{"id":199,"date":"2011-10-30T16:33:13","date_gmt":"2011-10-30T08:33:13","guid":{"rendered":"https:\/\/blog.rexdf.org\/?p=39"},"modified":"2011-10-30T16:33:13","modified_gmt":"2011-10-30T08:33:13","slug":"acm%e5%8d%9a%e5%bc%88%e6%80%bb%e7%bb%93","status":"publish","type":"post","link":"https:\/\/blog.rexdf.org\/en\/2011\/10\/acm%e5%8d%9a%e5%bc%88%e6%80%bb%e7%bb%93\/","title":{"rendered":"ACM\u535a\u5f08\u603b\u7ed3"},"content":{"rendered":"

\u4ee5\u4e0b\u662f\u6211\u4ece\u7f51\u4e0a\u6536\u96c6\u7684\u5173\u4e8e\u7ec4\u5408\u535a\u5f08\u7684\u8d44\u6599\u6c47\u603b\uff1a
\n\u6709\u4e00\u79cd\u5f88\u6709\u610f\u601d\u7684\u6e38\u620f\uff0c\u5c31\u662f\u6709\u7269\u4f53\u82e5\u5e72\u5806\uff0c\u53ef\u4ee5\u662f\u706b\u67f4\u68cd\u6216\u662f\u56f4\u68cb\u5b50\u7b49\u7b49\u5747\u53ef\u3002\u4e24\u4e2a
\n\u4eba\u8f6e\u6d41\u4ece\u5806\u4e2d\u53d6\u7269\u4f53\u82e5\u5e72\uff0c\u89c4\u5b9a\u6700\u540e\u53d6\u5149\u7269\u4f53\u8005\u53d6\u80dc\u3002\u8fd9\u662f\u6211\u56fd\u6c11\u95f4\u5f88\u53e4\u8001\u7684\u4e00\u4e2a\u6e38\u620f
\n\uff0c\u522b\u770b\u8fd9\u6e38\u620f\u6781\u5176\u7b80\u5355\uff0c\u5374\u8574\u542b\u7740\u6df1\u523b\u7684\u6570\u5b66\u539f\u7406\u3002\u4e0b\u9762\u6211\u4eec\u6765\u5206\u6790\u4e00\u4e0b\u8981\u5982\u4f55\u624d\u80fd\u591f
\n\u53d6\u80dc\u3002
\n\uff08\u4e00\uff09\u5df4\u4ec0\u535a\u5955\uff08Bash Game\uff09\uff1a\u53ea\u6709\u4e00\u5806n\u4e2a\u7269\u54c1\uff0c\u4e24\u4e2a\u4eba\u8f6e\u6d41\u4ece\u8fd9\u5806\u7269\u54c1\u4e2d\u53d6\u7269\uff0c\u89c4
\n\u5b9a\u6bcf\u6b21\u81f3\u5c11\u53d6\u4e00\u4e2a\uff0c\u6700\u591a\u53d6m\u4e2a\u3002\u6700\u540e\u53d6\u5149\u8005\u5f97\u80dc\u3002
\n\u663e\u7136\uff0c\u5982\u679cn=m+1\uff0c\u90a3\u4e48\u7531\u4e8e\u4e00\u6b21\u6700\u591a\u53ea\u80fd\u53d6m\u4e2a\uff0c\u6240\u4ee5\uff0c\u65e0\u8bba\u5148\u53d6\u8005\u62ff\u8d70\u591a\u5c11\u4e2a\uff0c
\n\u540e\u53d6\u8005\u90fd\u80fd\u591f\u4e00\u6b21\u62ff\u8d70\u5269\u4f59\u7684\u7269\u54c1\uff0c\u540e\u8005\u53d6\u80dc\u3002\u56e0\u6b64\u6211\u4eec\u53d1\u73b0\u4e86\u5982\u4f55\u53d6\u80dc\u7684\u6cd5\u5219\uff1a\u5982\u679c
