/span><\/span>d<\/span>aim<\/span>(<\/span>o<\/span>)<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>d<\/span>iam<\/span>(<\/span>\u03c3<\/span>)<\/span>\/<\/span><\/span>2<\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u82e5\u4ee54\u4e2a\u9876\u70b9\u5706\u5fc3，\u76f4\u5f84\u4e3a<\/p>\n

d<\/p>\n

i<\/p>\n

a<\/p>\n

m<\/p>\n

(<\/p>\n

\u03c3<\/p>\n

)<\/p>\n

\/<\/p>\n

2<\/p>\n

\u7684\u5706\u76d8<\/p>\n

D<\/p>\n

1<\/p>\n

,<\/p>\n

D<\/p>\n

2<\/p>\n

,<\/p>\n

D<\/p>\n

3<\/p>\n

,<\/p>\n

D<\/p>\n

4<\/p>\n

\u8986\u76d6<\/p>\n

\u03c3<\/p>\n

diam(\\\\sigma)\/2\u7684\u5706\u76d8D_1,D_2,D_3,D_4\u8986\u76d6\\\\sigma<\/p>\n

<\/span><\/span>d<\/span>iam<\/span>(<\/span>\u03c3<\/span>)<\/span>\/2<\/span>\u7684\u5706\u76d8<\/span>D<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>D<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>D<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>D<\/span><\/span>4<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8986\u76d6<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>，\u5219\u7269\u4f53o\u5fc5\u4e0e\u5176\u4e2d\u81f3\u5c11\u4e00\u4e2a\u5706\u76d8<\/p>\n

D<\/p>\n

i<\/p>\n

D_i<\/p>\n

<\/span><\/span>D<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u76f8\u4ea4\u3002\u5c06o\u8ba1\u5165<\/p>\n

D<\/p>\n

i<\/p>\n

D_i<\/p>\n

<\/span><\/span>D<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u540d\u4e0b\u3002\u4e8e\u662f\u6709： <\/p>\n

d<\/p>\n

i<\/p>\n

a<\/p>\n

m<\/p>\n

(<\/p>\n

o<\/p>\n

)<\/p>\n

\u2265<\/p>\n

d<\/p>\n

i<\/p>\n

a<\/p>\n

m<\/p>\n

(<\/p>\n

\u03c3<\/p>\n

)<\/p>\n

\/<\/p>\n

2<\/p>\n

\u2265<\/p>\n

d<\/p>\n

i<\/p>\n

a<\/p>\n

m<\/p>\n

(<\/p>\n

\u03c3<\/p>\n

)<\/p>\n

\/<\/p>\n

2<\/p>\n

=<\/p>\n

d<\/p>\n

i<\/p>\n

a<\/p>\n

m<\/p>\n

(<\/p>\n

D<\/p>\n

i<\/p>\n

)<\/p>\n

diam(o) \\\\ge diam(\\\\sigma)\/\\\\sqrt 2 \\\\ge diam(\\\\sigma) \/2 = diam(D_i)<\/p>\n

<\/span><\/span>d<\/span>iam<\/span>(<\/span>o<\/span>)<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>d<\/span>iam<\/span>(<\/span>\u03c3<\/span>)<\/span>\/<\/span><\/span>2<\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2265<\/span><\/span><\/span><\/span>d<\/span>iam<\/span>(<\/span>\u03c3<\/span>)<\/span>\/2<\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>iam<\/span>(<\/span>D<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u65e2\u7136S\u2019\u7684\u5bc6\u5ea6\u4e0d\u8d85\u8fc7<\/p>\n

\u03bb<\/p>\n

\\\\lambda<\/p>\n

<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>，\u6545\u6bcf\u4e2a<\/p>\n

D<\/p>\n

i<\/p>\n

D_i<\/p>\n

<\/span><\/span>D<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u81f3\u591a\u6709<\/p>\n

\u03bb<\/p>\n

\u9879\u5165\u8d26<\/p>\n

\\\\lambda\u9879\u5165\u8d26<\/p>\n

<\/span><\/span>\u03bb<\/span>\u9879\u5165\u8d26<\/span><\/span><\/span><\/span><\/span>\u3002\u56e0\u6b64，<\/p>\n

s<\/p>\n

i<\/p>\n

g<\/p>\n

m<\/p>\n

a<\/p>\n

\u81f3\u591a\u4e0e<\/p>\n

S<\/p>\n

\u2032<\/p>\n

\u4e2d\u7684<\/p>\n

4<\/p>\n

\u03bb<\/p>\n

\u4e2a\u7269\u4f53\u76f8\u4ea4<\/p>\n

sigma\u81f3\u591a\u4e0eS'\u4e2d\u76844\\\\lambda\u4e2a\u7269\u4f53\u76f8\u4ea4<\/p>\n

