{"id":678,"date":"2011-12-15T15:00:53","date_gmt":"2011-12-15T07:00:53","guid":{"rendered":"http:\/\/www.hawkwithwind.net\/blog\/?p=678"},"modified":"2011-12-16T00:16:00","modified_gmt":"2011-12-15T16:16:00","slug":"%e9%9b%86%e5%90%88%e8%ae%ba%e7%a0%94%e5%ad%a6%e5%88%9d%e5%bf%83","status":"publish","type":"post","link":"https:\/\/www.hawkwithwind.net\/blog\/2011\/12\/15\/%e9%9b%86%e5%90%88%e8%ae%ba%e7%a0%94%e5%ad%a6%e5%88%9d%e5%bf%83\/","title":{"rendered":"\u96c6\u5408\u8bba\u7814\u5b66\u521d\u5fc3"},"content":{"rendered":"

\u6700\u8fd1\u5728\u7f51\u4e0a\u770b\u4e86\u51e0\u4f4d\u5927\u725b\u7684\u535a\u5ba2\uff0c\u5bf9\u96c6\u5408\u8bba\u9010\u6e10\u4ea7\u751f\u5174\u8da3\u3002\u8fdb\u800c\u53bb\u7ef4\u57fa\u4e0a\u7ffb\u4e86\u7ffb\uff0c\u5bf9\u96c6\u5408\u8bba\u6709\u4e86\u4e2a\u521d\u6b65\u7684\u4e86\u89e3\u3002\u8fd9\u91cc\u505a\u70b9\u7b14\u8bb0\u3002<\/p>\n

\u96c6\u5408\u8bba\u662f\u4e00\u4e2a\u76ee\u6807\u7edf\u4e00\u5168\u5b87\u5b99\u7684\u8d85\u7ea7\u7406\u8bba\u3002\u5f53\u7136\u4e5f\u6709\u53ef\u80fd\u4ed6\u7edf\u4e00\u4e0d\u4e86\u4e86\uff0c\u4f46\u900f\u8fc7\u96c6\u5408\u8bba\uff0c\u53bb\u7406\u89e3\u4eba\u7c7b\u903b\u8f91\u7684\u56fa\u6709\u5b9a\u5f0f\uff0c\u53bb\u7406\u89e3\u6570\u5b66\u5982\u4f55\u89e3\u91ca\u4e16\u754c\uff0c\u662f\u5f88\u6709\u610f\u601d\u7684\u4e8b\u60c5\u3002<\/p>\n

\u6734\u7d20\u96c6\u5408\u8bba\u662f\u5f88\u5bb9\u6613\u7406\u89e3\u7684\u4e8b\u60c5\u3002\u9996\u5148\u6709\u5143\u7d20\u8fd9\u4e2a\u6982\u5ff5\u3002\u7136\u540e\u5143\u7d20\u53ef\u4ee5\u5c5e\u4e8e\u96c6\u5408\u3002\u4e24\u4e2a\u96c6\u5408\u76f8\u7b49\u5b8c\u5168\u7531\u5176\u5143\u7d20\u4e00\u4e00\u76f8\u7b49\u6765\u5224\u5b9a(\u5916\u5ef6\u516c\u7406<\/a>)\u3002\u7136\u540e\u96c6\u5408\u7684\u5143\u7d20\u4e5f\u53ef\u4ee5\u662f\u96c6\u5408\uff0c\u96c6\u5408\u53ef\u4ee5\u4e3a\u7a7a(\u7a7a\u96c6\u516c\u7406<\/a>)\u3002
\n\u8fd9\u5c31\u662f\u9ad8\u4e2d\u8bfe\u672c\u4e0a\u7684\u96c6\u5408\u5b9a\u4e49\u4e86\u5427\u3002\u4f46\u8fd9\u6837\u7684\u5b9a\u4e49\u5b58\u5728\u5de8\u5927\u7684\u95ee\u9898\u3002<\/p>\n