\nn=\uff08m+1\uff09r+s\uff0c\uff08r\u4e3a\u4efb\u610f\u81ea\u7136\u6570\uff0cs\u2264m),\u90a3\u4e48\u5148\u53d6\u8005\u8981\u62ff\u8d70s\u4e2a\u7269\u54c1\uff0c\u5982\u679c\u540e\u53d6\u8005\u62ff\u8d70
\nk\uff08\u2264m)\u4e2a\uff0c\u90a3\u4e48\u5148\u53d6\u8005\u518d\u62ff\u8d70m+1-k\u4e2a\uff0c\u7ed3\u679c\u5269\u4e0b\uff08m+1\uff09\uff08r-1\uff09\u4e2a\uff0c\u4ee5\u540e\u4fdd\u6301\u8fd9\u6837\u7684
\n\u53d6\u6cd5\uff0c\u90a3\u4e48\u5148\u53d6\u8005\u80af\u5b9a\u83b7\u80dc\u3002\u603b\u4e4b\uff0c\u8981\u4fdd\u6301\u7ed9\u5bf9\u624b\u7559\u4e0b\uff08m+1\uff09\u7684\u500d\u6570\uff0c\u5c31\u80fd\u6700\u540e\u83b7\u80dc\u3002
\n\u8fd9\u4e2a\u6e38\u620f\u8fd8\u53ef\u4ee5\u6709\u4e00\u79cd\u53d8\u76f8\u7684\u73a9\u6cd5\uff1a\u4e24\u4e2a\u4eba\u8f6e\u6d41\u62a5\u6570\uff0c\u6bcf\u6b21\u81f3\u5c11\u62a5\u4e00\u4e2a\uff0c\u6700\u591a\u62a5\u5341
\n\u4e2a\uff0c\u8c01\u80fd\u62a5\u5230100\u8005\u80dc\u3002
\n\uff08\u4e8c\uff09\u5a01\u4f50\u592b\u535a\u5955\uff08Wythoff Game\uff09\uff1a\u6709\u4e24\u5806\u5404\u82e5\u5e72\u4e2a\u7269\u54c1\uff0c\u4e24\u4e2a\u4eba\u8f6e\u6d41\u4ece\u67d0\u4e00\u5806\u6216\u540c
\n\u65f6\u4ece\u4e24\u5806\u4e2d\u53d6\u540c\u6837\u591a\u7684\u7269\u54c1\uff0c\u89c4\u5b9a\u6bcf\u6b21\u81f3\u5c11\u53d6\u4e00\u4e2a\uff0c\u591a\u8005\u4e0d\u9650\uff0c\u6700\u540e\u53d6\u5149\u8005\u5f97\u80dc\u3002<\/p>\n

\u8fd9\u79cd\u60c5\u51b5\u4e0b\u662f\u9887\u4e3a\u590d\u6742\u7684\u3002\u6211\u4eec\u7528\uff08ak\uff0cbk\uff09\uff08ak \u2264 bk ,k=0\uff0c1\uff0c2\uff0c\u2026,n)\u8868\u793a
\n\u4e24\u5806\u7269\u54c1\u7684\u6570\u91cf\u5e76\u79f0\u5176\u4e3a\u5c40\u52bf\uff0c\u5982\u679c\u7532\u9762\u5bf9\uff080\uff0c0\uff09\uff0c\u90a3\u4e48\u7532\u5df2\u7ecf\u8f93\u4e86\uff0c\u8fd9\u79cd\u5c40\u52bf\u6211\u4eec
\n\u79f0\u4e3a\u5947\u5f02\u5c40\u52bf\u3002\u524d\u51e0\u4e2a\u5947\u5f02\u5c40\u52bf\u662f\uff1a\uff080\uff0c0\uff09\u3001\uff081\uff0c2\uff09\u3001\uff083\uff0c5\uff09\u3001\uff084\uff0c7\uff09\u3001\uff086\uff0c