<\/span><\/span>s<\/span>i<\/span>g<\/span>ma<\/span>\u81f3\u591a\u4e0e<\/span>S<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684<\/span>4<\/span>\u03bb<\/span>\u4e2a\u7269\u4f53\u76f8\u4ea4<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7531\u5f15\u740612.6，\u53ef\u4ee5\u5bfc\u51fa\u4ee5\u4e0b\u4e24\u6bb5\u5f0fBSP\u6784\u6210\u7b97\u6cd5\u3002\u4ee4U\u4e3a\u5305\u542bS\u4e2d\u6240\u6709\u7269\u4f53\u7684\u4e00\u4e2a\u6b63\u65b9\u5f62\u3002\u7b2c\u4e00\u9636\u6bb5：\u9012\u5f52\u5730\u5bf9U\u505a\u6b63\u65b9\u5f62\u5212\u5206，\u76f4\u5230\u6bcf\u4e2a\u6b63\u65b9\u5f62\u5305\u542b\u7684\u54e8\u5175\u4e0d\u8d85\u8fc7\u4e00\u4e2a\u3002\u5c31\u662f\u9012\u5f52\u5efa\u7acb\u56db\u53c9\u6811，\u6bcf\u4e2a\u8c61\u9650\u4e00\u4e2a\u5b50\u6811\u3002\u7b2c\u4e8c\u9636\u6bb5：\u56db\u53c9\u6811\u5bfc\u51faBSP\u6811\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u53ef\u80fd\u7684\u95ee\u9898，\u53f6\u5b50\u7684\u6570\u91cf\u5f88\u591a\u3002\u8c03\u6574\u4e00：\u9002\u5f53\u9009\u53d6\u4e00\u4e2a\u53c2\u6570k，\u4efb\u4e00\u533a\u57df\u4e00\u65e6\u53ea\u5305\u542b\u4e0d\u8d85\u8fc7k\u4e2a（\u800c\u4e0d\u662f\u4e00\u4e2a）\u54e8\u5175，\u5219\u4e0d\u518d\u7ec6\u5206\u3002\u53e6\u4e00\u9879\u8c03\u6574\u5982\u4e0b\u3002\u9012\u5f52\u5212\u5206\u7684\u8fc7\u7a0b\u4e2d，\u9700\u8981\u5bf9\u67d0\u4e00\u4e2a\u6b63\u65b9\u5f62<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u505a\u7ec6\u5206\u3002\u8003\u5bdf<\/p>\n

\u03c3<\/p>\n

\\\\sigma<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u7684\u56db\u4e2a\u8c61\u9650，\u82e5\u5176\u4e2d\u7684\u81f3\u5c11\u4e24\u4e2a\u8c61\u9650\u7684\u5185\u90e8\u542b\u6709\u8d85\u8fc7k\u4e2a\u54e8\u5175，\u5219\u6cbf\u7528\u6b64\u524d\u7684\u65b9\u6cd5\u5b9e\u65bd\u4e00\u6b21\u56db\u53c9\u6811\u5206\u88c2\u3002\u5982\u679c\u67d0\u4e2a\u8c61\u9650\u54e8\u5175\u5747\u4e0d\u8d85\u8fc7k\u4e2a\u3002\u4e5f\u8981\u6267\u884c\u4e00\u6b21\u56db\u53c9\u6811\u5206\u88c2\u3002\u5982\u679c\u53ea\u6709\u5176\u4e2d\u4e00\u4e2a\u8c61\u9650<\/p>\n

\u03c3<\/p>\n

\u2032<\/p>\n

\\\\sigma'<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5185\u5305\u542b\u591a\u4f59k\u4e2a\u54e8\u5175，\u5219\u9700\u8981\u8fdb\u884c\u4e00\u6b21\u7d27\u7f29(shrinking)\u64cd\u4f5c,\u76f4\u89c2\u6548\u679c\u662f\u4e0d\u65ad\u538b\u7f29<\/p>\n

\u03c3<\/p>\n

\u2032<\/p>\n

\\\\sigma'<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u76f4\u5230\u81f3\u5c11\u6709k\u4e2a\u54e8\u5175\u843d\u5230<\/p>\n

\u03c3<\/p>\n

\u2032<\/p>\n

\\\\sigma'<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u5916\u90e8\u3002\u8fd9\u610f\u5473\u77402k\u4e2a\u54e8\u5175\u540e，\u53ea\u9700\u8981\u9012\u5f52\u4e00\u6b21\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u4efb\u4e00\u975e\u6b63\u65b9\u5f62\u53f6\u5b50<\/p>\n