\u4f8b\u5982\u8457\u540d\u7684\u7f57\u7d20\u6096\u8bba\uff1a\u8bbe\u5b58\u5728\u96c6\u5408R, \u5b83\u5305\u542b\u7684\u5143\u7d20\u7531\u5bf9\u201c\u6240\u6709\u96c6\u5408\u201d\u5e94\u7528\u7684\u4e00\u4e2a\u51fd\u6570(\u8c13\u8bcd)\u6765\u786e\u5b9a\uff0c\u5373\u201c\u4e0d\u5305\u542b\u81ea\u8eab\u7684\u96c6\u5408\u201d(\u56fa\u6709\u524d\u63d0\uff0c\u8be5\u5143\u7d20\u662f\u4e00\u4e2a\u96c6\u5408)\u3002\u8fd9\u4e2a\u8c13\u8bcd\u662f\u5408\u7406\u7684\uff0c\u56e0\u4e3a\u5728”\u6240\u6709\u96c6\u5408”\u8fd9\u4e2a\u8303\u56f4\u5185\u786e\u5b9e\u5b58\u5728\u4e0d\u5305\u542b\u81ea\u8eab\u7684\u96c6\u5408\u3002\u90a3\u4e48\uff0c\u5c06\u6240\u6709\u8fd9\u6837\u7684\u96c6\u5408\u4f5c\u4e3a\u5143\u7d20\uff0c\u653e\u5230\u8fd9\u4e2a\u96c6\u5408R\u91cc\uff0c\u7406\u8bba\u4e0a\u4f3c\u4e4e\u53ef\u884c\u3002\u90a3\u4e48\u6211\u4eec\u770b\u8fd9\u6837\u7684\u96c6\u5408R\u6709\u4ec0\u4e48\u7279\u6027\u5462? \u4ed6\u6216\u8bb8\u4e0d\u5305\u542b\u81ea\u8eab(R\u4e0d\u5c5e\u4e8eR)\uff0c\u5982\u679c\u662f\u8fd9\u6837\uff0c\u90a3\u4e48\u4ed6\u5c31\u5e94\u8be5\u5305\u542bR(\u56e0\u4e3aR\u662f\u6240\u6709\u4e0d\u5305\u542b\u81ea\u5df1\u7684\u96c6\u5408\u561b)\u3002\u4f46\u662f\u5982\u679c\u4ed6\u5305\u542b\u4e86\u81ea\u5df1\uff0c\u4ed6\u7acb\u523b\u5c31\u4e0d\u5e94\u8be5\u5305\u542b\u81ea\u5df1\u4e86(\u5305\u542b\u81ea\u5df1\u7684\u96c6\u5408\u4e0d\u5e94\u8be5\u5c5e\u4e8eR)\u3002<\/p>\n