\n10\uff09\u3001\uff088\uff0c13\uff09\u3001\uff089\uff0c15\uff09\u3001\uff0811\uff0c18\uff09\u3001\uff0812\uff0c20\uff09\u3002
\n\u53ef\u4ee5\u770b\u51fa,a0=b0=0,ak\u662f\u672a\u5728\u524d\u9762\u51fa\u73b0\u8fc7\u7684\u6700\u5c0f\u81ea\u7136\u6570,\u800c bk= ak + k\uff0c\u5947\u5f02\u5c40\u52bf\u6709
\n\u5982\u4e0b\u4e09\u6761\u6027\u8d28\uff1a
\n1\u3002\u4efb\u4f55\u81ea\u7136\u6570\u90fd\u5305\u542b\u5728\u4e00\u4e2a\u4e14\u4ec5\u6709\u4e00\u4e2a\u5947\u5f02\u5c40\u52bf\u4e2d\u3002
\n\u7531\u4e8eak\u662f\u672a\u5728\u524d\u9762\u51fa\u73b0\u8fc7\u7684\u6700\u5c0f\u81ea\u7136\u6570\uff0c\u6240\u4ee5\u6709ak > ak-1 \uff0c\u800c bk= ak + k > ak
\n-1 + k-1 = bk-1 > ak-1 \u3002\u6240\u4ee5\u6027\u8d281\u3002\u6210\u7acb\u3002
\n2\u3002\u4efb\u610f\u64cd\u4f5c\u90fd\u53ef\u5c06\u5947\u5f02\u5c40\u52bf\u53d8\u4e3a\u975e\u5947\u5f02\u5c40\u52bf\u3002
\n\u4e8b\u5b9e\u4e0a\uff0c\u82e5\u53ea\u6539\u53d8\u5947\u5f02\u5c40\u52bf\uff08ak\uff0cbk\uff09\u7684\u67d0\u4e00\u4e2a\u5206\u91cf\uff0c\u90a3\u4e48\u53e6\u4e00\u4e2a\u5206\u91cf\u4e0d\u53ef\u80fd\u5728\u5176
\n\u4ed6\u5947\u5f02\u5c40\u52bf\u4e2d\uff0c\u6240\u4ee5\u5fc5\u7136\u662f\u975e\u5947\u5f02\u5c40\u52bf\u3002\u5982\u679c\u4f7f\uff08ak\uff0cbk\uff09\u7684\u4e24\u4e2a\u5206\u91cf\u540c\u65f6\u51cf\u5c11\uff0c\u5219\u7531
\n\u4e8e\u5176\u5dee\u4e0d\u53d8\uff0c\u4e14\u4e0d\u53ef\u80fd\u662f\u5176\u4ed6\u5947\u5f02\u5c40\u52bf\u7684\u5dee\uff0c\u56e0\u6b64\u4e5f\u662f\u975e\u5947\u5f02\u5c40\u52bf\u3002
\n3\u3002\u91c7\u7528\u9002\u5f53\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5c06\u975e\u5947\u5f02\u5c40\u52bf\u53d8\u4e3a\u5947\u5f02\u5c40\u52bf\u3002
\n\u5047\u8bbe\u9762\u5bf9\u7684\u5c40\u52bf\u662f\uff08a,b\uff09\uff0c\u82e5 b = a\uff0c\u5219\u540c\u65f6\u4ece\u4e24\u5806\u4e2d\u53d6\u8d70 a \u4e2a\u7269\u4f53\uff0c\u5c31\u53d8\u4e3a\u4e86
\n\u5947\u5f02\u5c40\u52bf\uff080\uff0c0\uff09\uff1b\u5982\u679ca = ak \uff0cb > bk\uff0c\u90a3\u4e48\uff0c\u53d6\u8d70b\u00a0 \u2013 bk\u4e2a\u7269\u4f53\uff0c\u5373\u53d8\u4e3a\u5947\u5f02\u5c40
