{"id":24292,"date":"2021-03-07T17:50:21","date_gmt":"2021-03-07T09:50:21","guid":{"rendered":"https:\/\/swarma.org\/?p=24292"},"modified":"2021-03-07T17:50:21","modified_gmt":"2021-03-07T09:50:21","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e8%b7%af%e5%be%84%ef%bc%9a%e5%af%b9%e6%af%94%e9%80%9a%e8%b7%af%e3%80%81%e8%bd%a8%e8%bf%b9%e4%b8%8e%e8%b7%af%e5%be%84-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=24292","title":{"rendered":"\u4ec0\u4e48\u662f\u8def\u5f84\uff1a\u5bf9\u6bd4\u901a\u8def\u3001\u8f68\u8ff9\u4e0e\u8def\u5f84 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"

\u201c\u96c6\u667a\u767e\u79d1\u7cbe\u9009\u201d\u662f\u4e00\u4e2a\u957f\u671f\u4e13\u680f\uff0c\u6301\u7eed\u4e3a\u5927\u5bb6\u63a8\u9001\u590d\u6742\u6027\u79d1\u5b66\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8d44\u6e90\u4fe1\u606f\u3002\u4f5c\u4e3a\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u96c6\u667a\u767e\u79d1\u5e0c\u671b\u6253\u9020\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u6700\u5168\u9762\u7684\u767e\u79d1\u5168\u4e66\uff0c\u6b22\u8fce\u5bf9\u590d\u6742\u6027\u79d1\u5b66\u611f\u5174\u8da3\u3001\u70ed\u7231\u77e5\u8bc6\u6574\u7406\u548c\u5206\u4eab\u7684\u670b\u53cb\u52a0\u5165\uff01<\/p>\n

\u672c\u6587\u662f\u5bf9\u96c6\u667a\u767e\u79d1\u4e2d\u201c\u8def\u5f84\u201d\u8bcd\u6761\u7684\u6458\u5f55\uff0c\u53c2\u8003\u8d44\u6599\u53ca\u76f8\u5173\u8bcd\u6761\u8bf7\u53c2\u9605\u767e\u79d1\u8bcd\u6761\u539f\u6587\u3002
\u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\u6216\u8005\u524d\u5f80\u5bf9\u5e94\u7684\u767e\u79d1\u8bcd\u6761\u9875\u9762\u8fdb\u884c\u4fee\u6539\uff0c\u4e00\u7ecf\u4fee\u6539\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01
\u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\u6216\u8005\u524d\u5f80\u5bf9\u5e94\u7684\u767e\u79d1\u8bcd\u6761\u9875\u9762\u8fdb\u884c\u4fee\u6539\uff0c\u4e00\u7ecf\u4fee\u6539\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01<\/p>\n

\u76ee\u5f55<\/p>\n

\u4e00\u3001\u5b9a\u4e49\u4e8c\u3001\u4f8b\u5b50\u4e09\u3001\u8def\u5f84\u5bfb\u627e
\u56db\u3001\u7f16\u8005\u63a8\u8350\u4e94\u3001\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u5fd7\u613f\u8005\u62db\u52df\u5728\u56fe\u8bba Graph theory\u4e2d\uff0c\u56fe\u4e2d\u7684\u8def\u5f84 path\u662f\u4e00\u4e2a\u6709\u9650\u6216\u65e0\u9650\u7684\u8fb9\u5e8f\u5217\uff0c\u8fd9\u4e9b\u8fb9\u8fde\u63a5\u7740\u4e00\u7cfb\u5217\u9876\u70b9\uff0c\u8fd9\u4e9b\u9876\u70b9\u5728\u5927\u591a\u6570\u5b9a\u4e49\u4e2d\u90fd\u662f\u4e0d\u540c\u7684(\u53c8\u56e0\u4e3a\u8fd9\u4e9b\u9876\u70b9\u662f\u4e0d\u540c\u7684\uff0c\u6240\u4ee5\u56fe\u4e2d\u7684\u8fb9\u4e5f\u662f\u4e0d\u540c\u7684)\u3002\u6709\u5411\u56fe\u4e2d\u7684\u6709\u5411\u8def\u5f84 directed path\uff08\u6709\u65f6\u4e5f\u79f0\u4e3adipath\uff09\uff0c\u662f\u4e00\u4e2a\u6709\u9650\u6216\u65e0\u9650\u7684\u8fb9\u5e8f\u5217\uff0c\u5b83\u8fde\u63a5\u4e00\u7cfb\u5217\u4e0d\u540c\u7684\u9876\u70b9\uff0c\u5e76\u5177\u6709\u9644\u52a0\u4e00\u4e2a\u6761\u4ef6\uff1a\u5e8f\u5217\u4e2d\u6240\u6709\u7684\u8fb9\u90fd\u65b9\u5411\u90fd\u76f8\u540c\u3002
\u56fe1\uff1a\u4e00\u4e2a\u4e09\u7ef4\u7684\u8d85\u7acb\u65b9\u4f53\u56fe\u8868\u663e\u793a\u4e00\u4e2a\u7ea2\u8272\u7684\u54c8\u5bc6\u987f\u56fe\uff0c\u548c\u4e00\u4e2a\u9ed1\u8272\u7684\u6700\u957f\u8bf1\u5bfc\u8def\u5f84<\/p>\n