\u4e3a\u4e86\u963b\u6b62\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\uff0c\u4e25\u8c28\u7684\u96c6\u5408\u8bba\u4e0d\u5f97\u4e0d\u589e\u52a0\u4e00\u4e9b\u516c\u7406\u548c\u6982\u5ff5\u6765\u56de\u907f\u8fd9\u4e2a\u95ee\u9898\u3002\u9996\u5148\uff0c\u4f7f\u7528\u4e00\u4e2a\u8c13\u8bcd\u786e\u5b9a\u7684\u96c6\u5408\u4e0d\u518d\u786e\u4fdd\u6784\u6210\u4e00\u4e2a\u96c6\u5408\u3002\u4ed6\u4eec\u53ea\u662f\u5c5e\u4e8e\u4e00\u7c7b(\u5185\u6db5\u516c\u7406<\/a>\uff0c\u66ff\u4ee3\u516c\u7406<\/a>)\u3002\u56e0\u6b64\u201c\u7c7b<\/a>\u201d\u8fd9\u4e2a\u6982\u5ff5\u6bd4\u96c6\u5408\u66f4\u5e7f\u6cdb\u3002\u5982\u679c\u4e00\u4e2a\u7c7b\u4e0d\u662f\u4e00\u4e2a\u96c6\u5408(\u4f8b\u5982\u201c\u4e0d\u5305\u542b\u81ea\u8eab\u7684\u6240\u6709\u96c6\u5408\u201d)\uff0c\u90a3\u4e48\u4ed6\u5c31\u662f\u4e00\u4e2a\u201c\u771f\u7c7b\u201d\u3002
\n\u53e6\u5916\uff0c\u5728\u4e00\u4e2a\u96c6\u5408\u4e0a\u4f7f\u7528\u4e00\u4e2a\u8c13\u8bcd\u4ecd\u7136\u53ef\u4ee5\u5f97\u5230\u6240\u6709\u7b26\u5408\u8fd9\u4e2a\u8c13\u8bcd\u7684\u5143\u7d20\u7684\u96c6\u5408\u3002\u8fd9\u79f0\u4e4b\u4e3a\u5206\u7c7b\u516c\u7406<\/a>\u3002
\n\u4e4b\u540e\u5f15\u5165\u201c\u6b63\u5219\u6027\u516c\u7406<\/a>\u201d\u6765\u786e\u4fdd\u96c6\u5408\u7684\u5408\u7406\u6027\u3002\u8fd9\u4e2a\u516c\u7406\u63cf\u8ff0\u8d77\u6765\u6709\u70b9\u8d39\u529b\u3002\u9996\u5148\uff0c\u516c\u7406\u5316\u96c6\u5408\u8bba\u4e00\u822c\u8ba4\u4e3a\u6240\u6709\u96c6\u5408\u90fd\u662f\u96c6\u5408\u7684\u96c6\u5408\uff0c\u4e0d\u5b58\u5728\u96c6\u5408\u4e4b\u5916\u7684\u6982\u5ff5\u3002\u96c6\u5408\u7684\u5143\u7d20\u4e5f\u662f\u96c6\u5408(\u6709\u53ef\u80fd\u662f\u7a7a\u96c6\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5b9a\u4e49\u662f\u53ef\u4ee5\u7ec8\u6b62\u7684)\u3002\u7136\u540e\u6b63\u5219\u6027\u516c\u7406\u662f\u8bf4\uff0c\u4efb\u610f\u975e\u7a7a\u96c6\u5408\uff0c\u603b\u5b58\u5728\u4e00\u4e2a\u5143\u7d20\uff0c\u8fd9\u4e2a\u5143\u7d20(\u540c\u65f6\u4e5f\u662f\u96c6\u5408)\u4e0e\u8fd9\u4e2a\u96c6\u5408\u7684\u4ea4\u96c6\u4e3a\u7a7a\u3002\u8fd9\u6837\u7406\u89e3\u5f88\u56f0\u96be\uff0c\u6211\u4eec\u53cd\u8fc7\u6765\u7406\u89e3\u3002\u4efb\u610f\u975e\u7a7a\u96c6\u5408\uff0c\u4e0d\u53ef\u80fd\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\uff1a\u4ed6\u7684\u6240\u6709\u5143\u7d20\u90fd\u4e0e\u5176\u76f8\u4ea4\u3002\u8fd9\u4ecd\u7136\u5f88\u96be\u60f3\u8c61\uff0c\u6211\u4eec\u4e3e\u4e2a\u4f8b\u5b50\u6765\u89c2\u5bdf\u8fd9\u6837\u7684\u96c6\u5408\u7684\u7279\u6027\u3002
\n\u5047\u8bbeR\u7b26\u5408\u8fd9\u4e2a\u6761\u4ef6\uff0c\u5047\u8bbe\u4ed6\u5305\u542b\u4e00\u4e2a\u5143\u7d20\u3002\u5219 R = {A}
\n\u8fd9\u91ccA\u548cR\u76f8\u4ea4\u975e\u7a7a\uff0c\u5219A\u4ea4R = B
\nB\u662fA\u548cR\u7684\u4ea4\u96c6\uff0c\u5219B\u662fR\u7684\u5b50\u96c6\u3002\u540c\u65f6B\u975e\u7a7a\u3002\u5219B\u53ea\u80fd\u662f{A}\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cB = R\u3002
\n\u6240\u4ee5A\u4ea4R = B\u3002A = {A, …}
\n\u800cR = {A}, \u6240\u4ee5R = {{A, …}} = {{{A, …}, …}} = {{{{A, …}, …}, …}}
\n\u8fd9\u6837\u7684A\u662f\u65e0\u7a77\u9012\u5f52\u5b9a\u4e49\u7684\u3002\u6216\u8005\u8bf4\uff0c\u5728\u6709\u9650\u65f6\u95f4\u5185\u65e0\u6cd5\u5199\u51faR\u7684\u5b9a\u4e49\u3002\u8fd9\u548c\u65e0\u7a77\u96c6\u5408\u5e76\u4e0d\u76f8\u540c\u3002\u65e0\u7a77\u96c6\u5408\u53ea\u662f\u5728\u6709\u9650\u65f6\u95f4\u5185\u65e0\u6cd5\u5199\u51fa\u8fd9\u4e2a\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u800c\u5df2\u3002\u5982\u679c\u4e00\u4e2a\u96c6\u5408\u65e0\u6cd5\u88ab\u5b9a\u4e49\uff0c\u6211\u4eec\u5e94\u8be5\u8ba4\u4e3a\u4ed6\u5c31\u662f\u4e0d\u5b58\u5728\u7684\u5427\u3002
\nR\u5305\u542b\u66f4\u591a\u5143\u7d20\u7684\u60c5\u51b5\u6bd4\u8f83\u590d\u6742\uff0c\u4e0d\u8fc7\u5f52\u7ed3\u5230\u6700\u540e\u90fd\u662f\u5982\u8fd9\u6837\u5f62\u5f0f\u7684\u65e0\u7a77\u9012\u5f52\u3002\u53ef\u4ee5\u8bf4\u8fd9\u4e2a\u516c\u7406\u9632\u6b62\u4e86\u8fd9\u6837\u7684\u4e0d\u826f\u5b9a\u4e49\u7684\u96c6\u5408\u51fa\u73b0\u3002\u6240\u4ee5\u201c\u7981\u6b62\u81ea\u5305\u542b\u201d\u5c31\u662f\u6b63\u5219\u516c\u7406\u7684\u5185\u6db5\u4e4b\u4e00\u3002<\/p>\n

