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\u4f5c\u8005\u7c21\u4ecb<\/span><\/strong><\/p>\n

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\u91d1\u535a\u7537\uff0c\u535a\u58eb\uff0c\u5927\u9023\u7406\u5de5\u5927\u5b78\u6559\u6388\u3002 \u81f4\u529b\u65bc\u8cc7\u6599\u6316\u6398\u3001\u5927\u8cc7\u6599\u5206\u6790\u3001\u5275\u65b0\u7ba1\u7406\u3001\u5546\u52d9\u667a\u80fd\u7b49\u9818\u57df\u7684\u79d1\u5b78\u7814\u7a76\u3002 \u4e3b\u6301\u548c\u53c3\u8207\u591a\u9805\u548c\u7701\u90e8\u7d1a\u8ab2\u984c\uff0c\u5728\u76f8\u95dc\u9818\u57df\u91cd\u8981\u570b\u969b\u671f\u520a\u53ca\u6703\u8b70\u4e0a\u767c\u8868\u8ad6\u658760\u9918\u7bc7\uff0c\u4e26\u64d4\u4efb\u8cc7\u6599\u6316\u6398\u9818\u57df\u4e09\u5927\u6703\u8b70KDD\u3001ICDM\u3001SDM\u7684\u7a0b\u5f0f\u59d4\u54e1\u6703\u59d4\u54e1\uff0c\u662fACM\u3001IEEE\u548cCCF\u9ad8\u7d1a\u6703\u54e1\u3002<\/p>\n

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\u76ee\u9304<\/span><\/strong><\/p>\n

\u7b2cI\u90e8\u5206\u6578\u5b78\u8b49\u660e<\/p>\n

\u5f15\u8a003<\/p>\n

0.1\u53c3\u8003\u6587\u737b4<\/p>\n

\u7b2c1\u7ae0\u4ec0\u9ebc\u662f\u8b49\u660e5<\/p>\n

1.1\u547d\u984c5<\/p>\n

1.2\u8b02\u8a5e8<\/p>\n

1.3\u516c\u7406\u5316\u65b9\u6cd58<\/p>\n

1.4\u6211\u5011\u7684\u516c\u74069<\/p>\n

1.4.1\u908f\u8f2f\u63a8\u74069<\/p>\n

1.4.2\u8b49\u660e\u7684\u6a21\u5f0f10<\/p>\n

1.5\u8b49\u660e\u860a\u6db510<\/p>\n

1.5.1\u65b9\u6cd5#1 11<\/p>\n

1.5.2\u65b9\u6cd5#2\uff1a\u8b49\u660e\u9006\u53cd\u547d\u984c12<\/p>\n

1.6\u8b49\u660e\u201c\u7576\u4e14\u50c5\u7576\u201d13<\/p>\n

1.6.1\u65b9\u6cd5#1\uff1a\u8b49\u660e\u5169\u500b\u8a9e\u53e5\u76f8\u4e92\u860a\u6db513<\/p>\n

1.6.2\u65b9\u6cd5#2\uff1a\u69cb\u5efaiff\u93c813<\/p>\n

1.7\u6848\u4f8b\u8b49\u660e\u6cd514<\/p>\n

1.8\u53cd\u8b49\u6cd515<\/p>\n

1.9\u6578\u5b78\u8b49\u660e\u7684\u512a\u79c0\u5be6\u8e1016<\/p>\n

1.10\u53c3\u8003\u6587\u737b18<\/p>\n

1.1\u7bc0\u7fd2\u984c18<\/p>\n

1.5\u7bc0\u7fd2\u984c21<\/p>\n

1.7\u7bc0\u7fd2\u984c21<\/p>\n

1.8\u7bc0\u7fd2\u984c23<\/p>\n

\u7b2c2\u7ae0\u826f\u5e8f\u539f\u740626<\/p>\n

2.1\u826f\u5e8f\u8b49\u660e26<\/p>\n

2.2\u826f\u5e8f\u8b49\u660e\u7bc4\u672c27<\/p>\n

2.2.1\u6574\u6578\u6c42\u548c27<\/p>\n

2.3\u8cea\u56e0\u6578\u5206\u89e329<\/p>\n

2.4\u826f\u5e8f\u96c6\u540829<\/p>\n

2.4.1\u4e0d\u4e00\u6a23\u7684\u826f\u5e8f\u96c6\u5408\uff08\u9078\u5b78\uff0930<\/p>\n