\u8def\u5f84\u662f\u56fe\u8bba\u7684\u57fa\u672c\u6982\u5ff5\uff0c\u5728\u5927\u591a\u6570\u56fe\u8bba\u6587\u672c\u7684\u5bfc\u8bba\u90e8\u5206\u90fd\u6709\u63cf\u8ff0\uff0c\u89c1Bondy and Murty\uff081976\uff09 \uff0c Gibbons\uff081985\uff09\uff0c\u6216Diestel\uff082005\uff09\u3002Korte\uff081990\uff09\u7b49\u4eba\u8457\u4f5c\u4e2d\uff0c\u6db5\u76d6\u4e86\u66f4\u591a\u5173\u4e8e\u56fe\u4e2d\u8def\u5f84\u7684\u9ad8\u7ea7\u7b97\u6cd5\u7684\u8bdd\u9898\u3002






\u5b9a\u4e49


<\/p>\n

\u901a\u8def \u8f68\u8ff9 \u8def\u5f84 Walk, trail, path
\u56fe2\uff1a\u4eceA\u5230E\u7684\u8f68\u8ff9\uff0c\u975e\u8def\u5f84<\/p>\n

\u901a\u8def Walk\uff1a\u662f\u8fde\u63a5\u4e00\u7cfb\u5217\u9876\u70b9\u5f62\u6210\u7684\u6709\u9650\u6216\u65e0\u9650\u7684\u8fb9\u5e8f\u5217\u3002\u4ee5\u4e00\u4e2a\u56fe\u4e3a\u4f8b G = ( V, E, \u03d5 ) \u3002\u6709\u9650\u901a\u8def finite walk\u662f\u4e00\u7cfb\u5217\u7684\u8fb9 ( e1, e2, \u2026, en \u2212 1 )\uff0c\u5176\u9876\u70b9\u5e8f\u5217( v1, v2, \u2026, vn ) \u3002 \u03d5 ( ei ) = {vi, vi + 1}\u5bf9\u4e8ei = 1, 2, \u2026, n \u2212 1\u3002( v1, v2, \u2026, vn ) \u662f\u79fb\u52a8\u7684\u9876\u70b9\u5e8f\u5217\u3002\u5982\u679c v1 = vn \uff0c\u5219\u6b64\u901a\u8def\u5c01\u95ed\uff0c\u53cd\u4e4b\u5219\u5f00\u653e\u3002\u65e0\u9650\u901a\u8def infinite walk\u662f\u7531\u4e00\u7cfb\u5217\u8fb9\u7ec4\u6210\u7684\uff0c\u5b83\u4eec\u7684\u7c7b\u578b\u4e0e\u8fd9\u91cc\u63cf\u8ff0\u7684\u76f8\u540c\uff0c\u4f46\u6ca1\u6709\u8d77\u70b9\u6216\u7ec8\u70b9\uff0c\u800c\u4e00\u4e2a\u534a\u65e0\u9650\u901a\u8def(\u6216\u5149\u7ebf)\u5219\u6709\u8d77\u70b9\u4f46\u662f\u6ca1\u6709\u7ec8\u70b9\u3002\u8f68\u8ff9 trail\u662f\u6240\u6709\u7684\u8fb9\u7f18\u90fd\u6e05\u6670\u53ef\u89c1\u7684\u901a\u8def\u3002\u8def\u5f84 path\u662f\u4e00\u6761\u6240\u6709\u9876\u70b9\uff08\u5305\u62ec\u6240\u6709\u8fb9\uff09\u90fd\u662f\u4e0d\u540c\u7684\u8f68\u8ff9\u3002
\u5982\u679c w = ( e1, e2, \u2026, en \u2212 1 )\u662f\u6709\u9876\u70b9\u7684\u5e8f\u5217 (v1, v2, \u2026, vn)\uff0c\u90a3\u4e48w \u5c31\u662f\u4ece v1 \u5230 vn\u7684\u6709\u9650\u901a\u8def\u3002\u540c\u6837\uff0c\u5bf9\u4e8e\u4e00\u6761\u8f68\u8ff9\u6216\u8005\u4e00\u6761\u8def\u5f84\u4e5f\u662f\u5982\u6b64\u3002\u5982\u679c\u4e24\u4e2a\u4e0d\u540c\u7684\u9876\u70b9\u4e4b\u95f4\u6709\u4e00\u4e2a\u6709\u9650\u901a\u8def\uff0c\u90a3\u4e48\u5728\u5b83\u4eec\u4e4b\u95f4\u4e5f\u6709\u4e00\u6761\u6709\u9650\u7684\u8f68\u8ff9\u548c\u4e00\u6761\u6709\u9650\u7684\u8def\u5f84\u3002