\u4ee5\u4e0a\u51e0\u4e2a\u516c\u7406\u5b9a\u4e49\u4e86\u96c6\u5408\u7684\u5185\u6db5\u548c\u5916\u5ef6\uff0c\u4ee5\u53ca\u4e00\u4e2a\u64cd\u4f5c(\u5206\u7c7b)\u3002\u63a5\u4e0b\u6765\u8fd8\u9700\u5b9a\u4e49\u96c6\u5408\u7684\u5e76(\u5e76\u96c6\u516c\u7406<\/a>)\u8fd9\u4e2a\u64cd\u4f5c\u3002\u8fd9\u4e2a\u64cd\u4f5c\u7684\u5b9a\u4e49\u4e0e\u6734\u7d20\u96c6\u5408\u8bba\u4e2d\u7684\u5b9a\u4e49\u7565\u6709\u4e0d\u540c\u3002
\n\u8fd9\u4e2a\u5b9a\u4e49\u7684\u5f62\u5f0f\u63cf\u8ff0\u6709\u70b9\u7ed5\uff0c\u8fd9\u91cc\u5f62\u8c61\u7684\u8bf4\u660e\u5c31\u662f\uff1a\u4e00\u4e2a\u5f62\u5982R = {{A},{B},{C}, …}\u7684\u96c6\u5408\uff0c\u4ed6\u7684\u5e76U R = {A, B, C, …}\u3002
\n\u6240\u4ee5\uff0c{A, B, C}U{D} = U{{A, B, C},{D}} = {A, B, C, D}
\n\u76f8\u4fe1\u8bfb\u5230\u8fd9\u91cc\u5f88\u591alisp\u73a9\u5bb6\u5df2\u7ecf\u611f\u5230\u4f3c\u66fe\u76f8\u8bc6\u4e86\u3002\u786e\u5b9e\u51fd\u6570\u5f0f\u8bed\u8a00\u3001\u56fe\u7075\u673a\u7b49\u7b49\u8ba1\u7b97\u673a\u79d1\u5b66\u57fa\u672c\u6982\u5ff5\u90fd\u53ef\u4ee5\u8bf4\u662f\u81ea\u96c6\u5408\u8bba\u6d3e\u751f\u51fa\u6765\u3002\u8fd9\u4e5f\u662f\u6211\u4f1a\u5ffd\u7136\u8df3\u8fd9\u4e2a\u5927\u5751\u7684\u539f\u56e0\u3002<\/p>\n

\u5b9a\u4e49\u4e86\u5e76\u4e4b\u540e\uff0c\u96c6\u5408\u64cd\u4f5c\u57fa\u672c\u5b9a\u4e49\u5b8c\u5168\u3002\u81f3\u4e8e\u8bf4\u4ea4\u96c6\u8fd9\u4e2a\u5b9a\u4e49\u5462\uff0c\u56e0\u4e3a\u5b58\u5728\u5206\u7c7b\u516c\u7406\uff0c\u4ea4\u96c6\u5176\u5b9e\u662f\u5206\u7c7b\u516c\u7406\u4f7f\u7528\u201c\u5c5e\u4e8e\u67d0\u4e2a\u96c6\u5408\u201d\u8fd9\u4e2a\u8c13\u8bcd\u7684\u4e00\u79cd\u7279\u5316\u5f62\u5f0f\u3002\u56e0\u6b64\u65e0\u9700\u4f7f\u7528\u516c\u7406\u5b9a\u4e49\u51fa\u6765\u3002
\n\u8fd8\u6709\u51e0\u4e2a\u516c\u7406\uff0c\u6211\u8fd9\u91cc\u914d\u5408\u63cf\u8ff0\u96c6\u5408\u8bba\u6784\u9020\u81ea\u7136\u6570\u7684\u5b9a\u4e49\u6765\u63cf\u8ff0\u3002\u56e0\u4e3a\u8fd9\u4e00\u6bb5\u4f3c\u4e4e\u662f\u96c6\u5408\u8bba\u4e2d\u6700\u5bb9\u6613\u61c2\u7684\u4e00\u90e8\u5206\u4e86<\/p>\n

\u8fd9\u91cc\u76f4\u63a5\u7ed9\u51fa\u5b9a\u4e49\u7684\u5f62\u5f0f\uff0c\u4ed6\u6bd4\u63cf\u8ff0\u8fd8\u5bb9\u6613\u61c2\u3002\u4e4b\u540e\u6839\u636e\u8fd9\u4e2a\u5f62\u5f0f\u4e2d\u51fa\u73b0\u7684\u51e0\u4e2a\u7279\u5f81\uff0c\u5f15\u51fa\u51e0\u4e2a\u5b9a\u4e49\u3002<\/p>\n

0 = {} (\u7a7a\u96c6)
\n1 = {0} = { {} }
\n2 = {0,1} = { {}, { {} } }
\n3 = {0,1,2} = {{}, { {} }, { {}, { {} } }}
\n4 = {0,1,2,3} = { {}, { {} }, { {}, { {} } }, {{}, { {} }, { {}, { {} } }} }<\/p>\n