2.2\u7bc0\u7fd2\u984c31<\/p>\n

2.4\u7bc0\u7fd2\u984c38<\/p>\n

\u7b2c3\u7ae0\u908f\u8f2f\u516c\u5f0f40<\/p>\n

3.1\u547d\u984c\u7684\u547d\u984c41<\/p>\n

3.1.1 NOT\uff0cAND\u548cOR 41<\/p>\n

3.1.2\u7576\u4e14\u50c5\u757642<\/p>\n

3.1.3 IMPLIES 42<\/p>\n

3.2\u96fb\u8166\u7a0b\u5f0f\u7684\u547d\u984c\u908f\u8f2f44<\/p>\n

3.2.1\u771f\u503c\u8868\u8a08\u7b9745<\/p>\n

3.2.2\u7b26\u865f\u8868\u793a46<\/p>\n

3.3\u7b49\u50f9\u6027\u548c\u6709\u6548\u602747<\/p>\n

3.3.1\u860a\u6db5\u548c\u9006\u542647<\/p>\n

3.3.2\u6c38\u771f\u6027\u548c\u53ef\u6eff\u8db3\u602748<\/p>\n

3.4\u547d\u984c\u4ee3\u657849<\/p>\n

3.4.1\u547d\u984c\u7bc4\u5f0f49<\/p>\n

3.4.2\u7b49\u50f9\u6027\u8b49\u660e50<\/p>\n

3.5 SAT\u554f\u984c53<\/p>\n

3.6\u8b02\u8a5e\u516c\u5f0f54<\/p>\n

3.6.1\u91cf\u8a5e54<\/p>\n

3.6.2\u6df7\u5408\u91cf\u8a5e55<\/p>\n

3.6.3\u91cf\u8a5e\u7684\u9806\u5e8f56<\/p>\n

3.6.4\u8b8a\u6578\u8207\u57df56<\/p>\n

3.6.5\u5426\u5b9a\u91cf\u8a5e57<\/p>\n

3.6.6\u8b02\u8a5e\u516c\u5f0f\u7684\u6c38\u771f\u602757<\/p>\n

3.7\u53c3\u8003\u6587\u737b58<\/p>\n

3.1\u7bc0\u7fd2\u984c59<\/p>\n

3.2\u7bc0\u7fd2\u984c61<\/p>\n

3.3\u7bc0\u7fd2\u984c65<\/p>\n

3.4\u7bc0\u7fd2\u984c68<\/p>\n

3.5\u7bc0\u7fd2\u984c69<\/p>\n

3.6\u7bc0\u7fd2\u984c71<\/p>\n

\u7b2c4\u7ae0\u6578\u5b78\u8cc7\u6599\u985e\u578b79<\/p>\n

4.1\u96c6\u540879<\/p>\n

4.1.1\u5e38\u7528\u96c6\u540880<\/p>\n

4.1.2\u96c6\u5408\u7684\u6bd4\u8f03\u548c\u7d44\u540880<\/p>\n

4.1.3\u5e42\u96c681<\/p>\n

4.1.4\u96c6\u5408\u69cb\u9020\u5668\u6a19\u8a1882<\/p>\n

4.1.5\u8b49\u660e\u96c6\u5408\u76f8\u7b4982<\/p>\n

4.2\u5e8f\u521783<\/p>\n

4.3\u51fd\u657884<\/p>\n

4.3.1\u57df\u548c\u50cf84<\/p>\n

4.3.2\u51fd\u6578\u8907\u540886<\/p>\n

4.4\u4e8c\u5143\u95dc\u4fc286<\/p>\n

4.4.1\u95dc\u4fc2\u571687<\/p>\n

4.4.2\u95dc\u4fc2\u7684\u50cf89<\/p>\n

4.5\u6709\u9650\u57fa\u657890<\/p>\n

4.5.1\u6709\u9650\u96c6\u6709\u591a\u5c11\u500b\u5b50\u96c691<\/p>\n

4.1\u7bc0\u7fd2\u984c92<\/p>\n

4.2\u7bc0\u7fd2\u984c96<\/p>\n

4.4\u7bc0\u7fd2\u984c97<\/p>\n

4.5\u7bc0\u7fd2\u984c105<\/p>\n

\u7b2c5\u7ae0\u6b78\u7d0d\u6cd5107<\/p>\n

5.1\u4e00\u822c\u6b78\u7d0d\u6cd5107<\/p>\n

5.1.1\u4e00\u822c\u6b78\u7d0d\u6cd5\u7684\u898f\u5247108<\/p>\n

5.1.2\u8209\u4f8b\u8aaa\u660e108<\/p>\n

5.1.3\u6b78\u7d0d\u6cd5\u8b49\u660e\u7684\u7bc4\u672c109<\/p>\n

5.1.4\u4e00\u822c\u6b78\u7d0d\u6cd5\u7684\u7c21\u6f54\u5beb\u6cd5110<\/p>\n

5.1.5\u66f4\u8907\u96dc\u7684\u4f8b\u5b50111<\/p>\n

5.1.6\u932f\u8aa4\u7684\u6b78\u7d0d\u8b49\u660e113<\/p>\n

5.2\u5f3a\u6b78\u7d0d\u6cd5115<\/p>\n

5.2.1\u5f3a\u6b78\u7d0d\u6cd5\u7684\u898f\u5247115<\/p>\n

5.2.2\u6590\u6ce2\u90a3\u5951\u6578\u5217116<\/p>\n

5.2.3\u8cea\u6578\u7684\u4e58\u7a4d117<\/p>\n

5.2.4\u627e\u96f6\u554f\u984c118<\/p>\n

5.2.5\u5806\u76d2\u5b50\u904a\u6232119<\/p>\n

5.3\u5f3a\u6b78\u7d0d\u6cd5\u3001\u4e00\u822c\u6b78\u7d0d\u6cd5\u548c\u826f\u5e8f\u6cd5\u7684\u6bd4\u8f03120<\/p>\n

5.1\u7bc0\u7fd2\u984c121<\/p>\n

5.2\u7bc0\u7fd2\u984c131<\/p>\n

\u7b2c6\u7ae0\u72c0\u614b\u6a5f136<\/p>\n

6.1\u72c0\u614b\u548c\u8f49\u79fb136<\/p>\n

6.2\u4e0d\u8b8a\u6027\u539f\u7406137<\/p>\n

6.2.1\u6cbf\u5c0d\u89d2\u7dda\u79fb\u52d5\u7684\u6a5f\u5668\u4eba137<\/p>\n

6.2.2\u4e0d\u8b8a\u6027\u539f\u7406\u7684\u5b9a\u7fa9139<\/p>\n

6.2.3\u793a\u4f8b\uff1a\u300a\u864e\u81bd\u9f8d\u5a01\u300b141<\/p>\n

6.3\u504f\u5e8f\u6b63\u78ba\u6027\u548c\u7d42\u6b62\u6027143<\/p>\n

6.3.1\u5feb\u901f\u6c42\u5e42143<\/p>\n

6.3.2\u6d3e\u751f\u8b8a\u6578145<\/p>\n

6.3.3\u57fa\u65bc\u826f\u5e8f\u96c6\u5408\u7684\u7d42\u6b62\u6027\uff08\u9078\u5b78\uff09146<\/p>\n

6.3.4\u6771\u5357\u65b9\u5411\u8df3\u8e8d\u7684\u6a5f\u5668\u4eba\uff08\u9078\u5b78\uff09146<\/p>\n