\u03c3<\/p>\n

\u2032<\/p>\n

\u2032<\/p>\n

\\\\sigma''<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span>\u2032\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u90fd\u662f\u67d0\u6b21\u7d27\u7f29\u7684\u4ea7\u7269，\u4e00\u65e6\u6709k\u6d3b\u66f4\u591a\u4e2a\u54e8\u5175\u4e0d\u518d\u843d\u5728\u88ab\u7d27\u7f29\u8c61\u9650<\/p>\n

\u03c3<\/p>\n

\u2032<\/p>\n

\\\\sigma'<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u5185\u90e8，\u7d27\u7f29\u64cd\u4f5c\u65cb\u5373\u7ec8\u6b62\u3002\u8fd9\u4e9b\u54e8\u5175\u4e2d，\u81f3\u5c11\u6709\u4e00\u4e2a\u88ab<\/p>\n

\u03c3<\/p>\n

\u2032<\/p>\n

\\\\sigma '<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u8fb9\u754c\u7a7f\u8fc7，\u6545\u800c\u5b9e\u9645\u843d\u5728<\/p>\n

\u03c3<\/p>\n

\u2032<\/p>\n

\\\\sigma'<\/p>\n

<\/span><\/span>\u03c3<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5916\u5305\u7684\u54e8\u5175\u4e0d\u8db3k\u4e2a\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u5f15\u740612.7：\u6784\u9020\u7684BSP\u6811\u4e2d，\u53f6\u5b50\u6570\u4e0d\u8d85\u8fc7O(n\/k)，\u5176\u4e2d\u6bcf\u5757\u53f6\u5b50\u533a\u57df\u81f3\u591a<\/p>\n

k<\/p>\n

+<\/p>\n

4<\/p>\n

\u03bb<\/p>\n

k+4\\\\lambda<\/p>\n

<\/span><\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>4<\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u4e2a\u7269\u4f53\u76f8\u4ea4\u3002 \u9009\u53d6\u6700\u4f73k\u503c\u5e94\u9075\u5faa\u5982\u4e0b\u539f\u5219：\u65e2\u80fd\u5c3d\u53ef\u80fd\u5730\u51cf\u5c11\u53f6\u5b50\u533a\u57df，\u540c\u65f6\u4e5f\u4e0d\u81f3\u4e8e\u663e\u8457\u589e\u52a0\u5404\u5757\u53f6\u5b50\u533a\u57df\u5305\u542b\u7684\u7269\u4f53\u3002\u8f83\u597d\u7684\u503c<\/p>\n

k<\/p>\n

:<\/p>\n

=<\/p>\n

\u03bb<\/p>\n

k:= \\\\lambda<\/p>\n

<\/span><\/span>k<\/span><\/span>:=<\/span><\/span><\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u3002\u6211\u4eec\u5e76\u4e0d\u77e5\u9053<\/p>\n

\u03bb<\/p>\n

\\\\lambda<\/p>\n

<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>，\u4ee4 k=2，\u5982\u679c\u53f6\u5b50\u533a\u57df\u76f8\u4ea4\u7684\u7269\u4f53\u6ca1\u6709\u8d85\u8fc72k，\u5219\u8fdb\u884c\u7b97\u6cd5\u7684\u4e0b\u4e00\u9636\u6bb5；\u5426\u5219k=2k，\u91cd\u65b0\u5c1d\u8bd5\u3002 \u5b9a\u740612.8：\u7531\u5e73\u9762\u4e0a\u4efb\u610fn\u4e2a\u4e92\u4e0d\u76f8\u4ea4\u7269\u4f53\u7ec4\u6210\u7684\u6bcf\u4e00\u4e2a\u96c6\u5408S，\u90fd\u62e5\u6709\u4e00\u4e2a\u89c4\u6a21\u4e3aO(nlog<\/p>\n

\u03bb<\/p>\n

)<\/p>\n

\\\\lambda)<\/p>\n

<\/span><\/span>\u03bb<\/span>)<\/span><\/span><\/span><\/span><\/span>\u7684BSP，\u5176\u4e2d<\/p>\n

\u03bb<\/p>\n

\\\\lambda<\/p>\n

<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span>\u4e3aS\u7684\u5bc6\u5ea6\u3002 \u5b9a\u740612.9:\u7531<\/p>\n

R<\/p>\n

3<\/p>\n

R^3<\/p>\n

<\/span><\/span>R<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u4efb\u610fn\u4e2a\u4e92\u4e0d\u76f8\u4ea4\u4e09\u89d2\u5f62\u7ec4\u6210\u7684\u6bcf\u4e00\u4e2a\u96c6\u5408S，\u90fd\u62e5\u6709\u4e00\u4e2a\u89c4\u6a21\u4e3aO(n<\/p>\n

