1.\u7b54\u6848\uff1a\u628a\u6251\u514b\u724c\u5206\u6210\u4e24\u5806\uff0c\u4e00\u580610\u5f20\uff0c\u4e00\u580642\u5f20\u3002\u7136\u540e\uff0c\u628a\u5c0f\u7684\u90a3\u4e00\u5806\u91cc\u7684\u6240\u6709\u724c\u5168\u90e8\u7ffb\u8fc7\u6765\u3002<\/p>\n
2.\u7b54\u6848\uff1a\u5982\u679c\u662f\u516c\u6b63\u7684\u786c\u5e01\uff0c\u5219\u6295\u63b7\u4e24\u6b21\uff0c\u201c\u6b63\u53cd\u201d\u4e3a1\uff0c\u201c\u53cd\u6b63\u201d\u4e3a2\uff0c\u201c\u6b63\u6b63\u201d\u4e3a3\uff0c\u201c\u53cd\u53cd\u201d\u91cd\u6765\u3002
\n\u5982\u679c\u662f\u4e0d\u516c\u6b63\u7684\u786c\u5e01\uff0c\u6ce8\u610f\u5230\u51fa\u73b0\u201c\u6b63\u53cd\u201d\u548c\u201c\u53cd\u6b63\u201d\u7684\u6982\u7387\u4e00\u6837\uff0c\u56e0\u6b64\u4ee4\u201c\u6b63\u53cd\u53cd\u6b63\u201d\u3001\u201c\u53cd\u6b63\u6b63\u53cd\u201d\u3001\u201c\u6b63\u53cd\u6b63\u53cd\u201d\u5206\u522b\u4e3a1\u30012\u30013\uff0c\u5176\u4f59\u60c5\u51b5\u91cd\u6765\u3002\u53e6\u4e00\u79cd\u66f4\u5999\u7684\u529e\u6cd5\u662f\uff0c\u6295\u63b7\u4e09\u6b21\u786c\u5e01\uff0c\u201c\u6b63\u53cd\u53cd\u201d\u4e3a1\uff0c\u201c\u53cd\u6b63\u53cd\u201d\u4e3a2\uff0c\u201c\u53cd\u53cd\u6b63\u201d\u4e3a3\uff0c\u5176\u4f59\u60c5\u51b5\u91cd\u6765\u3002<\/p>\n
3.\u7b54\u6848\uff1a\u5148\u53d6\u8005\u53ef\u4ee5\u8ba9\u81ea\u5df1\u603b\u662f\u53d6\u5947\u6570\u4f4d\u7f6e\u4e0a\u7684\u786c\u5e01\u6216\u8005\u603b\u662f\u53d6\u5076\u6570\u4f4d\u7f6e\u4e0a\u7684\u786c\u5e01\u3002\u6570\u4e00\u6570\u662f\u5947\u6570\u4f4d\u7f6e\u4e0a\u7684\u9762\u503c\u603b\u548c\u591a\u8fd8\u662f\u5076\u6570\u4f4d\u7f6e\u4e0a\u7684\u9762\u503c\u603b\u548c\u591a\uff0c\u7136\u540e\u603b\u662f\u53d6\u8fd9\u4e9b\u4f4d\u7f6e\u4e0a\u7684\u786c\u5e01\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n
4.\u7b54\u6848\uff1a\u603b\u5b58\u5728\u4e00\u4e2a\u52a0\u6cb9\u7ad9\uff0c\u4ec5\u7528\u5b83\u7684\u6cb9\u5c31\u8db3\u591f\u8dd1\u5230\u4e0b\u4e00\u4e2a\u52a0\u6cb9\u7ad9\uff08\u5426\u5219\u6240\u6709\u52a0\u6cb9\u7ad9\u7684\u6cb9\u91cf\u52a0\u8d77\u6765\u5c06\u4e0d\u591f\u5168\u7a0b\uff09\u3002\u628a\u4e0b\u4e00\u4e2a\u52a0\u6cb9\u7ad9\u7684\u6240\u6709\u6cb9\u90fd\u63d0\u524d\u642c\u5230\u8fd9\u4e2a\u52a0\u6cb9\u7ad9\u6765\uff0c\u5e76\u628a\u6cb9\u5df2\u88ab\u642c\u8d70\u7684\u52a0\u6cb9\u7ad9\u65e0\u89c6\u6389\u3002\u5728\u5269\u4e0b\u7684\u52a0\u6cb9\u7ad9\u4e2d\u7ee7\u7eed\u5bfb\u627e\u6cb9\u91cf\u8db3\u4ee5\u5230\u8fbe\u4e0b\u4e2a\u52a0\u6cb9\u7ad9\u7684\u5730\u65b9\uff0c\u4e0d\u65ad\u5408\u5e76\u52a0\u6cb9\u7ad9\uff0c\u76f4\u5230\u53ea\u5269\u4e00\u4e2a\u52a0\u6cb9\u7ad9\u4e3a\u6b62\u3002\u663e\u7136\u4ece\u8fd9\u91cc\u51fa\u53d1\u5c31\u80fd\u987a\u5229\u8dd1\u5b8c\u5168\u7a0b\u3002