6.4\u7a69\u5b9a\u7684\u5a5a\u59fb147<\/p>\n

6.4.1\u914d\u5c0d\u5100\u5f0f148<\/p>\n

6.4.2\u6211\u5011\u7d50\u5a5a\u5427150<\/p>\n

6.4.3\u4ed6\u5011\u5f9e\u6b64\u5e78\u798f\u5730\u751f\u6d3b\u5728\u4e00\u8d77150<\/p>\n

6.4.4\u7adf\u7136\u662f\u7537\u6027\u2026\u2026151<\/p>\n

6.4.5\u61c9\u7528152<\/p>\n

6.3\u7bc0\u7fd2\u984c153<\/p>\n

6.4\u7bc0\u7fd2\u984c165<\/p>\n

\u7b2c7\u7ae0\u905e\u8ff4\u8cc7\u6599\u985e\u578b172<\/p>\n

7.1\u905e\u8ff4\u5b9a\u7fa9\u548c\u7d50\u69cb\u6b78\u7d0d\u6cd5172<\/p>\n

7.1.1\u7d50\u69cb\u6b78\u7d0d\u6cd5174<\/p>\n

7.2\u5339\u914d\u5e36\u62ec\u5f27\u7684\u5b57\u4e32175<\/p>\n

7.3\u975e\u8ca0\u6574\u6578\u4e0a\u7684\u905e\u8ff4\u51fd\u6578179<\/p>\n

7.3.1 N\u4e0a\u7684\u4e00\u4e9b\u6a19\u6e96\u905e\u8ff4\u51fd\u6578179<\/p>\n

7.3.2\u4e0d\u898f\u7bc4\u7684\u51fd\u6578\u5b9a\u7fa9179<\/p>\n

7.4\u7b97\u8853\u904b\u7b97\u5f0f181<\/p>\n

7.4.1 Aexp\u7684\u66ff\u63db\u548c\u6c42\u503c181<\/p>\n

7.5\u8a08\u7b97\u6a5f\u79d1\u5b78\u4e2d\u7684\u6b78\u7d0d185<\/p>\n

7.1\u7bc0\u7fd2\u984c185<\/p>\n

7.2\u7bc0\u7fd2\u984c193<\/p>\n

7.3\u7bc0\u7fd2\u984c201<\/p>\n

7.4\u7bc0\u7fd2\u984c202<\/p>\n

\u7b2c8\u7ae0\u7121\u9650\u96c6206<\/p>\n

8.1\u7121\u9650\u57fa\u6578\u96c6206<\/p>\n

8.1.1\u4e0d\u540c\u4e4b\u8655209<\/p>\n

8.1.2\u53ef\u6578\u96c6209<\/p>\n

8.1.3\u5e42\u96c6\u7684\u52e2\u56b4\u683c\u5927\u65bc\u539f\u96c6\u5408211<\/p>\n