\u7531\u4e8e\u81ea\u7136\u6570\u662f\u65e0\u7a77\u7684\uff0c\u5fc5\u987b\u4f7f\u7528\u5f52\u7eb3\u6cd5\u5b9a\u4e49\u5168\u4f53\u81ea\u7136\u6570\u3002\u524d\u9762\u96c6\u5408\u7684\u5e76\u96c6\u7684\u5b9a\u4e49\u662f\u4e00\u4e2a\u94fa\u57ab\uff1a
\n\u9996\u5148 0 = {} \u662f\u81ea\u7136\u6570\u3002
\n\u7136\u540e \u5047\u8bbex\u662f\u81ea\u7136\u6570\uff0c\u5219x\u7684\u4e0b\u4e00\u4e2a\u81ea\u7136\u6570x’ = x U {x}<\/p>\n

\u7531\u662f\u81ea\u7136\u63a8\u51fa\u4e86\u5143\u7d20\u7684\u201c\u540e\u7ee7\u201d\u8fd9\u4e2a\u6982\u5ff5\u3002x’\u662fx\u7684\u540e\u7ee7\uff0c\u5219x’ = x U {x}\u3002\u5e76\u4f9d\u636e\u540e\u7ee7\u8fd9\u4e2a\u6982\u5ff5\u5b9a\u4e49\u5f52\u7eb3\u6cd5(\u65e0\u7a77\u516c\u7406<\/a>):
\n\u5b58\u5728\u96c6\u5408A,\u9996\u5148\uff0c\u7a7a\u96c6\u5c5e\u4e8eA\uff0c\u5e76\u4e14\u5bf9\u4e8e\u4efb\u610f\u7684\u5143\u7d20x\u5c5e\u4e8eA\uff0c\u5219x\u7684\u540e\u7ee7x’ = x U {x}\u4e5f\u5c5e\u4e8eA\u3002
\n\u8fd9\u4e0d\u7834\u574f\u6b63\u5219\u516c\u7406\uff0c\u56e0\u4e3a\u7a7a\u96c6\u5c5e\u4e8eA\u3002\u56e0\u6b64A\u4e2d\u5b58\u5728\u4e00\u4e2a\u5143\u7d20\uff0c{}\uff0c\u4ed6\u4e0eA\u7684\u4ea4\u96c6\u662f\u7a7a\u3002
\n\u8fd9\u5e76\u4e0d\u662f\u6587\u5b57\u6e38\u620f\u3002\u8981\u6c42\u7a7a\u96c6\u5305\u542b\u4e8eA\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002\u8fd9\u76f8\u5f53\u4e8e\u662f\u6570\u5b66\u5f52\u7eb3\u6cd5\u4e2d\u7684\u521d\u59cb\u6761\u4ef6\u3002\u5426\u5219\u5f52\u7eb3\u6cd5\u65e0\u6cd5\u6210\u7acb\u3002<\/p>\n

\u6b64\u5916\u8fd8\u5f15\u51fa\u4e86\u96c6\u5408\u4e2d\u5143\u7d20\u7684\u987a\u5e8f\u95ee\u9898\u3002\u79f0x’\u662fx\u7684\u540e\u7ee7\uff0c\u5c31\u662f\u8bf4\uff0cx\u548cx’\u4e4b\u95f4\u5b58\u5728\u987a\u5e8f\u5173\u7cfb\u3002\u5e76\u4e14\u8fd9\u4e2a\u987a\u5e8f\u5173\u7cfb\u53ef\u4ee5\u4f20\u5bfc\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cx1\u662fx0\u7684\u540e\u7ee7\uff0cx2\u662fx1\u7684\u540e\u7ee7\uff0c\u5219x0\u548cx2\u4e5f\u5b58\u5728x0\u5728\u524d, x2\u5728\u540e\u8fd9\u6837\u7684\u5173\u7cfb\u3002 \u901a\u8fc7\u8fd9\u4e2a\u5173\u7cfb\uff0c\u53ef\u4ee5\u5f97\u51fa\u96c6\u5408\u7684\u5e8f\u7684\u6982\u5ff5\u3002<\/p>\n