\n\u52bf\uff1b\u5982\u679c a = ak \uff0c\u00a0 b < bk ,\u5219\u540c\u65f6\u4ece\u4e24\u5806\u4e2d\u62ff\u8d70 ak \u2013 ab \u2013 ak\u4e2a\u7269\u4f53,\u53d8\u4e3a\u5947\u5f02\u5c40 \u52bf\uff08 ab \u2013 ak , ab \u2013 ak+ b \u2013 ak\uff09\uff1b\u5982\u679ca > ak \uff0cb= ak + k,\u5219\u4ece\u7b2c\u4e00\u5806\u4e2d\u62ff\u8d70\u591a\u4f59
\n\u7684\u6570\u91cfa \u2013 ak \u5373\u53ef\uff1b\u5982\u679ca < ak \uff0cb= ak + k,\u5206\u4e24\u79cd\u60c5\u51b5\uff0c\u7b2c\u4e00\u79cd\uff0ca=aj \uff08j < k\uff09
\n,\u4ece\u7b2c\u4e8c\u5806\u91cc\u9762\u62ff\u8d70 b \u2013 bj \u5373\u53ef\uff1b\u7b2c\u4e8c\u79cd\uff0ca=bj \uff08j < k\uff09,\u4ece\u7b2c\u4e8c\u5806\u91cc\u9762\u62ff\u8d70 b \u2013 a
\nj \u5373\u53ef\u3002
\n\u4ece\u5982\u4e0a\u6027\u8d28\u53ef\u77e5\uff0c\u4e24\u4e2a\u4eba\u5982\u679c\u90fd\u91c7\u7528\u6b63\u786e\u64cd\u4f5c\uff0c\u90a3\u4e48\u9762\u5bf9\u975e\u5947\u5f02\u5c40\u52bf\uff0c\u5148\u62ff\u8005\u5fc5\u80dc
\n\uff1b\u53cd\u4e4b\uff0c\u5219\u540e\u62ff\u8005\u53d6\u80dc\u3002
\n\u90a3\u4e48\u4efb\u7ed9\u4e00\u4e2a\u5c40\u52bf\uff08a\uff0cb\uff09\uff0c\u600e\u6837\u5224\u65ad\u5b83\u662f\u4e0d\u662f\u5947\u5f02\u5c40\u52bf\u5462\uff1f\u6211\u4eec\u6709\u5982\u4e0b\u516c\u5f0f\uff1a
\nak =[k\uff081+\u221a5\uff09\/2]\uff0cbk= ak + k\u00a0 \uff08k=0\uff0c1\uff0c2\uff0c\u2026,n \u65b9\u62ec\u53f7\u8868\u793a\u53d6\u6574\u51fd\u6570)<\/p>\n

\u5947\u5999\u7684\u662f\u5176\u4e2d\u51fa\u73b0\u4e86\u9ec4\u91d1\u5206\u5272\u6570\uff081+\u221a5\uff09\/2 = 1\u3002618\u2026,\u56e0\u6b64,\u7531ak\uff0cbk\u7ec4\u6210\u7684\u77e9\u5f62\u8fd1
\n\u4f3c\u4e3a\u9ec4\u91d1\u77e9\u5f62\uff0c\u7531\u4e8e2\/\uff081+\u221a5\uff09=\uff08\u221a5-1\uff09\/2\uff0c\u53ef\u4ee5\u5148\u6c42\u51faj=[a\uff08\u221a5-1\uff09\/2]\uff0c\u82e5a=[
\nj\uff081+\u221a5\uff09\/2]\uff0c\u90a3\u4e48a = aj\uff0cbj = aj + j\uff0c\u82e5\u4e0d\u7b49\u4e8e\uff0c\u90a3\u4e48a = aj+1\uff0cbj+1 = aj+1
\n+ j + 1\uff0c\u82e5\u90fd\u4e0d\u662f\uff0c\u90a3\u4e48\u5c31\u4e0d\u662f\u5947\u5f02\u5c40\u52bf\u3002\u7136\u540e\u518d\u6309\u7167\u4e0a\u8ff0\u6cd5\u5219\u8fdb\u884c\uff0c\u4e00\u5b9a\u4f1a\u9047\u5230\u5947\u5f02
\n\u5c40\u52bf\u3002