\n\u53e6\u4e00\u79cd\u8bc1\u660e\u65b9\u6cd5\uff1a\u5148\u8ba9\u6c7d\u8f66\u6cb9\u7bb1\u91cc\u88c5\u597d\u8db3\u591f\u591a\u7684\u6cb9\uff0c\u968f\u4fbf\u4ece\u54ea\u4e2a\u52a0\u6cb9\u7ad9\u51fa\u53d1\u8bd5\u8dd1\u4e00\u5708\u3002\u8f66\u6bcf\u5230\u4e00\u4e2a\u52a0\u6cb9\u7ad9\u65f6\uff0c\u8bb0\u5f55\u6b64\u65f6\u6cb9\u7bb1\u91cc\u5269\u4e0b\u7684\u6cb9\u91cf\uff0c\u7136\u540e\u628a\u90a3\u4e2a\u52a0\u6cb9\u7ad9\u7684\u6cb9\u5168\u90e8\u88c5\u4e0a\u3002\u8bd5\u8dd1\u5b8c\u4e00\u5708\u540e\uff0c\u68c0\u67e5\u521a\u624d\u8def\u4e0a\u5230\u54ea\u4e2a\u52a0\u6cb9\u7ad9\u65f6\u5269\u7684\u6cb9\u91cf\u6700\u5c11\uff0c\u90a3\u4e48\u7a7a\u7740\u6cb9\u7bb1\u4ece\u90a3\u91cc\u51fa\u53d1\u663e\u7136\u4e00\u5b9a\u80fd\u8dd1\u5b8c\u5168\u7a0b\u3002<\/p>\n
5.\u7b54\u6848\uff1a\u5148\u8003\u8651\u4e00\u4e2a\u770b\u4f3c\u65e0\u5173\u7684\u95ee\u9898\u2014\u2014\u600e\u6837\u4ea7\u751f\u4e00\u4e2a1\u5230n\u7684\u968f\u673a\u6392\u5217\u3002\u9996\u5148\uff0c\u5728\u7eb8\u4e0a\u5199\u4e0b\u6570\u5b571\uff1b\u7136\u540e\uff0c\u628a2\u5199\u57281\u7684\u5de6\u8fb9\u6216\u8005\u53f3\u8fb9\uff1b\u7136\u540e\uff0c\u628a3\u5199\u5728\u6700\u5de6\u8fb9\uff0c\u6700\u53f3\u8fb9\uff0c\u6216\u8005\u63d2\u8fdb1\u548c2\u4e4b\u95f4\u2026\u2026\u603b\u4e4b\uff0c\u628a\u6570\u5b57i\u7b49\u6982\u7387\u5730\u653e\u8fdb\u7531\u524d\u9762i-1\u4e2a\u6570\u4ea7\u751f\u7684\uff08\u5305\u62ec\u6700\u5de6\u7aef\u548c\u6700\u53f3\u7aef\u5728\u5185\u7684\uff09\u5171i\u4e2a\u7a7a\u4f4d\u4e2d\u7684\u4e00\u4e2a\u3002\u8fd9\u6837\u751f\u6210\u7684\u663e\u7136\u662f\u4e00\u4e2a\u5b8c\u5168\u968f\u673a\u7684\u6392\u5217\u3002
\n\u6211\u4eec\u6362\u4e00\u4e2a\u89d2\u5ea6\u6765\u770b\u9898\u76ee\u63cf\u8ff0\u7684\u8fc7\u7a0b\uff1a\u5047\u60f3\u7528\u4e00\u6839\u7ef3\u5b50\u628a\u4e24\u4e2a\u7403\u62f4\u5728\u4e00\u8d77\uff0c\u628a\u8fd9\u6839\u7ef3\u5b50\u6807\u53f7\u4e3a1\u3002\u63a5\u4e0b\u6765\uff0c\u628a\u5176\u4e2d\u4e00\u4e2a\u5c0f\u7403\u5206\u88c2\u6210\u4e24\u4e2a\u5c0f\u7403\uff0c\u8fd9\u4e24\u4e2a\u5c0f\u7403\u7528\u6807\u53f7\u4e3a2\u7684\u7ef3\u5b50\u76f8\u8fde\u3002\u603b\u4e4b\uff0c\u628a\u201c\u653e\u8fdb\u7b2ci\u4e2a\u7403\u201d\u7684\u64cd\u4f5c\u60f3\u8c61\u6210\u628a\u5176\u4e2d\u4e00\u4e2a\u7403\u5206\u88c2\u6210\u4e24\u4e2a\u7528\u6807\u6709i-1\u7684\u7ef3\u5b50\u76f8\u8fde\u7684\u5c0f\u7403\u3002\u8054\u60f3\u6211\u4eec\u524d\u9762\u7684