\u9996\u5148\u5b9a\u4e49\u826f\u5e8f\u96c6\u5408<\/a>\u3002\u6240\u8c13\u826f\u5e8f\u96c6\u5408\uff0c\u901a\u4fd7\u5730\u8bf4\uff0c\u9700\u8981\u7b26\u5408\u4e24\u4e2a\u6761\u4ef6\u3002\u5176\u4e00\uff0c\u9996\u5148\u7ed9\u5b9a\u4e00\u4e2a\u5224\u5b9a\u5173\u7cfb\u7684\u8fd0\u7b97\u7b26\uff0c\u4efb\u610f\u4e3e\u51fa\u8fd9\u4e2a\u96c6\u5408\u4e2d\u7684\u4e24\u4e2a\u5143\u7d20\uff0c\u5728\u8fd9\u4e2a\u8fd0\u7b97\u7b26\u4e0a\u80fd\u591f\u5224\u5b9a\u987a\u5e8f\u5173\u7cfb(\u56e0\u6b64\u8fd9\u662f\u4e00\u4e2a\u7ebf\u6027\u7684\u987a\u5e8f\u5173\u7cfb\uff0c\u6bcf\u4e2a\u5143\u7d20\u5982\u679c\u6709\uff0c\u90fd\u4ec5\u6709\u4e00\u4e2a\u540e\u7ee7\u548c\u4e00\u4e2a\u524d\u9a71)\uff1b\u5176\u4e8c\uff0c\u4efb\u610f\u7ed9\u5b9a\u8fd9\u4e2a\u96c6\u5408\u7684\u5b50\u96c6\uff0c\u80fd\u591f\u627e\u51fa\u8be5\u5b50\u96c6\u7684\u6700\u5c0f\u5143\u7d20\uff08\u65e0\u9700\u4fdd\u8bc1\u6700\u5927\u5143\u7d20\uff09\u3002\u7b26\u5408\u8fd9\u4e2a\u6761\u4ef6\u7684\u96c6\u5408\u548c\u8fd9\u4e2a\u5173\u7cfb\u4e00\u8d77\u5c31\u79f0\u4f5c\u826f\u5e8f\u96c6\u3002\u56e0\u6b64\u81ea\u7136\u6570\u5728<=\u8fd9\u4e2a\u5173\u7cfb\u4e0a\u662f\u826f\u5e8f\u7684\u3002\u4f46\u662f\u6574\u6570\u5728<=\u8fd9\u4e2a\u5173\u7cfb\u4e0a\u5c31\u4e0d\u662f\u826f\u5e8f\u3002\u56e0\u4e3a\u4e0d\u5b58\u5728\u8fd9\u4e2a\u96c6\u5408\u7684\u6700\u5c0f\u5143\u7d20\u3002\u4f46\u662f\u5982\u679c\u7528\u5176\u4ed6\u7684\u987a\u5e8f\u5173\u7cfb\u8fd0\u7b97\uff0c\u4ecd\u7136\u53ef\u4ee5\u7ed9\u51fa\u4e00\u4e2a\u826f\u5e8f\u7684\u6574\u6570\u96c6\u3002\u4f8b\u59820, -1, -2, ..., 1, 2, ... \u8fd9\u4e2a\u987a\u5e8f\uff0c0\u6700\u5c0f\uff0c\u7136\u540e\u8d1f\u6570\u6bd4\u6574\u6570\u5c0f\uff0c\u7136\u540e\u7edd\u5bf9\u503c\u5c0f\u7684\u6570\u66f4\u5c0f\uff0c\u5219\u5f97\u5230\u4e00\u4e2a\u826f\u5e8f\u96c6\u3002\u4e3a\u4f55\u4e00\u5b9a\u8981\u786e\u4fdd\u6700\u5c0f\u503c\uff0c\u5176\u5b9e\u5c31\u662f\u4e3a\u4e86\u4f7f\u5f52\u7eb3\u6cd5\u6210\u7acb\u3002\u540e\u7eed\u7684\u5927\u91cf\u8bba\u8bc1\u5c06\u4f1a\u5efa\u7acb\u5728\u826f\u5e8f\u96c6\u7684\u5f52\u7eb3\u6cd5\u4e4b\u4e0a(\u8d85\u9650\u5f52\u7eb3\u6cd5<\/a>)\u3002<\/p>\n