\u6709\u4e9b\u5b66\u8005\u5bf9\u8def\u5f84\u7684\u5b9a\u4e49\u4e2d\u5e76\u4e0d\u8981\u6c42\u5b83\u7684\u6240\u6709\u9876\u70b9\u90fd\u662f\u4e0d\u540c\u7684\uff0c\u800c\u662f\u4f7f\u7528\u672f\u8bed\u201c\u7b80\u5355\u8def\u5f84\u201d\u6765\u6307\u4ee3\u8fd9\u6837\u7684\u8def\u5f84\u3002
\u4e00\u4e2a\u52a0\u6743\u56fe weighted graph\u5c06\u4e00\u4e2a\u503c\uff08\u6743\u91cd\uff09\u4e0e\u56fe\u4e2d\u7684\u6bcf\u6761\u8fb9\u76f8\u5173\u8054\u3002\u4e00\u4e2a\u52a0\u6743\u56fe\u4e2d\u7684\u901a\u8def\uff08\u6216\u8f68\u8ff9\u6216\u8def\u5f84\uff09\u7684\u6743\u662f\u6240\u6709\u8fb9\u7684\u6743\u4e4b\u548c\u3002\u6709\u65f6\uff0c\u201c\u6210\u672c cost\u201d\u6216\u201c\u957f\u5ea6 length\u201d\u8fd9\u4e24\u4e2a\u8bcd\u53ef\u4ee5\u7528\u6765\u6307\u4ee3\u201c\u6743\u91cd\u201d\u8fd9\u4e00\u6982\u5ff5\u3002
\u6709\u5411\u7684\u901a\u8def\uff0c\u8f68\u8ff9\uff0c\u8def\u5f84 Directed walk, trail, path\u6709\u5411\u901a\u8def directed walk\u662f\u6307\u7531\u8fde\u63a5\u4e00\u7cfb\u5217\u9876\u70b9\u7684\u8fb9\u6cbf\u76f8\u540c\u65b9\u5411\u5b9a\u5411\u5f62\u6210\u7684\u6709\u9650\u6216\u65e0\u9650\u5e8f\u5217\u3002
\u4ee5\u4e00\u4e2a\u6709\u5411\u56fe G = ( V, E, \u03d5 ) \u4e3a\u4f8b\u3002\u6709\u9650\u6709\u5411\u901a\u8def\u7531\u4e00\u7cfb\u5217\u7684\u8fb9\u7ec4\u6210 ( e1, e2, \u2026, en \u2212 1 )\uff0c\u800c\u5bf9\u4e8e\u8fd9\u4e9b\u8fb9\uff0c\u53c8\u5b58\u5728\u4e00\u7cfb\u5217\u7684\u9876\u70b9 ( v1, v2, \u2026, vn )\u3002 \u03d5 ( ei ) = ( vi, vi + 1 )\u5bf9\u4e8e i = 1, 2, \u2026, n \u2212 1 \u3002( v1, v2, \u2026, vn )\u662f\u6709\u5411\u901a\u8def\u7684\u9876\u70b9\u5e8f\u5217\u3002\u65e0\u9650\u6709\u5411\u901a\u8def\u662f\u4e00\u4e2a\u8fb9\u5e8f\u5217\uff0c\u5176\u7c7b\u578b\u4e0e\u672c\u6587\u63cf\u8ff0\u7684\u76f8\u540c\uff0c\u4f46\u8d77\u70b9\u6216\u7ec8\u70b9\uff0c\u800c\u534a\u65e0\u9650\u6709\u5411\u901a\u8def\uff08\u6216\u5c04\u7ebf\uff09\u6709\u8d77\u70b9\uff0c\u4f46\u6ca1\u6709\u7ec8\u70b9\u3002
\u6709\u5411\u8f68\u8ff9 directed trail\u662f\u6307\u6240\u6709\u8fb9\u90fd\u53ef\u89c1\u7684\u8f68\u8ff9\u3002
\u6709\u5411\u8def\u5f84 directed path\u662f\u6307\u6240\u6709\u9876\u70b9\u90fd\u4e0d\u540c\u7684\u6709\u5411\u8def\u5f84\u3002<\/p>\n