\u8ba8\u8bba\uff0c\u8fd9\u4e9b\u7ef3\u5b50\u7684\u6807\u53f7\u4e8b\u5b9e\u4e0a\u662f\u4e00\u4e2a\u968f\u673a\u7684\u5168\u6392\u5217\uff0c\u4e5f\u5c31\u662f\u8bf4\u6700\u5f00\u59cb\u7ef3\u5b501\u7684\u4f4d\u7f6e\u6700\u540e\u7b49\u53ef\u80fd\u5730\u51fa\u73b0\u5728\u6bcf\u4e2a\u5730\u65b9\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4e24\u8fb9\u7684\u5c0f\u7403\u4e2a\u6570(1,n-1)\u3001(2,n-2)\u3001(3,n-3)\u3001\u2026\u2026\u3001(n-1,1)\u8fd9n-1\u79cd\u60c5\u51b5\u7b49\u53ef\u80fd\u5730\u53d1\u751f\u3002\u56e0\u6b64\uff0c\u5c0f\u888b\u5b50\u91cc\u7684\u7403\u6570\u5927\u7ea6\u4e3an\/4\u4e2a\u3002\u51c6\u786e\u5730\u8bf4\uff0c\u5f53n\u4e3a\u5947\u6570\u65f6\uff0c\u5c0f\u888b\u5b50\u91cc\u7684\u7403\u6570\u4e3a(n+1)\/4\uff1b\u5f53n\u4e3a\u5076\u6570\u65f6\uff0c\u5c0f\u888b\u5b50\u91cc\u7684\u7403\u6570\u4e3an^2\/(4n-4)\u3002<\/p>\n
6.\u7b54\u6848\uff1a\u81f3\u5c11\u8981n\u4e2a\uff0c\u6bd4\u5982\u4e00\u6761\u5bf9\u89d2\u7ebf\u4e0a\u7684n\u4e2a\u683c\u5b50\u3002n\u4e2a\u683c\u5b50\u4e5f\u662f\u5fc5\u9700\u7684\u3002\u5f53\u4e00\u4e2a\u65b0\u7684\u683c\u5b50\u88ab\u611f\u67d3\u540e\uff0c\u5168\u4f53\u88ab\u611f\u67d3\u7684\u683c\u5b50\u6240\u7ec4\u6210\u7684\u56fe\u5f62\u7684\u5468\u957f\u5c06\u51cf\u5c110\u4e2a\u30012\u4e2a\u62164\u4e2a\u5355\u4f4d\uff08\u5177\u4f53\u51cf\u5c11\u4e86\u591a\u5c11\u8981\u770b\u5b83\u5468\u56f4\u88ab\u611f\u67d3\u7684\u683c\u5b50\u6709\u591a\u5c11\u4e2a\uff09\u3002\u53c8\u56e0\u4e3a\u5f53\u6240\u6709\u683c\u5b50\u90fd\u88ab\u611f\u67d3\u540e\uff0c\u56fe\u5f62\u7684\u5468\u957f\u4e3a4n\uff0c\u56e0\u6b64\u521d\u59cb\u65f6\u81f3\u5c11\u8981\u6709n\u4e2a\u88ab\u611f\u67d3\u7684\u683c\u5b50\u3002<\/p>\n
7.\u7b54\u6848\uff1a\u53ef\u4ee5\u3002\u5efa\u4e00\u4e2a\u4e8c\u5206\u56feG(X,Y)\uff0c\u5176\u4e2dX\u6709m\u4e2a\u9876\u70b9\u4ee3\u8868\u4e86\u68cb\u76d8\u7684m\u4e2a\u884c\uff0cY\u6709n\u4e2a\u9876\u70b9\u4ee3\u8868\u4e86\u68cb\u76d8\u7684n\u4e2a\u5217\u3002\u7b2ci\u884c\u7b2cj\u5217\u6709\u68cb\u5b50\u5c31\u5728X(i)\u548cY(j)\u4e4b\u95f4\u8fde\u4e00\u6761\u8fb9\u3002\u5148\u627e\u51fa\u56feG\u91cc\u7684\u6240\u6709\u73af\uff08\u7531\u4e8e\u662f\u4e8c\u5206\u56fe\uff0c\u73af\u7684\u957f\u5ea6\u4e00\u5b9a\u662f\u5076\u6570\uff09\uff0c\u628a\u73af\u91cc\u7684\u8fb9\u7ea2\u84dd\u4ea4\u66ff\u67d3\u8272\u3002\u5269\u4e0b\u7684\u6ca1\u67d3\u8272\u7684\u56fe\u4e00\u5b9a\u662f\u4e00\u4e9b\u6811\u3002\u5bf9\u6bcf\u68f5\u6811\u9012\u5f52\u5730\u8fdb\u884c\u64cd\u4f5c\uff1a\u53bb\u6389\u4e00\u4e2a\u53f6\u5b50\u8282\u70b9\u548c\u5bf9\u5e94\u8fb9\uff0c\u628a\u5269\u4e0b\u7684\u6811\u8fdb\u884c\u5408\u6cd5\u7684\u7ea2\u84dd\u4e8c\u67d3\u8272\uff0c\u518d\u628a\u521a\u624d\u53bb\u6389\u7684\u9876\u70b9\u548c\u8fb9\u52a0\u56de\u53bb\uff0c\u7ed9\u8fd9\u4e2a\u8fb9\u9002\u5f53\u7684\u989c\u8272\u4ee5\u6ee1\u8db3\u8981\u6c42\u3002<\/p>\n