\u597d\u4e86\uff0c\u5bf9\u4e8e\u826f\u5e8f\u96c6\uff0c\u65e2\u7136\u540e\u7ee7\u662f\u552f\u4e00\u786e\u5b9a\u7684\uff0c\u5c31\u53ef\u4ee5\u4e0d\u505c\u5730\u5411\u540e\u5217\u4e3e\u4e0b\u4e00\u4e2a\u540e\u7ee7\u3002\u5982\u679c\u8fd9\u4e2a\u96c6\u5408\u662f\u6709\u9650\u96c6\uff0c\u5219\u6700\u540e\u4e00\u4e2a\u540e\u7ee7\u7684\u5e8f\u53f7(\u5e8f\u6570<\/a>)\u5c31\u662f\u4e00\u4e2a\u81ea\u7136\u6570\u3002\u5982\u679c\u662f\u53ef\u6570\u65e0\u7a77\u96c6\u5408\uff0c\u5219\u8fd9\u4e2a\u6700\u5927\u7684\u5e8f\u6570\u65e0\u6cd5\u5728\u6709\u9650\u65f6\u95f4\u5185\u83b7\u53d6\u5230\u3002\u6211\u4eec\u8bbe\u8fd9\u4e2a\u6570\u4e3a\u03c9 (\u81ea\u7136\u6570\u7684\u5e8f\u6570)\u3002\u4ecd\u7136\u5b58\u5728\u5e8f\u6570\u6bd4\u03c9\u8fd8\u5927\u7684\u53ef\u6570\u65e0\u9650\u96c6\u5408\u3002\u4f8b\u5982\u6574\u6570\uff0c\u5047\u5982\u6309\u7167\u4e0a\u8ff0\u6392\u5e8f\u65b9\u5f0f\uff0c\u5219\u5176\u5e8f\u6570\u76f8\u5f53\u4e8e\u662f\u03c9+\u03c9\u3002\u53c8\u6bd4\u5982\uff0c\u81ea\u7136\u6570\u5982\u679c\u91c7\u53d6\u53e6\u4e00\u79cd\u6392\u5e8f\u65b9\u5f0f0, 3, 6, 9, …, 1, 4, 7, …, 2, 5, 8, …\u5219\u81ea\u7136\u6570\u7684\u5e8f\u6570\u662f\u03c9+\u03c9+\u03c9\u3002\u6211\u4eec\u770b\u5230\uff0c\u5e8f\u4f5c\u4e3a\u8861\u91cf\u96c6\u5408\u5927\u5c0f\u7684\u6307\u6807\u6709\u4e00\u4e2a\u4e0d\u8db3\uff0c\u5c31\u662f\u5e8f\u662f\u7531\u4e00\u4e2a\u4eba\u4e3a\u786e\u5b9a\u7684\u5173\u7cfb\u8fd0\u7b97\u7b26\u6765\u786e\u5b9a\u7684\u3002\u5173\u7cfb\u4e0d\u540c\uff0c\u5c31\u6709\u53ef\u80fd\u6539\u53d8\u5e8f\u5927\u5c0f\u3002\u56e0\u6b64\u8fd8\u9700\u8981\u66f4\u901a\u7528\u7684\uff0c\u4ec5\u4e0e\u96c6\u5408\u672c\u8eab\u76f8\u5173\u7684\u6307\u6807\u6765\u8861\u91cf\u96c6\u5408\u7684\u5927\u5c0f\u3002<\/p>\n

\u63a5\u4e0b\u6765\u5e94\u8be5\u5f15\u5165\u57fa\u6570\u7684\u6982\u5ff5\u3002\u4f46\u7531\u4e8e\u8fd9\u4e00\u5757\u6211\u8fd8\u6ca1\u6709\u5b8c\u5168\u7406\u89e3\uff0c\u6240\u4ee5\u6682\u4e14\u5199\u5230\u8fd9\u91cc\u4e86\u3002<\/p>\n

\u540e\u7eed\u4f1a\u5199\u4e00\u7bc7\u6587\u7ae0\u8bb0\u5f55\u8bfb\u5230\u76ee\u524d\u4e3a\u6b62\u6211\u7684\u5404\u79cd\u7591\u95ee\u3002\u4f5c\u4e3a\u601d\u8003\u9898\uff0c\u63a8\u52a8\u81ea\u5df1\u63a5\u4e0b\u6765\u7ee7\u7eed\u53bb\u5b66\u4e60\uff5e
\n\u5f15\u7528:
\n\u7ef4\u57fa\u767e\u79d1:\u516c\u7406\u5316\u96c6\u5408\u8bba<\/a>
\n\u5218\u672a\u9e4f:\u6c38\u6052\u7684\u91d1\u8272\u5bf9\u89d2\u7ebf<\/a>
\nMatrix67:\u5bf9\u89d2\u7ebf\u65b9\u6cd5\u4e4b\u540e\u7684\u6545\u4e8b<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