\n\uff08\u4e09\uff09\u5c3c\u59c6\u535a\u5955\uff08Nimm Game\uff09\uff1a\u6709\u4e09\u5806\u5404\u82e5\u5e72\u4e2a\u7269\u54c1\uff0c\u4e24\u4e2a\u4eba\u8f6e\u6d41\u4ece\u67d0\u4e00\u5806\u53d6\u4efb\u610f\u591a\u7684
\n\u7269\u54c1\uff0c\u89c4\u5b9a\u6bcf\u6b21\u81f3\u5c11\u53d6\u4e00\u4e2a\uff0c\u591a\u8005\u4e0d\u9650\uff0c\u6700\u540e\u53d6\u5149\u8005\u5f97\u80dc\u3002
\n\u8fd9\u79cd\u60c5\u51b5\u6700\u6709\u610f\u601d\uff0c\u5b83\u4e0e\u4e8c\u8fdb\u5236\u6709\u5bc6\u5207\u5173\u7cfb\uff0c\u6211\u4eec\u7528\uff08a\uff0cb\uff0cc\uff09\u8868\u793a\u67d0\u79cd\u5c40\u52bf\uff0c\u9996
\n\u5148\uff080\uff0c0\uff0c0\uff09\u663e\u7136\u662f\u5947\u5f02\u5c40\u52bf\uff0c\u65e0\u8bba\u8c01\u9762\u5bf9\u5947\u5f02\u5c40\u52bf\uff0c\u90fd\u5fc5\u7136\u5931\u8d25\u3002\u7b2c\u4e8c\u79cd\u5947\u5f02\u5c40\u52bf\u662f
\n\uff080\uff0cn\uff0cn\uff09\uff0c\u53ea\u8981\u4e0e\u5bf9\u624b\u62ff\u8d70\u4e00\u6837\u591a\u7684\u7269\u54c1\uff0c\u6700\u540e\u90fd\u5c06\u5bfc\u81f4\uff080\uff0c0\uff0c0\uff09\u3002\u4ed4\u7ec6\u5206\u6790\u4e00
\n\u4e0b\uff0c\uff081\uff0c2\uff0c3\uff09\u4e5f\u662f\u5947\u5f02\u5c40\u52bf\uff0c\u65e0\u8bba\u5bf9\u624b\u5982\u4f55\u62ff\uff0c\u63a5\u4e0b\u6765\u90fd\u53ef\u4ee5\u53d8\u4e3a\uff080\uff0cn\uff0cn\uff09\u7684\u60c5
\n\u5f62\u3002
\n\u8ba1\u7b97\u673a\u7b97\u6cd5\u91cc\u9762\u6709\u4e00\u79cd\u53eb\u505a\u6309\u4f4d\u6a212\u52a0\uff0c\u4e5f\u53eb\u505a\u5f02\u6216\u7684\u8fd0\u7b97\uff0c\u6211\u4eec\u7528\u7b26\u53f7\uff08+\uff09\u8868\u793a
\n\u8fd9\u79cd\u8fd0\u7b97\u3002\u8fd9\u79cd\u8fd0\u7b97\u548c\u4e00\u822c\u52a0\u6cd5\u4e0d\u540c\u7684\u4e00\u70b9\u662f1+1=0\u3002\u5148\u770b\uff081\uff0c2\uff0c3\uff09\u7684\u6309\u4f4d\u6a212\u52a0\u7684\u7ed3
\n\u679c\uff1a
\n1 =\u4e8c\u8fdb\u523601
\n2 =\u4e8c\u8fdb\u523610
\n3 =\u4e8c\u8fdb\u523611 \uff08+\uff09
\n\u2014\u2014\u2014\u2014\u2014\u2014\u2014
\n0 =\u4e8c\u8fdb\u523600 \uff08\u6ce8\u610f\u4e0d\u8fdb\u4f4d\uff09
\n\u5bf9\u4e8e\u5947\u5f02\u5c40\u52bf\uff080\uff0cn\uff0cn\uff09\u4e5f\u4e00\u6837\uff0c\u7ed3\u679c\u4e5f\u662f0\u3002