8.\u7b54\u6848\uff1a\u4e0d\u80fd\u3002\u5927\u77e9\u9635\u4e2d\u670936\u4e2a3*3\u7684\u5c0f\u77e9\u9635\u548c25\u4e2a4*4\u7684\u5c0f\u77e9\u9635\uff0c\u56e0\u6b64\u603b\u5171\u670961\u79cd\u53ef\u80fd\u7684\u64cd\u4f5c\u3002\u663e\u7136\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u64cd\u4f5c\u5e8f\u5217\uff0c\u8fd9\u4e9b\u64cd\u4f5c\u7684\u5148\u540e\u987a\u5e8f\u662f\u65e0\u5173\u7d27\u8981\u7684\uff1b\u53e6\u5916\uff0c\u5728\u4e00\u4e2a\u64cd\u4f5c\u5e8f\u5217\u4e2d\u4f7f\u7528\u4e24\u79cd\u6216\u4e24\u79cd\u4ee5\u4e0a\u76f8\u540c\u7684\u64cd\u4f5c\u4e5f\u662f\u65e0\u7528\u7684\u3002\u56e0\u6b64\uff0c\u5b9e\u8d28\u4e0d\u540c\u7684\u64cd\u4f5c\u5e8f\u5217\u53ea\u67092^61\u79cd\u3002\u4f468*8\u768401\u77e9\u9635\u4e00\u5171\u67092^64\u79cd\uff0c\u56e0\u6b64\u4e0d\u662f\u6bcf\u79cd\u60c5\u51b5\u90fd\u6709\u529e\u6cd5\u8fbe\u5230\u76ee\u7684\u3002<\/p>\n
9.\u7b54\u6848\uff1a\u6309\u71672, 3, 4, 2, 3, 4\u7684\u987a\u5e8f\u68c0\u67e5\u72d0\u72f8\u6d1e\u53ef\u4ee5\u4fdd\u8bc1\u6293\u4f4f\u72d0\u72f8\u3002\u4e3a\u4e86\u8bf4\u660e\u8fd9\u4e2a\u65b9\u6848\u662f\u53ef\u884c\u7684\uff0c\u7528\u96c6\u5408F\u8868\u793a\u72d0\u72f8\u53ef\u80fd\u51fa\u73b0\u7684\u4f4d\u7f6e\uff0c\u521d\u59cb\u65f6F = {1, 2, 3, 4, 5}\u3002\u5982\u679c\u5b83\u4e0d\u57282\u53f7\u6d1e\uff0c\u5219\u7b2c\u4e8c\u5929\u72d0\u72f8\u5df2\u7ecf\u8dd1\u5230\u4e86F = {2, 3, 4, 5}\u3002\u5982\u679c\u6b64\u65f6\u5b83\u4e0d\u57283\u53f7\u6d1e\uff0c\u5219\u7b2c\u4e09\u5929\u72d0\u72f8\u4e00\u5b9a\u8dd1\u5230\u4e86F = {1, 3, 4, 5}\u3002\u5982\u679c\u6b64\u65f6\u5b83\u4e0d\u57284\u53f7\u6d1e\uff0c\u5219\u518d\u8fc7\u4e00\u665a\u540eF = {2, 4}\u3002\u5982\u679c\u6b64\u65f6\u5b83\u4e0d\u57282\u53f7\u6d1e\uff0c\u5219\u518d\u8fc7\u4e00\u5929F = {3, 5}\u3002\u5982\u679c\u6b64\u65f6\u5b83\u4e0d\u57283\u53f7\u6d1e\uff0c\u518d\u8fc7\u4e00\u5929\u5b83\u5c31\u4e00\u5b9a\u8dd1\u52304\u53f7\u6d1e\u4e86\u3002
\n\u65b9\u6848\u4e0d\u662f\u552f\u4e00\u7684\uff0c\u4e0b\u9762\u8fd9\u4e9b\u65b9\u6848\u90fd\u662f\u53ef\u884c\u7684\uff1a
\n2, 3, 4, 4, 3, 2
\n4, 3, 2, 2, 3, 4
\n4, 3, 2, 4, 3, 2<\/p>\n