\u5047\u8bbe\u4e00\u4e2a\u901a\u8def w = ( e1, e2, \u2026, en \u2212 1 )\u662f\u9876\u70b9\u5e8f\u5217\u6709\u9650\u7684( v1, v2, \u2026, vn )\u6709\u5411\u901a\u8def\uff0c\u90a3\u4e48w\u5c31\u662f\u4ece v1 \u5230 vn\u7684\u901a\u8def\u3002\u540c\u6837\uff0c\u5bf9\u4e8e\u6709\u5411\u8f68\u8ff9\u6216\u8def\u5f84\u4e5f\u662f\u5982\u6b64\u3002\u5982\u679c\u5728\u4e24\u4e2a\u4e0d\u540c\u7684\u9876\u70b9\u4e4b\u95f4\u5b58\u5728\u6709\u9650\u6709\u5411\u901a\u8def\uff0c\u90a3\u4e48\u5728\u5b83\u4eec\u4e4b\u95f4\u4e5f\u5b58\u5728\u6709\u9650\u6709\u5411\u8f68\u8ff9\u548c\u6709\u9650\u6709\u5411\u8def\u5f84\u3002
\u6709\u4e9b\u5b66\u8005\u5e76\u4e0d\u8981\u6c42\u6709\u5411\u8def\u5f84\u7684\u6240\u6709\u9876\u70b9\u90fd\u662f\u4e0d\u540c\u7684\uff0c\u56e0\u6b64\u4ed6\u4eec\u7528\u201c\u7b80\u5355\u6709\u5411\u8def\u5f84 simple directed path\u201d\u8fd9\u4e2a\u672f\u8bed\u6765\u8868\u793a\u5b83\u3002
\u4e00\u4e2a\u52a0\u6743\u6709\u5411\u56fe\u5c06\u4e00\u4e2a\u503c\uff08\u6743\u91cd\uff09\u4e0e\u6709\u5411\u56fe\u4e2d\u7684\u6bcf\u6761\u8fb9\u76f8\u5173\u8054\u3002\u52a0\u6743\u6709\u5411\u56fe\u4e2d\u6709\u5411\u901a\u8def\uff08\u6216\u8def\u5f84\uff09\u7684\u6743\u662f\u6709\u5411\u8fb9\u6743\u91cd\u7684\u548c\u3002\u6709\u65f6\uff0c\u201c\u6210\u672c cost\u201d\u6216\u201c\u957f\u5ea6 length\u201d\u8fd9\u4e24\u4e2a\u8bcd\u53ef\u4ee5\u7528\u6765\u6307\u4ee3\u201c\u6743\u91cd\u201d\u8fd9\u4e00\u6982\u5ff5\u3002