\u03bb<\/p>\n

)<\/p>\n

\u7684<\/p>\n

B<\/p>\n

S<\/p>\n

P<\/p>\n

，\u5176\u4e2d<\/p>\n

\u03bb<\/p>\n

\u4e3a<\/p>\n

S<\/p>\n

\u7684\u5bc6\u5ea6<\/p>\n

\\\\lambda)\u7684BSP，\u5176\u4e2d\\\\lambda\u4e3aS\u7684\u5bc6\u5ea6<\/p>\n

<\/span><\/span>\u03bb<\/span>)<\/span>\u7684<\/span>B<\/span>S<\/span>P<\/span>，\u5176\u4e2d<\/span>\u03bb<\/span>\u4e3a<\/span>S<\/span>\u7684\u5bc6\u5ea6<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\"\"<\/p>\n

\u6269\u5c55\u9605\u8bfb<\/h2>\n\n\u8ba1\u7b97\u51e0\u4f55\u4e3a\u9aa8，\u6392\u6837\u4f18\u5316\u4e3a\u9b42<\/tr>\n\n\n\n\n\n
\u67e5\u9605\u9119\u4eba\u7684\u535a\u6587，\u8bf7\u70b9\u51fb\u535a\u6587\u4e0b\u8f7d\u5b66\u9662\u5bfc\u822a<\/td>\n<\/tr>\n
\u7ecf\u5178\u6587\u7ae0\u63a8\u8350：\u4e8c\u7ef4\u6392\u6837<\/td>\n<\/tr>\n
\u6d3b\u5230\u8001，\u5b66\u5230\u8001\u3002\u660e\u671d\u4e2d\u540e\u671f，\u5927\u7ea650%\u7684\u8fdb\u58eb\u80fd\u5f53\u4e0a\u5802\u5b98(\u526f\u90e8\u53ca\u66f4\u9ad8)；\u80fd\u5f53\u4e0a\u5802\u5b98\u7684\u4e3e\u4eba\u53ea\u6709\u5341\u4f59\u4eba\u3002<\/td>\n<\/tr>\n
\u5b50\u58a8\u5b50\u8a00\u4e4b：\u4e8b\u65e0\u7ec8\u59cb，\u65e0\u52a1\u591a\u4e1a\u3002\u4e5f\u5c31\u662f\u6211\u4eec\u5e38\u8bf4\u7684\u4e13\u4e1a\u7684\u4eba\u505a\u4e13\u4e1a\u7684\u4e8b\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6d4b\u8bd5\u73af\u5883<\/h3>\n

\u64cd\u4f5c\u7cfb\u7edf：win7 \u5f00\u53d1\u73af\u5883： VS2019 C++17 \u6216\u8005 \u64cd\u4f5c\u7cfb\u7edf：win10 \u5f00\u53d1\u73af\u5883： VS2022 C++17 \u5982\u65e0\u7279\u6b8a\u8bf4\u660e，\u672c\u7b97\u6cd5\u7528**C++**\u5b9e\u73b0\u3002<\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

\u672c\u6587\u6d89\u53ca\u77e5\u8bc6\u70b9
\n\u6570\u5b66 \u51e0\u4f55
\n\u9884\u5907\u77e5\u8bc6
\nO (Big O)：\u8868\u793a\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6，\u63cf\u8ff0\u7684\u662f\u7b97\u6cd5\u7684\u4e0a\u9650\u6216\u6700\u5dee\u8868\u73b0\u3002 \u03a9 (Big Omega)：\u8868\u793a\u6700\u597d\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6，\u63cf\u8ff0\u7684\u662f\u7b97\u6cd5\u7684\u4e0b\u9650\u6216\u6700\u4f73\u8868\u73b0\u3002 \u0398(1) \u2014 \u786e\u754c（\u7d27\u786e\u754c）\u5b83\u8868\u793a\u7b97\u6cd5\u7684\u8fd0\u884c\u65f6\u95f4\u65e2\u4e0d\u4f1a\u8d85\u8fc7\u67d0\u4e2a\u5e38\u6570，\u4e5f\u4e0d\u4f1a\u4f4e\u4e8e\u53e6\u4e00\u4e2a\u5e38\u6570\u3002 \u5706\u76d8：\u5706\u4e0a\u7684\u70b9\u548c\u5706\u5185\u7684\u70b9，\u662f\u4e00\u4e2a\u533a\u57df\u800c\u4e0d\u662f\u66f2\u7ebf\u3002 <\/p>\n","protected":false},"author":2,"featured_media":99211,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11349,11348,8511,3595,427],"topic":[],"class_list":["post-99224","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-11349","tag-11348","tag-8511","tag-3595","tag-427"],"yoast_head":"\n\u3010\u8ba1\u7b97\u51e0\u4f55 \u5341\u4e8c\u7ae0\u3011\u7a7a\u95f4\u4e8c\u5206\uff1a\u753b\u5bb6\u7b97\u6cd5 - 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