8.1.4\u5c0d\u89d2\u7dda\u8b49\u660e213<\/p>\n

8.2\u505c\u6b62\u554f\u984c214<\/p>\n

8.3\u96c6\u5408\u908f\u8f2f217<\/p>\n

8.3.1\u7f85\u7d20\u6096\u8ad6217<\/p>\n

8.3.2\u96c6\u5408\u7684ZFC\u516c\u7406\u7cfb\u7d71218<\/p>\n

8.3.3\u907f\u514d\u7f85\u7d20\u6096\u8ad6220<\/p>\n

8.4\u9019\u4e9b\u771f\u7684\u6709\u6548\u55ce220<\/p>\n

8.4.1\u8a08\u7b97\u6a5f\u79d1\u5b78\u4e2d\u7684\u7121\u7aae\u5927221<\/p>\n

8.1\u7bc0\u7fd2\u984c221<\/p>\n

8.2\u7bc0\u7fd2\u984c228<\/p>\n

8.3\u7bc0\u7fd2\u984c233<\/p>\n

8.4\u7bc0\u7fd2\u984c236<\/p>\n

\u7b2c\u2161\u90e8\u5206\u7d50\u69cb<\/p>\n

\u5f15\u8a00241<\/p>\n

\u7b2c9\u7ae0\u6578\u8ad6242<\/p>\n

9.1\u6574\u9664242<\/p>\n

9.1.1\u6574\u9664\u7684\u6027\u8cea243<\/p>\n

9.1.2\u4e0d\u53ef\u6574\u9664\u554f\u984c244<\/p>\n

9.1.3\u7ec8\u6781\u8b66\u63a2245<\/p>\n

9.2\u516c\u7d04\u6578247<\/p>\n

9.2.1\u6b50\u5e7e\u88e1\u5f97\u7b97\u704b247<\/p>\n

9.2.2\u7c89\u788e\u6a5f249<\/p>\n

9.2.3\u6c34\u58fa\u554f\u984c\u7684\u901a\u89e3251<\/p>\n

9.2.4\u516c\u7d04\u6578\u7684\u6027\u8cea252<\/p>\n

9.3\u8cea\u6578\u7684\u5967\u79d8253<\/p>\n

9.4\u7b97\u8853\u57fa\u672c\u5b9a\u7406255<\/p>\n

9.4.1\u5206\u89e3\u5b9a\u7406\u7684\u8b49\u660e256<\/p>\n

9.5\u963f\u862d\u00b7\u5716\u9748257<\/p>\n

9.5.1\u5716\u9748\u7de8\u78bc\uff081.0\u7248\uff09258<\/p>\n

9.5.2\u7834\u89e3\u5716\u9748\u7de8\u78bc\uff081.0\u7248\uff09260<\/p>\n

9.6\u6a21\u904b\u7b97260<\/p>\n

9.7\u9918\u904b\u7b97262<\/p>\n

9.7.1\u74b0Z_ n 264<\/p>\n

9.8\u5716\u9748\u7de8\u78bc\uff082.0\u7248\uff09265<\/p>\n

9.9\u5012\u6578\u8207\u7d04\u53bb266<\/p>\n

9.9.1\u4e92\u8cea267<\/p>\n

9.9.2\u7d04\u53bb268<\/p>\n

9.9.3\u89e3\u5bc6\uff082.0\u7248\uff09268<\/p>\n

9.9.4\u7834\u89e3\u5716\u9748\u7de8\u78bc\uff082.0\u7248\uff09269<\/p>\n

9.9.5\u5716\u9748\u5f8c\u8a18269<\/p>\n

9.10\u6b50\u62c9\u5b9a\u7406271<\/p>\n

9.10.1\u8a08\u7b97\u6b50\u62c9\uff1f \u51fd\u6578273<\/p>\n

9.11 RSA\u516c\u958b\u91d1\u9470\u52a0\u5bc6274<\/p>\n

9.12 SAT\u8207RSA\u6709\u4ec0\u9ebc\u95dc\u4fc2276<\/p>\n

9.13\u53c3\u8003\u6587\u737b277<\/p>\n

9.1\u7bc0\u7fd2\u984c277<\/p>\n

9.2\u7bc0\u7fd2\u984c278<\/p>\n

9.3\u7bc0\u7fd2\u984c285<\/p>\n

9.4\u7bc0\u7fd2\u984c285<\/p>\n

9.6\u7bc0\u7fd2\u984c287<\/p>\n

9.7\u7bc0\u7fd2\u984c288<\/p>\n

9.8\u7bc0\u7fd2\u984c293<\/p>\n

9.9\u7bc0\u7fd2\u984c293<\/p>\n

9.10\u7bc0\u7fd2\u984c295<\/p>\n

9.11\u7bc0\u7fd2\u984c303<\/p>\n

\u7b2c10\u7ae0\u6709\u5411\u5716\u548c\u504f\u5e8f309<\/p>\n

10.1\u9802\u9ede\u7684\u5ea6311<\/p>\n

10.2\u8def\u548c\u901a\u8def311<\/p>\n

10.2.1\u67e5\u627e\u901a\u8def313<\/p>\n

10.3\u9130\u63a5\u77e9\u9663314<\/p>\n

10.3.1\u77ed\u8def\u5f91315<\/p>\n

10.4\u8def\u95dc\u4fc2316<\/p>\n

10.4.1\u8907\u5408\u95dc\u4fc2316<\/p>\n

10.5\u6709\u5411\u7121\u74b0\u5716\uff06\u8abf\u5ea6317<\/p>\n

10.5.1\u8abf\u5ea6318<\/p>\n

10.5.2\u4e26\u884c\u4efb\u52d9\u8abf\u5ea6320<\/p>\n

10.5.3 Dilworth\u5f15\u7406322<\/p>\n

10.6\u504f\u5e8f323<\/p>\n

10.6.1 DAG\u4e2d\u8def\u95dc\u4fc2\u7684\u6027\u8cea323<\/p>\n

10.6.2\u56b4\u683c\u504f\u5e8f324<\/p>\n

10.6.3\u5f31\u504f\u5e8f325<\/p>\n

10.7\u7528\u96c6\u5408\u5305\u542b\u8868\u793a\u504f\u5e8f326<\/p>\n

10.8\u7dda\u6027\u5e8f327<\/p>\n

10.9\u4e58\u7a4d\u5e8f327<\/p>\n

10.10\u7b49\u50f9\u95dc\u4fc2328<\/p>\n

10.10.1\u7b49\u50f9\u985e328<\/p>\n

10.11\u95dc\u4fc2\u6027\u8cea\u7684\u7e3d\u7d50329<\/p>\n

10.1\u7bc0\u7fd2\u984c330<\/p>\n

10.2\u7bc0\u7fd2\u984c331<\/p>\n

10.3\u7bc0\u7fd2\u984c334<\/p>\n

10.4\u7bc0\u7fd2\u984c335<\/p>\n

10.5\u7bc0\u7fd2\u984c338<\/p>\n

10.6\u7bc0\u7fd2\u984c344<\/p>\n

10.7\u7bc0\u7fd2\u984c347<\/p>\n

10.8\u7bc0\u7fd2\u984c349<\/p>\n

10.9\u7bc0\u7fd2\u984c352<\/p>\n

10.10\u7bc0\u7fd2\u984c354<\/p>\n

\u7b2c11\u7ae0\u901a\u4fe1\u7db2\u7d61357<\/p>\n

11.1\u8def\u7531357<\/p>\n

11.1.1\u5b8c\u5168\u4e8c\u53c9\u6a39357<\/p>\n

11.1.2\u8def\u7531\u554f\u984c358<\/p>\n

11.2\u8def\u7531\u7684\u8a55\u4f30\u540d\u984d358<\/p>\n

11.2.1\u7db2\u7d61\u76f4\u5f91358<\/p>\n

11.2.2\u4ea4\u63db\u6a5f\u7684\u6578\u91cf359<\/p>\n

11.2.3\u7db2\u7d61\u6642\u5ef6359<\/p>\n

11.2.4\u64c1\u585e360<\/p>\n

11.3\u7db2\u8def\u8a2d\u8a08361<\/p>\n

11.3.1\u4e8c\u7dad\u9663\u5217361<\/p>\n

11.3.2\u8776\u5f62\u7db2\u7d61362<\/p>\n

11.3.3 Benes\uff1f \u7db2\u7d61363<\/p>\n

11.2\u7bc0\u7fd2\u984c368<\/p>\n

11.3\u7bc0\u7fd2\u984c368<\/p>\n

\u7b2c12\u7ae0\u7c21\u55ae\u5716373<\/p>\n

12.1\u9802\u9ede\u9130\u63a5\u548c\u5ea6373<\/p>\n

12.2\u7f8e\u570b\u5f02\u6027\u4f34\u4fb6\u7d71\u8a08375<\/p>\n

12.2.1\u63e1\u624b\u5f15\u7406376<\/p>\n

12.3\u4e00\u4e9b\u5e38\u898b\u7684\u5716377<\/p>\n

12.4\u540c\u69cb378<\/p>\n

12.5\u4e8c\u5206\u5716\u8207\u5339\u914d380<\/p>\n

12.5.1\u4e8c\u5206\u5339\u914d\u554f\u984c380<\/p>\n

12.5.2\u5339\u914d\u689d\u4ef6381<\/p>\n

12.6\u8457\u8272384<\/p>\n

12.6.1\u4e00\u500b\u8003\u8a66\u5b89\u6392\u554f\u984c384<\/p>\n

12.6.2\u4e00\u4e9b\u8457\u8272\u908a\u754c386<\/p>\n

12.6.3\u70ba\u4ec0\u9ebc\u8457\u8272387<\/p>\n

12.7\u7c21\u55ae\u8def388<\/p>\n

12.7.1\u7c21\u55ae\u5716\u4e2d\u7684\u8def\u3001\u901a\u8def\u548c\u5708388<\/p>\n