\u4f8b\u5b50



\u5982\u679c\u8def\u5f84\u5305\u542b\u6bcf\u4e00\u5bf9\u9876\u70b9\uff0c\u90a3\u4e48\u56fe\u5c31\u662f\u8fde\u901a\u7684\u3002
\u5982\u679c\u4e00\u4e2a\u6709\u5411\u56fe\u4e2d\u5b58\u5728\u5305\u542b\u6bcf\u5bf9\u9876\u70b9\u7684\u76f8\u5bf9\u6709\u5411\u8def\u5f84\uff0c\u90a3\u4e48\u8fd9\u5c31\u662f\u5f3a\u8fde\u63a5\u6709\u5411\u56fe Strongly-connected digraph\u3002
\u6ca1\u6709\u8fb9\u8fde\u63a5\u4e24\u4e2a\u4e0d\u8fde\u7eed\u7684\u8def\u5f84\u9876\u70b9\u7684\u8def\u5f84\u79f0\u4e3a\u8bf1\u5bfc\u8def\u5f84 induced path\u3002
\u5305\u542b\u56fe\u7684\u6bcf\u4e2a\u9876\u70b9\u7684\u8def\u5f84\u79f0\u4e3a\u54c8\u5bc6\u987f\u8def\u5f84 Hamiltonian Path\u3002
\u5982\u679c\u4e24\u6761\u8def\u5f84\u6ca1\u6709\u4efb\u4f55\u5171\u540c\u7684\u5185\u90e8\u9876\u70b9\uff0c\u90a3\u4e48\u5b83\u4eec\u4e0e\u9876\u70b9\u65e0\u5173\uff08\u6362\u8a00\u4e4b\uff0c\u5185\u90e8\u9876\u70b9\u4e0d\u76f8\u4ea4\uff09\u3002\u7c7b\u4f3c\u5730\uff0c\u5982\u679c\u4e24\u6761\u8def\u5f84\u6ca1\u6709\u4efb\u4f55\u5171\u540c\u7684\u5185\u8fb9\uff0c\u90a3\u4e48\u5b83\u4eec\u662f\u8fb9\u72ec\u7acb\u7684\uff08\u6216\u8fb9\u4e0d\u76f8\u4ea4\uff09\u3002\u4e24\u6761\u5185\u90e8\u9876\u70b9\u4e0d\u76f8\u4ea4\u7684\u8def\u5f84\u7684\u8fb9\u4e5f\u4e0d\u76f8\u4ea4\uff0c\u4f46\u53cd\u4e4b\u672a\u5fc5\u6b63\u786e\u7684\u3002
\u56fe\u4e2d\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\uff0c\u5982\u679c\u6700\u77ed\u8def\u5f84\u5b58\u5728\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u7684\u8ddd\u79bb\u662f\u6700\u77ed\u8def\u5f84\u7684\u957f\u5ea6\uff0c\u5426\u5219\u8be5\u8ddd\u79bb\u662f\u65e0\u7a77\u5927\u3002
\u8fde\u63a5\u56fe\u7684\u76f4\u5f84\u662f\u56fe\u7684\u9876\u70b9\u5bf9\u4e4b\u95f4\u7684\u6700\u5927\u8ddd\u79bb\uff08\u5982\u4e0a\u5b9a\u4e49\uff09\u3002<\/p>\n



\u8def\u5f84\u5bfb\u627e



\u6c42\u89e3\u56fe\u7684\u6700\u77ed\u548c\u6700\u957f\u8def\u5f84\u6709\u591a\u79cd\u7b97\u6cd5\uff0c\u4f46\u662f\u524d\u8005\u7684\u8ba1\u7b97\u6bd4\u540e\u8005\u7b80\u5355\u5f97\u591a\u3002Dijkstra \u7b97\u6cd5\u4ea7\u751f\u4e86\u4e00\u4e2a\u4ece\u6e90\u9876\u70b9\u5230\u65e0\u5411\u6216\u6709\u5411\u56fe\u4e2d\u6bcf\u4e2a\u9876\u70b9\u7684\u6700\u77ed\u8def\u5f84\u5217\u8868\uff0c\u800cBellman-Ford \u7b97\u6cd5 \u53ef\u4ee5\u5e94\u7528\u4e8e\u5177\u6709\u8d1f\u8fb9\u6743\u91cd\u7684\u6709\u5411\u56fe\u3002\u5229\u7528 Floyd-Warshall \u7b97\u6cd5\u53ef\u4ee5\u6c42\u51fa\u52a0\u6743\u6709\u5411\u56fe\u4e2d\u6240\u6709\u9876\u70b9\u5bf9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n