10.\u7b54\u6848\uff1a\u4e8b\u5b9e\u4e0a\uff0c\u4ece\u4e00\u4e2a\u66f4\u5f3a\u7684\u547d\u9898\u51fa\u53d1\u53cd\u800c\u80fd\u4f7f\u95ee\u9898\u53d8\u5f97\u66f4\u7b80\u5355\u3002\u5bf9\u4e8e\u4e00\u4e2aa*b*c\u7684\u957f\u65b9\u4f53\uff0c\u6211\u4eec\u9700\u8981f(a)+f(b)+f(c)\u5200\uff0c\u5176\u4e2df(x)=log(x)\/log(2)\u3002\u53ea\u9700\u8981\u6ce8\u610f\u5230\uff0c\u5728\u6574\u4e2a\u8fc7\u7a0b\u4e2d\u7684\u4efb\u4f55\u4e00\u6b65\uff0c\u5207\u5b8c\u5f53\u524d\u6700\u5927\u7684\u5757\u6240\u9700\u8981\u7684\u5200\u6570\u4e5f\u5c31\u7b49\u4e8e\u6574\u4e2a\u8fc7\u7a0b\u8fd8\u9700\u8981\u7684\u5200\u6570\uff0c\u56e0\u4e3a\u5176\u5b83\u5c0f\u5757\u9700\u8981\u7684\u5200\u6570\u90fd\u4e0d\u4f1a\u8d85\u8fc7\u6700\u5927\u5757\u6240\u9700\u5200\u6570\uff0c\u5b83\u4eec\u90fd\u53ef\u4ee5\u4e0e\u6700\u5927\u5757\u4e00\u9053\u5e76\u884c\u5904\u7406\u3002\u8fd9\u8868\u660e\uff0c\u6211\u4eec\u7684\u6700\u4f18\u51b3\u7b56\u5373\u662f\u8ba9\u5f53\u524d\u7684\u6700\u5927\u5757\u5c3d\u53ef\u80fd\u7684\u5c0f\uff0c\u4e5f\u5c31\u662f\u8bf4\u8981\u628a\u5f53\u524d\u7684\u6700\u5927\u5757\u5c3d\u53ef\u80fd\u76f8\u7b49\u5730\u5207\u6210\u4e24\u534a\u3002\u5229\u7528\u6570\u5b66\u5f52\u7eb3\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u5f88\u5feb\u5f97\u5230\u672c\u6bb5\u5f00\u5934\u7684\u7ed3\u8bba\u3002<\/p>\n
11.\u7b54\u6848\uff1a\u5148\u884c\u8005\u5728\u684c\u5b50\u4e2d\u5fc3\u653e\u7f6e\u4e00\u679a\u786c\u5e01\uff0c\u4ee5\u540e\u7684\u786c\u5e01\u603b\u662f\u653e\u5728\u4e0e\u540e\u884c\u8005\u521a\u624d\u653e\u7684\u5730\u65b9\u76f8\u5bf9\u79f0\u7684\u4f4d\u7f6e\u3002\u8fd9\u6837\uff0c\u53ea\u8981\u540e\u884c\u8005\u80fd\u653e\uff0c\u5148\u884c\u8005\u4e00\u5b9a\u4e5f\u6709\u5730\u65b9\u653e\u3002\u5148\u884c\u8005\u5fc5\u80dc\u3002<\/p>\n
12.\u7b54\u6848\uff1a\u5148\u5c06\u6574\u7bc7\u6587\u7ae0\u7684\u6240\u6709\u5b57\u7b26\u9006\u5e8f\uff08\u4ece\u4e24\u5934\u8d77\u4e0d\u65ad\u4ea4\u6362\u4f4d\u7f6e\u76f8\u5bf9\u79f0\u7684\u5b57\u7b26\uff09\uff1b\u7136\u540e\u7528\u540c\u6837\u7684\u529e\u6cd5\u5c06\u6bcf\u4e2a\u5355\u8bcd\u5185\u90e8\u7684\u5b57\u7b26\u9006\u5e8f\u3002\u8fd9\u6837\uff0c\u6574\u7bc7\u6587\u7ae0\u7684\u5355\u8bcd\u987a\u5e8f\u98a0\u5012\u4e86\uff0c\u4f46\u5355\u8bcd\u672c\u8eab\u53c8\u88ab\u8f6c\u56de\u6765\u4e86\u3002<\/p>\n
13.\u7b54\u6848\uff1a\u628a\u5b57\u7b26\u4e32\u5207\u6210\u957f\u4e3am\u548cn-m\u7684\u4e24\u534a\u3002\u5c06\u8fd9\u4e24\u4e2a\u90e8\u5206\u5206\u522b\u9006\u5e8f\uff0c\u518d\u5bf9\u6574\u4e2a\u5b57\u7b26\u4e32\u9006\u5e8f\u3002<\/p>\n