\u6700\u8fd1\u5728\u7f51\u4e0a\u770b\u4e86\u51e0\u4f4d\u5927\u725b\u7684\u535a\u5ba2\uff0c\u5bf9\u96c6\u5408\u8bba\u9010\u6e10\u4ea7\u751f\u5174\u8da3\u3002\u8fdb\u800c\u53bb\u7ef4\u57fa\u4e0a\u7ffb\u4e86\u7ffb\uff0c\u5bf9\u96c6\u5408\u8bba\u6709\u4e86\u4e2a\u521d\u6b65\u7684\u4e86\u89e3\u3002\u8fd9\u91cc\u505a\u70b9\u7b14\u8bb0\u3002 \u96c6\u5408\u8bba\u662f\u4e00\u4e2a\u76ee\u6807\u7edf\u4e00\u5168\u5b87\u5b99\u7684\u8d85\u7ea7\u7406\u8bba\u3002\u5f53\u7136\u4e5f\u6709\u53ef\u80fd\u4ed6\u7edf\u4e00\u4e0d\u4e86\u4e86\uff0c\u4f46\u900f\u8fc7\u96c6\u5408\u8bba\uff0c\u53bb\u7406\u89e3\u4eba\u7c7b\u903b\u8f91\u7684\u56fa\u6709\u5b9a\u5f0f\uff0c\u53bb\u7406\u89e3\u6570\u5b66\u5982\u4f55\u89e3\u91ca\u4e16\u754c\uff0c\u662f\u5f88\u6709\u610f\u601d\u7684\u4e8b\u60c5\u3002 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\u4e3a\u4e86\u963b\u6b62\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\uff0c\u4e25\u8c28\u7684\u96c6\u5408\u8bba\u4e0d\u5f97\u4e0d\u589e\u52a0\u4e00\u4e9b\u516c\u7406\u548c\u6982\u5ff5\u6765\u56de\u907f\u8fd9\u4e2a\u95ee\u9898\u3002\u9996\u5148\uff0c\u4f7f\u7528\u4e00\u4e2a\u8c13\u8bcd\u786e\u5b9a\u7684\u96c6\u5408\u4e0d\u518d\u786e\u4fdd\u6784\u6210\u4e00\u4e2a\u96c6\u5408\u3002\u4ed6\u4eec\u53ea\u662f\u5c5e\u4e8e\u4e00\u7c7b(\u5185\u6db5\u516c\u7406\uff0c\u66ff\u4ee3\u516c\u7406)\u3002\u56e0\u6b64\u201c\u7c7b\u201d\u8fd9\u4e2a\u6982\u5ff5\u6bd4\u96c6\u5408\u66f4\u5e7f\u6cdb\u3002\u5982\u679c\u4e00\u4e2a\u7c7b\u4e0d\u662f\u4e00\u4e2a\u96c6\u5408(\u4f8b\u5982\u201c\u4e0d\u5305\u542b\u81ea\u8eab\u7684\u6240\u6709\u96c6\u5408\u201d)\uff0c\u90a3\u4e48\u4ed6\u5c31\u662f\u4e00\u4e2a\u201c\u771f\u7c7b\u201d\u3002 \u53e6\u5916\uff0c\u5728\u4e00\u4e2a\u96c6\u5408\u4e0a\u4f7f\u7528\u4e00\u4e2a\u8c13\u8bcd\u4ecd\u7136\u53ef\u4ee5\u5f97\u5230\u6240\u6709\u7b26\u5408\u8fd9\u4e2a\u8c13\u8bcd\u7684\u5143\u7d20\u7684\u96c6\u5408\u3002\u8fd9\u79f0\u4e4b\u4e3a\u5206\u7c7b\u516c\u7406\u3002 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\u5047\u8bbeR\u7b26\u5408\u8fd9\u4e2a\u6761\u4ef6\uff0c\u5047\u8bbe\u4ed6\u5305\u542b\u4e00\u4e2a\u5143\u7d20\u3002\u5219 R = {A} \u8fd9\u91ccA\u548cR\u76f8\u4ea4\u975e\u7a7a\uff0c\u5219A\u4ea4R = B B\u662fA\u548cR\u7684\u4ea4\u96c6\uff0c\u5219B\u662fR\u7684\u5b50\u96c6\u3002\u540c\u65f6B\u975e\u7a7a\u3002\u5219B\u53ea\u80fd\u662f{A}\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cB = R\u3002 \u6240\u4ee5A\u4ea4R = B\u3002A = {A, …} \u800cR = {A}, \u6240\u4ee5R = {{A, …}} = {{{A, …}, …}} = {{{{A, …}, …}, …}} 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R\u5305\u542b\u66f4\u591a\u5143\u7d20\u7684\u60c5\u51b5\u6bd4\u8f83\u590d\u6742\uff0c\u4e0d\u8fc7\u5f52\u7ed3\u5230\u6700\u540e\u90fd\u662f\u5982\u8fd9\u6837\u5f62\u5f0f\u7684\u65e0\u7a77\u9012\u5f52\u3002\u53ef\u4ee5\u8bf4\u8fd9\u4e2a\u516c\u7406\u9632\u6b62\u4e86\u8fd9\u6837\u7684\u4e0d\u826f\u5b9a\u4e49\u7684\u96c6\u5408\u51fa\u73b0\u3002\u6240\u4ee5\u201c\u7981\u6b62\u81ea\u5305\u542b\u201d\u5c31\u662f\u6b63\u5219\u516c\u7406\u7684\u5185\u6db5\u4e4b\u4e00\u3002 \u4ee5\u4e0a\u51e0\u4e2a\u516c\u7406\u5b9a\u4e49\u4e86\u96c6\u5408\u7684\u5185\u6db5\u548c\u5916\u5ef6\uff0c\u4ee5\u53ca\u4e00\u4e2a\u64cd\u4f5c(\u5206\u7c7b)\u3002\u63a5\u4e0b\u6765\u8fd8\u9700\u5b9a\u4e49\u96c6\u5408\u7684\u5e76(\u5e76\u96c6\u516c\u7406)\u8fd9\u4e2a\u64cd\u4f5c\u3002\u8fd9\u4e2a\u64cd\u4f5c\u7684\u5b9a\u4e49\u4e0e\u6734\u7d20\u96c6\u5408\u8bba\u4e2d\u7684\u5b9a\u4e49\u7565\u6709\u4e0d\u540c\u3002 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