\u7f16\u8005\u63a8\u8350


<\/p>\n

\u7f51\u7edc\u52a8\u529b\u5b66\u8bfe\u7a0b<\/p>\n

\u96c6\u667a\u5b66\u56ed\u7279\u9080\u9648\u5173\u8363\u3001\u9879\u6797\u82f1\u3001\u6a0a\u745b\u3001\u5ba3\u7426\u3001\u674e\u7fd4\u3001\u53f2\u5b9a\u534e\u3001\u674e\u806a\u3001\u8363\u667a\u6d77\u3001\u5468\u8fdb\u3001\u738b\u7433\u7b49\u7f51\u7edc\u79d1\u5b66\u4e13\u5bb6\u4f5c\u4e3a\u5bfc\u5e08\uff0c\u4f9d\u6258\u6c6a\u5c0f\u5e06\u3001\u674e\u7fd4\u3001\u9648\u5173\u8363\u7684\u7ecf\u5178\u6559\u6750\u300a\u7f51\u7edc\u79d1\u5b66\u5bfc\u8bba\u300b\uff0c\u81ea2\u670827\u65e5\u8d77\u5f00\u5c55\u7cfb\u5217\u4e0a\u7ebf\u8bfe\u7a0b\uff0c\u4ee5\u7f51\u7edc\u52a8\u529b\u5b66\u4e3a\u4e3b\u7ebf\u6784\u5efa\u7f51\u7edc\u79d1\u5b66\u77e5\u8bc6\u4f53\u7cfb\u3002\u6b22\u8fce\u5e0c\u671b\u8fdb\u5165\u7f51\u7edc\u79d1\u5b66\u9886\u57df\u3001\u63d0\u9ad8\u7f51\u7edc\u5206\u6790\u80fd\u529b\u3001\u4e0e\u4e00\u7ebf\u4e13\u5bb6\u63a2\u8ba8\u95ee\u9898\u7684\u670b\u53cb\u62a5\u540d\u53c2\u52a0\uff01<\/p>\n

<\/a>
\u70b9\u51fb\u67e5\u770b\u8bfe\u7a0b\u8be6\u60c5\uff1a2021\u91cd\u78c5\u65b0\u8bfe\uff1a\u63a2\u7d22\u7f51\u7edc\u52a8\u529b\u5b66\u2014\u2014\u7f51\u7edc\u79d1\u5b66\u7b2c\u4e8c\u671f<\/a><\/p>\n

\u8bfe\u7a0b\u63a8\u8350\uff1a\u7f51\u7edc\u79d1\u5b66\u5bfc\u8bba | \u7f51\u7edc\u79d1\u5b66\u96c6\u667a\u8bfe\u5802\u7b2c\u4e8c\u671f https:\/\/campus.swarma.org\/course\/2328





\u767e\u79d1\u9879\u76ee\u5fd7\u613f\u8005\u62db\u52df




\u4f5c\u4e3a\u96c6\u667a\u767e\u79d1\u9879\u76ee\u56e2\u961f\u7684\u6210\u5458\uff0c\u672c\u6587\u5185\u5bb9\u7531Ryan\uff0cCecileLi\uff0c\u8584\u8377\u53c2\u4e0e\u8d21\u732e\u3002\u6211\u4eec\u4e5f\u4e3a\u6bcf\u4f4d\u4f5c\u8005\u548c\u5fd7\u613f\u8005\u51c6\u5907\u4e86\u4e13\u5c5e\u7b80\u4ecb\u548c\u4e2a\u4eba\u96c6\u667a\u767e\u79d1\u4e3b\u9875\uff0c\u66f4\u591a\u4fe1\u606f\u53ef\u4ee5\u8bbf\u95ee\u5176\u96c6\u667a\u767e\u79d1\u4e2a\u4eba\u4e3b\u9875\u3002<\/p>\n