14.\u7b54\u6848\uff1a\u6ce8\u610f\u5230\u5e73\u5206\u77e9\u5f62\u9762\u79ef\u7684\u7ebf\u90fd\u7ecf\u8fc7\u77e9\u5f62\u7684\u4e2d\u5fc3\u3002\u8fc7\u5927\u77e9\u5f62\u548c\u7a7a\u5fc3\u77e9\u5f62\u5404\u81ea\u7684\u4e2d\u5fc3\u753b\u4e00\u6761\u7ebf\uff0c\u8fd9\u6761\u7ebf\u663e\u7136\u628a\u4e24\u4e2a\u77e9\u5f62\u90fd\u5206\u6210\u4e86\u4e00\u534a\uff0c\u5b83\u4eec\u7684\u5dee\u5f53\u7136\u4e5f\u662f\u76f8\u7b49\u7684\u3002<\/p>\n
15.\u7b54\u6848\uff1aN x M – 1\u6b21\u663e\u7136\u8db3\u591f\u4e86\u3002\u8fd9\u4e2a\u6570\u76ee\u4e5f\u662f\u5fc5\u9700\u7684\uff0c\u56e0\u4e3a\u6bcf\u63b0\u4e00\u6b21\u540e\u5f53\u524d\u5de7\u514b\u529b\u7684\u5757\u6570\u53ea\u80fd\u589e\u52a0\u4e00\uff0c\u628a\u5de7\u514b\u529b\u5206\u6210N x M\u5757\u5f53\u7136\u9700\u8981\u81f3\u5c11\u63b0N x M – 1\u6b21\u3002<\/p>\n
16.\u7b54\u68481\uff08\u5173\u4e8e\u6570\u5b57\u4f4d\u6570\u7ebf\u6027\uff09\uff1afor(n=0; b; b >>= 1) if (b & 1) n++;
\n\u7b54\u68482\uff08\u5173\u4e8e”1″\u7684\u4e2a\u6570\u7ebf\u6027\uff09\uff1afor(n=0; b; n++) b &= b-1;<\/p>\n
17.\u7b54\u6848\uff1a\u8ba1\u7b97\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u6570\u7684\u548c\uff0c\u518d\u8ba1\u7b97\u51fa\u4ece1\u5230N-1\u7684\u6240\u6709\u6570\u7684\u548c\uff0c\u4e24\u8005\u4e4b\u5dee\u5373\u4e3a\u91cd\u590d\u7684\u90a3\u4e2a\u6570\u3002\u8ba1\u7b97\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u6570\u7684\u548c\uff0c\u518d\u8ba1\u7b97\u51fa\u4ece1\u5230N+1\u7684\u6240\u6709\u6570\u7684\u548c\uff0c\u4e24\u8005\u4e4b\u5dee\u5373\u4e3a\u7f3a\u5c11\u7684\u90a3\u4e2a\u6570\u3002<\/p>\n
18.\u7b54\u6848\uff1a(b & (b-1)) == 0<\/p>\n
19.\u7b54\u6848\uff1a\u201c\u5317\u6781\u70b9\u201d\u662f\u4e00\u4e2a\u4f20\u7edf\u7684\u7b54\u6848\uff0c\u5176\u5b9e\u8fd9\u4e2a\u95ee\u9898\u8fd8\u6709\u5176\u5b83\u7684\u7b54\u6848\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6ee1\u8db3\u8981\u6c42\u7684\u70b9\u6709\u65e0\u7a77\u591a\u4e2a\u3002\u6240\u6709\u8ddd\u79bb\u5357\u6781\u70b91 + 1\/(2\u03c0)\u82f1\u91cc\u7684\u5730\u65b9\u90fd\u662f\u6ee1\u8db3\u8981\u6c42\u7684\uff0c\u5411\u5357\u8d70\u4e00\u82f1\u91cc\u540e\u5230\u8fbe\u8ddd\u79bb\u5357\u6781\u70b91\/(2\u03c0)\u7684\u5730\u65b9\uff0c\u5411\u4e1c\u8d70\u4e00\u82f1\u91cc\u540e\u6b63\u597d\u7ed5\u884c\u7eac\u5ea6\u5708\u4e00\u5468\uff0c\u518d\u5411\u5317\u8d70\u539f\u8def\u8fd4\u56de\u5230\u8d77\u70b9\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4ecd\u7136\u4e0d\u662f\u6ee1\u8db3\u8981\u6c42\u7684\u5168\u90e8\u70b9\u3002\u8ddd\u79bb\u5357\u6781\u70b91 + 1\/(2k\u03c0)\u7684\u5730\u65b9\u90fd\u662f\u53ef\u4ee5\u7684\uff0c\u5176\u4e2dk\u53ef\u4ee5\u662f\u4efb\u610f\u4e00\u4e2a\u6b63\u6574\u6570\u3002<\/p>\n