12.7.2\u5708\u4f5c\u70ba\u5b50\u5716389<\/p>\n

12.8\u9023\u901a\u6027390<\/p>\n

12.8.1\u9023\u901a\u5206\u91cf390<\/p>\n

12.8.2\u5947\u6578\u9577\u5ea6\u7684\u5708\u548c2-\u8457\u8272\u6027391<\/p>\n

12.8.3 k\uff1f C\u9023\u901a\u5716392<\/p>\n

12.8.4\u9023\u901a\u5716\u7684\u5c0f\u908a\u6578393<\/p>\n

12.9\u68ee\u6797\u548c\u6a39394<\/p>\n

12.9.1\u8449\u5b50\u3001\u7236\u6bcd\u548c\u5b69\u5b50394<\/p>\n

12.9.2\u6027\u8cea395<\/p>\n

12.9.3\u751f\u6210\u6a39397<\/p>\n

12.9.4\u5c0f\u751f\u6210\u6a39397<\/p>\n

12.10\u53c3\u8003\u6587\u737b401<\/p>\n

12.2\u7bc0\u7fd2\u984c402<\/p>\n

12.4\u7bc0\u7fd2\u984c403<\/p>\n

12.5\u7bc0\u7fd2\u984c406<\/p>\n

12.6\u7bc0\u7fd2\u984c411<\/p>\n

12.7\u7bc0\u7fd2\u984c418<\/p>\n

12.8\u7bc0\u7fd2\u984c420<\/p>\n

12.9\u7bc0\u7fd2\u984c424<\/p>\n

\u7b2c13\u7ae0\u5e73\u9762\u5716431<\/p>\n

13.1\u5728\u5e73\u9762\u4e0a\u7e6a\u88fd\u5716\u5f62431<\/p>\n

13.2\u5e73\u9762\u5716\u7684\u5b9a\u7fa9433<\/p>\n

13.2.1\u9762434<\/p>\n

13.2.2\u5e73\u9762\u5d4c\u5165\u7684\u905e\u8ff4\u5b9a\u7fa9436<\/p>\n

13.2.3\u9019\u500b\u5b9a\u7fa9\u884c\u55ce438<\/p>\n

13.2.4\u5916\u8868\u9762\u5728\u54ea\u88e1\u5462438<\/p>\n

13.3\u6b50\u62c9\u516c\u5f0f439<\/p>\n

13.4\u5e73\u9762\u5716\u4e2d\u908a\u7684\u6578\u91cf\u9650\u5236440<\/p>\n

13.5\u8fd4\u56de\u5230K_ 5\u548cK_ 3,3 441<\/p>\n

13.6\u5e73\u9762\u5716\u7684\u8457\u8272442<\/p>\n

13.7\u591a\u9762\u9ad4\u7684\u5206\u985e443<\/p>\n

13.8\u5e73\u9762\u5716\u7684\u53e6\u4e00\u500b\u7279\u5fb5445<\/p>\n

13.2\u7bc0\u7fd2\u984c446<\/p>\n

13.8\u7bc0\u7fd2\u984c447<\/p>\n

\u7b2c\u2162\u90e8\u5206\u8a08\u6578<\/p>\n

\u5f15\u8a00455<\/p>\n

\u7b2c14\u7ae0\u6c42\u548c\u8207\u6f38\u8fd1\u6027457<\/p>\n

14.1\u5e74\u91d1\u7684\u503c458<\/p>\n

14.1.1\u9322\u672a\u4f86\u7684\u50f9\u503c458<\/p>\n

14.1.2\u64fe\u52d5\u6cd5459<\/p>\n

14.1.3\u5e74\u91d1\u50f9\u503c\u7684\u9589\u578b460<\/p>\n

14.1.4\u7121\u9650\u9577\u7684\u7b49\u6bd4\u6578\u5217460<\/p>\n

14.1.5\u793a\u4f8b461<\/p>\n

14.1.6\u7b49\u6bd4\u6578\u5217\u6c42\u548c\u7684\u8b8a\u5316462<\/p>\n

14.2\u5e42\u548c463<\/p>\n

14.3\u4f30\u7b97\u6c42\u548c\u5f0f\u5b50465<\/p>\n

14.4\u8d85\u51fa\u908a\u754c468<\/p>\n

14.4.1\u554f\u984c\u9673\u8ff0468<\/p>\n

14.4.2\u8abf\u548c\u6578471<\/p>\n

14.4.3\u6f38\u8fd1\u7b49\u5f0f473<\/p>\n

14.5\u4e58\u7a4d474<\/p>\n

14.5.1\u65af\u7279\u6797\u516c\u5f0f475<\/p>\n

14.6\u96d9\u500d\u7684\u9ebb\u7169477<\/p>\n

14.7\u6f38\u8fd1\u7b26\u865f479<\/p>\n

14.7.1\u5c0fo 479<\/p>\n

14.7.2\u5927O 479<\/p>\n

14.7.3 \u03b8  481<\/p>\n

14.7.4\u6f38\u8fd1\u7b26\u865f\u7684\u8aa4\u5340482<\/p>\n

14.7.5\u03a9\uff08\u9078\u5b78\uff09484<\/p>\n

14.1\u7bc0\u7fd2\u984c484<\/p>\n

14.2\u7bc0\u7fd2\u984c486<\/p>\n

14.3\u7bc0\u7fd2\u984c486<\/p>\n

14.4\u7bc0\u7fd2\u984c488<\/p>\n

14.7\u7bc0\u7fd2\u984c490<\/p>\n

\u7b2c15\u7ae0\u57fa\u6578\u6cd5\u5247499<\/p>\n

15.1\u901a\u904e\u5176\u4ed6\u8a08\u6578\u4f86\u8a08\u7b97\u7576\u524d\u8a08\u6578499<\/p>\n