\u4ee5\u4e0a\u5185\u5bb9\u90fd\u662f\u6211\u4eec\u505a\u8fd9\u9879\u76ee\u7684\u8d77\u70b9\uff0c\u4f5c\u4e3a\u6765\u81ea\u4e0d\u540c\u5b66\u79d1\u548c\u9886\u57df\u7684\u5fd7\u613f\u8005\uff0c\u6211\u4eec\u5efa\u7acb\u8d77\u4e00\u4e2a\u6709\u6548\u7684\u767e\u79d1\u56e2\u961f\uff0c\u5206\u914d\u6709\u5ba1\u6821\u3001\u7ffb\u8bd1\u3001\u7f16\u8f91\u3001\u5ba3\u4f20\u7b49\u5de5\u4f5c\u3002\u6211\u4eec\u79c9\u6301\uff1a\u77e5\u8bc6\u4ece\u6211\u800c\u6765\uff0c\u95ee\u9898\u5230\u6211\u4e3a\u6b62\u7684\u4fe1\u5ff5\uff0c\u8ba4\u771f\u8d1f\u8d23\u7f16\u64b0\u6bcf\u4e00\u4e2a\u8bcd\u6761\u3002<\/p>\n

<\/div>\n

\u5728\u8fd9\u91cc\u4ece\u590d\u6742\u6027\u77e5\u8bc6\u51fa\u53d1\u4e0e\u4f19\u4f34\u540c\u884c\uff0c\u540c\u65f6\u6211\u4eec\u5e0c\u671b\u6709\u66f4\u591a\u5fd7\u613f\u8005\u52a0\u5165\u8fd9\u4e2a\u56e2\u961f\uff0c\u4f7f\u767e\u79d1\u8bcd\u6761\u5185\u5bb9\u5f97\u5230\u6269\u5145\uff0c\u5e76\u4e3a\u6bcf\u4f4d\u5fd7\u613f\u8005\u63d0\u4f9b\u76f8\u5e94\u5956\u52b1\u4e0e\u8d44\u6e90\uff0c\u5efa\u7acb\u4e2a\u4eba\u4e3b\u9875\u4e0e\u8d21\u732e\u8bb0\u5f55\uff0c\u4f7f\u5176\u80fd\u591f\u7ee7\u7eed\u63a2\u7d22\u590d\u6742\u4e16\u754c\u3002<\/p>\n

\u5982\u679c\u4f60\u6709\u610f\u53c2\u4e0e\u66f4\u52a0\u7cfb\u7edf\u7cbe\u7ec6\u7684\u5206\u5de5\uff0c\u626b\u63cf\u4e8c\u7ef4\u7801\u586b\u5199\u62a5\u540d\u8868\uff0c\u6211\u4eec\u671f\u5f85\u4f60\u7684\u52a0\u5165\uff01<\/p>\n

\u96c6\u667a\u767e\u79d1\u62a5\u540d\u8868<\/p>\n

\u6765\u6e90\uff1a\u96c6\u667a\u767e\u79d1
\u7f16\u8f91\uff1a\u738b\u5efa\u840d<\/p>\n

\u63a8\u8350\u9605\u8bfb
\u4ec0\u4e48\u662f\u9e1f\u7fa4\u7b97\u6cd5 | \u96c6\u667a\u767e\u79d1<\/a>
\u4ec0\u4e48\u662f\u5ea6\u5206\u5e03 | \u96c6\u667a\u767e\u79d1<\/a><\/p>\n

\u4ec0\u4e48\u662f\u7cd6\u57df\u6a21\u578b | \u96c6\u667a\u767e\u79d1<\/a><\/p>\n

\u4ec0\u4e48\u662f\u6982\u7387\u56fe\u6a21\u578b\uff1a\u8868\u793a\u3001\u63a8\u7406\u4e0e\u5b66\u4e60 | \u96c6\u667a\u767e\u79d1 <\/a><\/p>\n

\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/a><\/p>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u9605\u8bfb\u8def\u5f84\u76f8\u5173\u5185\u5bb9\u4e0e\u53c2\u8003\u6587\u732e <\/div>\n","protected":false},"excerpt":{"rendered":"

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