20.\u7b54\u6848\uff1aA\u628a\u836f\u653e\u8fdb\u7bb1\u5b50\uff0c\u7528\u81ea\u5df1\u7684\u9501\u628a\u7bb1\u5b50\u9501\u4e0a\u3002B\u62ff\u5230\u7bb1\u5b50\u540e\uff0c\u518d\u5728\u7bb1\u5b50\u4e0a\u52a0\u4e00\u628a\u81ea\u5df1\u7684\u9501\u3002\u7bb1\u5b50\u8fd0\u56deA\u540e\uff0cA\u53d6\u4e0b\u81ea\u5df1\u7684\u9501\u3002\u7bb1\u5b50\u518d\u8fd0\u5230B\u624b\u4e2d\u65f6\uff0cB\u53d6\u4e0b\u81ea\u5df1\u7684\u9501\uff0c\u83b7\u5f97\u836f\u7269\u3002<\/p>\n
21.\u7b54\u6848\uff1a\u63e1\u624b\u6b21\u6570\u53ea\u53ef\u80fd\u662f\u4ece0\u52302N-2\u8fd92N-1\u4e2a\u6570\u3002\u9664\u53bb\u7537\u4e3b\u4eba\u5916\uff0c\u4e00\u5171\u67092N-1\u4e2a\u4eba\uff0c\u56e0\u6b64\u6bcf\u4e2a\u6570\u6070\u597d\u51fa\u73b0\u4e86\u4e00\u6b21\u3002\u5176\u4e2d\u6709\u4e00\u4e2a\u4eba(0)\u6ca1\u6709\u63e1\u624b\uff0c\u6709\u4e00\u4e2a\u4eba(2N-2)\u548c\u6240\u6709\u5176\u5b83\u7684\u592b\u5987\u90fd\u63e1\u4e86\u624b\u3002\u8fd9\u4e24\u4e2a\u4eba\u80af\u5b9a\u662f\u4e00\u5bf9\u592b\u59bb\uff0c\u5426\u5219\u540e\u8005\u5c06\u548c\u524d\u8005\u63e1\u624b\uff08\u4ece\u800c\u524d\u8005\u7684\u63e1\u624b\u6b21\u6570\u4e0d\u518d\u662f0\uff09\u3002\u9664\u53bb\u8fd9\u5bf9\u592b\u59bb\u5916\uff0c\u6709\u4e00\u4e2a\u4eba(1)\u53ea\u4e0e(2N-2)\u63e1\u8fc7\u624b\uff0c\u6709\u4e00\u4e2a\u4eba(2N-3)\u548c\u9664\u4e86(0)\u4ee5\u5916\u7684\u5176\u5b83\u592b\u5987\u90fd\u63e1\u4e86\u624b\u3002\u8fd9\u4e24\u4e2a\u4eba\u80af\u5b9a\u662f\u4e00\u5bf9\u592b\u59bb\uff0c\u5426\u5219\u540e\u8005\u5c06\u548c\u524d\u8005\u63e1\u624b\uff08\u4ece\u800c\u524d\u8005\u7684\u63e1\u624b\u6b21\u6570\u4e0d\u518d\u662f1\uff09\u3002\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230\u63e1\u8fc7N-2\u6b21\u624b\u7684\u4eba\u548c\u63e1\u8fc7N\u6b21\u624b\u7684\u4eba\u914d\u6210\u4e00\u5bf9\u3002\u6b64\u65f6\uff0c\u9664\u4e86\u7537\u4e3b\u4eba\u53ca\u5176\u914d\u5076\u4ee5\u5916\uff0c\u5176\u4f59\u6240\u6709\u4eba\u90fd\u5df2\u7ecf\u914d\u5bf9\u3002\u6839\u636e\u6392\u9664\u6cd5\uff0c\u6700\u540e\u5269\u4e0b\u6765\u7684\u90a3\u4e2a\u63e1\u624b\u6b21\u6570\u4e3aN-1\u7684\u4eba\u5c31\u662f\u5973\u4e3b\u4eba\u4e86\u3002<\/p>\n
22.\u7b54\u6848\uff1a\u4e24\u4e2a\u673a\u5668\u4eba\u540c\u65f6\u5f00\u59cb\u4ee5\u5355\u4f4d\u901f\u5ea6\u53f3\u79fb\uff0c\u76f4\u5230\u4e00\u4e2a\u673a\u5668\u4eba\u8d70\u5230\u53e6\u5916\u4e00\u4e2a\u673a\u5668\u4eba\u7684\u8d77\u70b9\u5904\u3002\u7136\u540e\uff0c\u8be5\u673a\u5668\u4eba\u4ee5\u53cc\u500d\u901f\u5ea6\u8ffd\u8d76\u5bf9\u65b9\u3002\u7a0b\u5e8f\u5982\u4e0b\u3002<\/p>\n