15.1.1\u96d9\u5c04\u898f\u5247499<\/p>\n

15.2\u5e8f\u5217\u8a08\u6578500<\/p>\n

15.2.1\u4e58\u7a4d\u6cd5\u5247501<\/p>\n

15.2.2 n-\u5143\u7d20\u96c6\u5408\u7684\u5b50\u96c6501<\/p>\n

15.2.3\u52a0\u548c\u6cd5\u5247502<\/p>\n

15.2.4\u5bc6\u78bc\u8a08\u6578502<\/p>\n

15.3\u5ee3\u7fa9\u4e58\u7a4d\u6cd5\u5247503<\/p>\n

15.3.1\u6709\u7f3a\u9677\u7684\u7f8e\u5143\u9214\u7968504<\/p>\n

15.3.2\u4e00\u500b\u8c61\u68cb\u554f\u984c505<\/p>\n

15.3.3\u6392\u5217505<\/p>\n

15.4\u9664\u6cd5\u6cd5\u5247506<\/p>\n

15.4.1\u53e6\u4e00\u500b\u8c61\u68cb\u554f\u984c506<\/p>\n

15.4.2\u5713\u684c\u9a0e\u58eb507<\/p>\n

15.5\u5b50\u96c6\u8a08\u6578508<\/p>\n

15.5.1\u5b50\u96c6\u6cd5\u5247509<\/p>\n

15.5.2\u6bd4\u7279\u5e8f\u5217510<\/p>\n

15.6\u91cd\u8907\u5e8f\u5217510<\/p>\n

15.6.1\u5b50\u96c6\u5e8f\u5217510<\/p>\n

15.6.2 Bookkee<\/p>\n

———————————————————–
<\/span><\/strong><\/p>\n

<\/span><\/strong>\u3010\u5177\u9ad4\u6578\u5b78\uff1a\u8a08\u7b97\u6a5f\u79d1\u5b78\u57fa\u790e\u3011<\/span><\/strong><\/p>\n

\u5167\u5bb9\u7c21\u4ecb<\/span><\/strong><\/p>\n

\u300a\u5177\u9ad4\u6578\u5b78\uff1a\u8a08\u7b97\u6a5f\u79d1\u5b78\u57fa\u790e\uff08\u7b2c2\u7248\uff09\u300b\u662f\u4e00\u672c\u5728\u5927\u5b78\u4e2d\u5ee3\u6cdb\u4f7f\u7528\u7684\u7d93\u5178\u6578\u5b78\u6559\u79d1\u66f8\u3002 \u66f8\u4e2d\u8b1b\u89e3\u4e86\u8a31\u591a\u8a08\u7b97\u6a5f\u79d1\u5b78\u4e2d\u7528\u5230\u7684\u6578\u5b78\u77e5\u8b58\u53ca\u6280\u5de7\uff0c\u6559\u4f60\u5982\u4f55\u628a\u4e00\u500b\u5be6\u969b\u554f\u984c\u4e00\u6b65\u6b65\u6f14\u5316\u70ba\u6578\u5b78\u6a21\u578b\uff0c\u7136\u5f8c\u901a\u904e\u96fb\u8166\u89e3\u51b3\u5b83\uff0c\u7279\u5225\u8457\u58a8\u65bc\u6f14\u7b97\u6cd5\u5206\u6790\u65b9\u9762\u3002 \u5176\u4e3b\u8981\u5167\u5bb9\u6d89\u53ca\u548c\u5f0f\u3001\u6574\u503c\u51fd\u6578\u3001\u6578\u8ad6\u3001\u4e8c\u9805\u5f0f\u4fc2\u6578\u3001\u7279\u6b8a\u7684\u6578\u3001\u751f\u6210\u51fd\u6578\u3001\u96e2\u6563\u6982\u7387\u3001\u6f38\u8fd1\u5f0f\u7b49\uff0c\u90fd\u662f\u7a0b\u5f0f\u8a2d\u8a08\u6240\u5fc5\u5099\u7684\u77e5\u8b58\u3002 \u53e6\u5916\uff0c\u300a\u5177\u9ad4\u6578\u5b78\uff1a\u8a08\u7b97\u6a5f\u79d1\u5b78\u57fa\u790e\uff08\u7b2c2\u7248\uff09\u300b\u5305\u62ec\u4e86\u516d\u5927\u985e500\u591a\u9053\u7fd2\u984c\uff0c\u4e26\u7d66\u51fa\u4e86\u6240\u6709\u7fd2\u984c\u7684\u89e3\u7b54\uff0c\u6709\u52a9\u8b80\u8005\u52a0\u6df1\u66f8\u4e2d\u5167\u5bb9\u7684\u7406\u89e3\u3002<\/p>\n

\u300a\u5177\u9ad4\u6578\u5b78\uff1a\u8a08\u7b97\u6a5f\u79d1\u5b78\u57fa\u790e\uff08\u7b2c2\u7248\uff09\u300b\u9762\u5411\u5f9e\u4e8b\u8a08\u7b97\u6a5f\u79d1\u5b78\u3001\u8a08\u7b97\u6578\u5b78\u3001\u8a08\u7b97\u79d1\u6280\u8af8\u65b9\u9762\u5de5\u4f5c\u7684\u4eba\u54e1\uff0c\u4ee5\u53ca\u9ad8\u7b49\u9662\u6821\u76f8\u95dc\u5c08\u696d\u7684\u5e2b\u751f\u3002<\/p>\n

\u4f5c\u8005\u7c21\u4ecb<\/span><\/strong><\/p>\n

Ronald L. Graham\uff08\u845b\u7acb\u6052\uff09\u8457\u540d\u6578\u5b78\u5bb6\uff0c\u7f8e\u570b\u52a0\u5dde\u5927\u5b78\u8056\u9054\u6208\u5206\u6821\u96fb\u8166\u8207\u8cc7\u8a0a\u79d1\u5b78\u5c08\u696d\u6559\u5e2d\uff08Jacobs Endowed Chair\uff09\uff0cAT&T\u5be6\u9a57\u5ba4\u7814\u7a76\u4e2d\u5fc3\u69ae\u8b7d\u9996\u5e2d\u79d1\u5b78\u5bb6\uff0c\u7f8e\u570b\u6578\u5b78\u5b78\u6703\u524d\u4efb\u4e3b\u5e2d\u3002 Graham\u65bc1999\u5e74\u6210\u70ba\u7f8e\u570b\u96fb\u8166\u5b78\u6703\u6703\u58eb\uff0c2003\u5e74\u7372\u5f97\u7f8e\u570b\u6578\u5b78\u5b78\u6703\u7684\u65af\u8482\u723e\u7d42\u8eab\u6210\u5c31\u734e\uff0c2012\u5e74\u6210\u70ba\u7f8e\u570b\u6578\u5b78\u5b78\u6703\u6703\u58eb\u3002 \u4ed6\u9084\u66fe\u7372\u5f97\u7f8e\u570b\u6578\u5b78\u5b78\u6703\u9812\u767c\u7684Lester R. Ford\u734e\u548cCarl Allendoerfer\u734e\u4ee5\u53ca\u5176\u4ed6\u773e\u591a\u734e\u9805\u3002<\/p>\n

Donald E. Knuth\uff08\u9ad8\u5fb7\u7d0d\uff09\u8457\u540d\u96fb\u8166\u79d1\u5b78\u5bb6\uff0c\u6f14\u7b97\u6cd5\u8207\u7a0b\u5f0f\u8a2d\u8a08\u79d1\u6280\u7684\u5148\u9a45\u8005\u3001\u65af\u5766\u798f\u5927\u5b78\u96fb\u8166\u7cfb\u69ae\u4f11\u6559\u6388\u3001\u96fb\u8166\u6392\u7248\u7cfb\u7d71TEX\u548cMETAFONT\u5b57\u9ad4\u7cfb\u7d71\u7684\u767c\u660e\u4eba\uff0c\u56e0\u8af8\u591a\u6210\u5c31\u4ee5\u53ca\u5927\u91cf\u5bcc\u65bc\u5275\u9020\u529b\u548c\u5177\u6709\u6df1\u9060\u5f71\u97ff\u7684\u8457\u4f5c\uff0819\u90e8\u66f8\uff0c1160\u7bc7\u8ad6\u6587\uff09\u800c\u8b7d\u6eff\u5168\u7403\u3002 \u8fd1\u4e9b\u5e74\uff0c\u4ed6\u5c07\u7cbe\u529b\u5168\u90e8\u6295\u5165\u5230\u300a\u8a08\u7b97\u6a5f\u7a0b\u5e8f\u8a2d\u8a08\u85dd\u8853\u300b\u4e03\u5377\u96c6\u7684\u53f2\u8a69\u822c\u5275\u4f5c\u4e2d\u3002 Knuth\u6559\u6388\u7372\u5f97\u904e\u8a31\u591a\u734e\u9805\u548c\u69ae\u8b7d\uff0c\u5305\u62ec\u7f8e\u570b\u96fb\u8166\u5354\u6703\u5716\u9748\u734e\u3001\u7f8e\u570b\u570b\u5bb6\u79d1\u5b78\u734e\u7ae0\u3001\u7f8e\u570b\u6578\u5b78\u5b78\u6703\u7684\u65af\u8482\u723e\u734e\uff0c\u4ee5\u53ca\u56e0\u767c\u660e\u5148\u9032\u79d1\u6280\u65bc1996\u5e74\u69ae\u7372\u7684\u4eac\u90fd\u734e\u3002 1996\u5e74\uff0c\u8a2d\u7acb\u4e86\u4ee5\u5176\u540d\u5b57\u547d\u540d\u7684Donald E. Knuth\u734e\uff0c\u6388\u4e88\u90a3\u4e9b\u70ba\u8a08\u7b97\u6a5f\u79d1\u5b78\u57fa\u790e\u505a\u51fa\u5091\u51fa\u8ca2\u737b\u7684\u4eba\u3002<\/p>\n

Oren Patashnik\u8457\u540d\u96fb\u8166\u79d1\u5b78\u5bb6\uff0cBibTeX\u7684\u5275\u59cb\u4eba\u4e4b\u4e00\uff0c\u662f\u4f4d\u65bc\u62c9\u8377\u4e9e\u7684\u901a\u4fe1\u7814\u7a76\u4e2d\u5fc3\u7684\u7814\u7a76\u54e1\u3002 \u4ed61976\u5e74\u7562\u696d\u65bc\u8036\u9b6f\u5927\u5b78\uff0c\u5f8c\u4f86\u5728\u65af\u5766\u798f\u5927\u5b78\u5e2b\u5f9eKnuth\uff0c1980\u5e74\u5c31\u8077\u65bc\u8c9d\u723e\u5be6\u9a57\u5ba4\u3002 1985\u5e74\u8207Leslie Lamport\u5408\u4f5c\u5275\u5efa\u4e86BibTeX\uff08LaTeX\u7684\u4e00\u7a2e\u5de5\u5177\uff0c\u7528\u65bc\u7ba1\u7406\u6587\u737b\u3001\u7522\u751f\u6587\u737b\u76ee\u9304\uff09\u3002<\/p>\n