while(!at_other_robots_start) {
\nmove_right 1
\n}
\nwhile(true) {
\nmove_right 2
\n}<\/p>\n
23.\u7b54\u6848\uff1a\u9009\u62e9\u7b2c\u4e00\u79cd\u6e38\u620f\uff0c\u5e76\u5199\u4e0b\u201c\u6211\u65e2\u4e0d\u4f1a\u5f97\u523010\u7f8e\u5143\uff0c\u4e5f\u4e0d\u4f1a\u5f97\u523010000000\u7f8e\u5143\u201d\u3002<\/p>\n
24.\u7b54\u6848\uff1a\u5728\u4e0b\u9762\u628a2,3\u8fde\u5728\u4e00\u8d77\uff0c\u628a4\u52306\u5168\u8fde\u5728\u4e00\u8d77\uff0c\u628a7\u523010\u5168\u8fde\u5728\u4e00\u8d77\uff0c\u7b49\u7b49\uff0c\u8fd9\u6837\u4f60\u5c31\u628a\u7535\u7ebf\u5206\u6210\u4e866\u4e2a\u201c\u7b49\u4ef7\u7c7b\u201d\uff0c\u5927\u5c0f\u5206\u522b\u4e3a1, 2, 3, 4, 5, 6\u3002\u7136\u540e\u5230\u697c\u9876\uff0c\u6d4b\u51fa\u54ea\u6839\u7ebf\u548c\u5176\u5b83\u6240\u6709\u7535\u7ebf\u90fd\u4e0d\u76f8\u8fde\uff0c\u54ea\u4e9b\u7ebf\u548c\u53e6\u5916\u4e00\u6839\u76f8\u8fde\uff0c\u54ea\u4e9b\u7ebf\u548c\u53e6\u5916\u4e24\u6839\u76f8\u8fde\uff0c\u7b49\u7b49\uff0c\u4ece\u800c\u786e\u5b9a\u51fa\u5b57\u6bcdA..U\u5404\u5c5e\u4e8e\u54ea\u4e2a\u7b49\u4ef7\u7c7b\u3002\u73b0\u5728\uff0c\u628a\u6bcf\u4e2a\u7b49\u4ef7\u7c7b\u4e2d\u7684\u7b2c\u4e00\u4e2a\u5b57\u6bcd\u8fde\u5728\u4e00\u8d77\uff0c\u5f62\u6210\u4e00\u4e2a\u5927\u5c0f\u4e3a6\u7684\u65b0\u7b49\u4ef7\u7c7b\uff1b\u518d\u628a\u540e5\u4e2a\u7b49\u4ef7\u7c7b\u4e2d\u7684\u7b2c\u4e8c\u4e2a\u5b57\u6bcd\u8fde\u5728\u4e00\u8d77\uff0c\u5f62\u6210\u4e00\u4e2a\u5927\u5c0f\u4e3a5\u7684\u65b0\u7b49\u4ef7\u7c7b\uff1b\u4ee5\u6b64\u7c7b\u63a8\u3002\u56de\u5230\u697c\u4e0b\uff0c\u628a\u65b0\u7684\u7b49\u4ef7\u7c7b\u533a\u522b\u51fa\u6765\u3002\u8fd9\u6837\uff0c\u4f60\u5c31\u77e5\u9053\u4e86\u6bcf\u4e2a\u6570\u5b57\u5bf9\u5e94\u4e86\u54ea\u4e00\u4e2a\u539f\u7b49\u4ef7\u7c7b\u7684\u7b2c\u51e0\u4e2a\u5b57\u6bcd\uff0c\u4ece\u800c\u89e3\u51b3\u95ee\u9898\u3002<\/p>\n
25.\u7b54\u6848\uff1a\u628a\u624b\u4e0a\u7684\u4e09\u7247\u836f\u5404\u81ea\u5207\u6210\u4e24\u534a\uff0c\u5206\u6210\u4e24\u5806\u6446\u653e\u3002\u518d\u53d6\u51fa\u4e00\u7c92\u836f\u7247A\uff0c\u4e5f\u628a\u5b83\u5207\u6210\u4e24\u534a\uff0c\u7136\u540e\u5728\u6bcf\u4e00\u5806\u91cc\u52a0\u4e0a\u534a\u7247\u7684A\u3002\u73b0\u5728\uff0c\u6bcf\u4e00\u5806\u836f\u7247\u6070\u597d\u5305\u542b\u4e24\u4e2a\u534a\u7247\u7684A\u548c\u4e24\u4e2a\u534a\u7247\u7684B\u3002\u4e00\u5929\u670d\u7528\u5176\u4e2d\u4e00\u5806\u5373\u53ef\u3002<\/p>\n
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