\u76ee\u9304<\/span><\/strong><\/p>\n

\u7b2c1\u7ae0\u905e\u8ff4\u554f\u984c1<\/p>\n

1.1\u6cb3\u5167\u58541<\/p>\n

1.2\u5e73\u9762\u4e0a\u7684\u76f4\u7dda4<\/p>\n

1.3\u7d04\u745f\u592b\u554f\u984c7<\/p>\n

\u7fd2\u984c14<\/p>\n

\u7b2c2\u7ae0\u548c\u5f0f18<\/p>\n

2.1\u8a18\u865f18<\/p>\n

2.2\u548c\u5f0f\u548c\u905e\u8ff4\u5f0f21<\/p>\n

2.3\u548c\u5f0f\u7684\u8655\u740625<\/p>\n

2.4\u591a\u91cd\u548c\u5f0f28<\/p>\n

2.5\u4e00\u822c\u6027\u7684\u65b9\u6cd535<\/p>\n

2.6\u6709\u9650\u5fae\u7a4d\u5206\u548c\u7121\u9650\u5fae\u7a4d\u520639<\/p>\n

2.7\u7121\u9650\u548c\u5f0f47<\/p>\n

\u7fd2\u984c52<\/p>\n

\u7b2c3\u7ae0\u6574\u503c\u51fd\u657856<\/p>\n

3.1\u5e95\u548c\u980256<\/p>\n

3.2\u5e95\u548c\u9802\u7684\u61c9\u752858<\/p>\n

3.3\u5e95\u548c\u9802\u7684\u905e\u8ff4\u5f0f66<\/p>\n

3.4 mod\uff1a\u4e8c\u5143\u904b\u7b9768<\/p>\n

3.5\u5e95\u548c\u9802\u7684\u548c\u5f0f72<\/p>\n

\u7fd2\u984c79<\/p>\n

\u7b2c4\u7ae0\u6578\u8ad685<\/p>\n

4.1\u6574\u9664\u602785<\/p>\n

4.2\u7d20\u657888<\/p>\n

4.3\u7d20\u6578\u7684\u4f8b\u5b5089<\/p>\n

4.4\u968e\u4e58\u7684\u56e0\u657893<\/p>\n

4.5\u4e92\u7d2096<\/p>\n

4.6 mod\uff1a\u540c\u9918\u95dc\u4fc2103<\/p>\n

4.7\u7368\u7acb\u5269\u9918105<\/p>\n

4.8\u9032\u4e00\u6b65\u7684\u61c9\u7528107<\/p>\n

4.9\u51fd\u6578\u548c\u51fd\u6578110<\/p>\n

\u7fd2\u984c119<\/p>\n

\u7b2c5\u7ae0\u4e8c\u9805\u5f0f\u4fc2\u6578126<\/p>\n

5.1\u57fa\u672c\u6052\u7b49\u5f0f126<\/p>\n

5.2\u57fa\u672c\u7df4\u7fd2143<\/p>\n

5.3\u8655\u7406\u7684\u6280\u5de7154<\/p>\n

5.4\u751f\u6210\u51fd\u6578164<\/p>\n

5.5\u8d85\u5e7e\u4f55\u51fd\u6578170<\/p>\n

5.6\u8d85\u5e7e\u4f55\u8b8a\u63db180<\/p>\n

5.7\u90e8\u5206\u8d85\u5e7e\u4f55\u548c\u5f0f186<\/p>\n

5.8\u6a5f\u68b0\u6c42\u548c\u6cd5191<\/p>\n

\u7fd2\u984c202<\/p>\n

\u7b2c6\u7ae0\u7279\u6b8a\u7684\u6578214<\/p>\n

6.1\u65af\u7279\u6797\u6578214<\/p>\n

6.2\u6b50\u62c9\u6578223<\/p>\n

6.3\u8abf\u548c\u6578228<\/p>\n

6.4\u8abf\u548c\u6c42\u548c\u6cd5233<\/p>\n

6.5\u4f2f\u52aa\u5229\u6578237<\/p>\n

6.6\u6590\u6ce2\u90a3\u5951\u6578244<\/p>\n

6.7\u9023\u9805\u5f0f252<\/p>\n

\u7fd2\u984c259<\/p>\n

\u7b2c7\u7ae0\u751f\u6210\u51fd\u6578268<\/p>\n

7.1\u591a\u7c73\u8afe\u7406\u8ad6\u8207\u63db\u96f6\u9322268<\/p>\n

7.2\u57fa\u672c\u7b56\u7565277<\/p>\n

7.3\u89e3\u905e\u8ff4\u5f0f282<\/p>\n

7.4\u7279\u6b8a\u7684\u751f\u6210\u51fd\u6578294<\/p>\n

7.5\u5377\u7a4d296<\/p>\n

7.6\u6307\u6578\u751f\u6210\u51fd\u6578305<\/p>\n

7.7\u72c4\u5229\u514b\u96f7\u751f\u6210\u51fd\u6578310<\/p>\n

\u7fd2\u984c312<\/p>\n

\u7b2c8\u7ae0\u96e2\u6563\u6982\u7387320<\/p>\n

8.1\u5b9a\u7fa9320<\/p>\n

8.2\u5e73\u5747\u503c\u548c\u65b9\u5dee325<\/p>\n

8.3\u6982\u7387\u751f\u6210\u51fd\u6578331<\/p>\n

8.4\u62cb\u64f2\u786c\u5e63336<\/p>\n

8.5\u6563\u5217\u6cd5344<\/p>\n

\u7fd2\u984c357<\/p>\n

\u7b2c9\u7ae0\u6f38\u8fd1\u5f0f367<\/p>\n

9.1\u91cf\u7684\u7b49\u7d1a368<\/p>\n

9.2\u5927O\u8a18\u865f370<\/p>\n

9.3 O\u904b\u7b97\u898f\u5247376<\/p>\n

9.4\u5169\u500b\u6f38\u8fd1\u6280\u5de7388<\/p>\n

9.5\u6b50\u62c9\u6c42\u548c\u516c\u5f0f393<\/p>\n

9.6 **\u5f8c\u7684\u6c42\u548c\u6cd5398<\/p>\n

\u7fd2\u984c410<\/p>\n

\u9644\u9304A\u7fd2\u984c\u7b54\u6848417<\/p>\n

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