\n\u4efb\u4f55\u5947\u5f02\u5c40\u52bf\uff08a\uff0cb\uff0cc\uff09\u90fd\u6709a\uff08+\uff09b\uff08+\uff09c =0\u3002
\n\u5982\u679c\u6211\u4eec\u9762\u5bf9\u7684\u662f\u4e00\u4e2a\u975e\u5947\u5f02\u5c40\u52bf\uff08a\uff0cb\uff0cc\uff09\uff0c\u8981\u5982\u4f55\u53d8\u4e3a\u5947\u5f02\u5c40\u52bf\u5462\uff1f\u5047\u8bbe a < b
\n< c,\u6211\u4eec\u53ea\u8981\u5c06 c \u53d8\u4e3a a\uff08+\uff09b,\u5373\u53ef,\u56e0\u4e3a\u6709\u5982\u4e0b\u7684\u8fd0\u7b97\u7ed3\u679c: a\uff08+\uff09b\uff08+\uff09(a\uff08+\uff09 b)=(a\uff08+\uff09a)\uff08+\uff09(b\uff08+\uff09b)=0\uff08+\uff090=0\u3002\u8981\u5c06c \u53d8\u4e3aa\uff08+\uff09b\uff0c\u53ea\u8981\u4ece c\u4e2d\u51cf\u53bb c-\uff08 a\uff08+\uff09b\uff09\u5373\u53ef\u3002 \u00a0 \u00a0 \u4f8b1\u3002\uff0814\uff0c21\uff0c39\uff09\uff0c14\uff08+\uff0921=27\uff0c39-27=12\uff0c\u6240\u4ee5\u4ece39\u4e2d\u62ff\u8d7012\u4e2a\u7269\u4f53\u5373\u53ef\u8fbe \u5230\u5947\u5f02\u5c40\u52bf\uff0814\uff0c21\uff0c27\uff09\u3002 \u00a0 \u00a0 \u4f8b2\u3002\uff0855\uff0c81\uff0c121\uff09\uff0c55\uff08+\uff0981=102\uff0c121-102=19\uff0c\u6240\u4ee5\u4ece121\u4e2d\u62ff\u8d7019\u4e2a\u7269\u54c1 \u5c31\u5f62\u6210\u4e86\u5947\u5f02\u5c40\u52bf\uff0855\uff0c81\uff0c102\uff09\u3002 \u00a0 \u00a0 \u4f8b3\u3002\uff0829\uff0c45\uff0c58\uff09\uff0c29\uff08+\uff0945=48\uff0c58-48=10\uff0c\u4ece58\u4e2d\u62ff\u8d7010\u4e2a\uff0c\u53d8\u4e3a\uff0829\uff0c4 5\uff0c48\uff09\u3002 \u00a0 \u00a0 \u4f8b4\u3002\u6211\u4eec\u6765\u5b9e\u9645\u8fdb\u884c\u4e00\u76d8\u6bd4\u8d5b\u770b\u770b\uff1a \u00a0 \u00a0 \u00a0 \u00a0 \u7532:(7,8,9)->(1,8,9)\u5947\u5f02\u5c40\u52bf
\n\u4e59:(1,8,9)->(1,8,4)
\n\u7532:(1,8,4)->(1,5,4)\u5947\u5f02\u5c40\u52bf
\n\u4e59:(1,5,4)->(1,4,4)
\n\u7532:(1,4,4)->(0,4,4)\u5947\u5f02\u5c40\u52bf
\n\u4e59:(0,4,4)->(0,4,2)
\n\u7532:(0.4,2)->(0,2,2)\u5947\u5f02\u5c40\u52bf
\n\u4e59:(0,2,2)->(0,2,1)
\n\u7532:(0,2,1)->(0,1,1)\u5947\u5f02\u5c40\u52bf
\n\u4e59:(0,1,1)->(0,1,0)
\n\u7532:(0,1,0)->(0,0,0)\u5947\u5f02\u5c40\u52bf
\n\u7532\u80dc\u3002
\n\u53d6\u706b\u67f4\u7684\u6e38\u620f
\n\u9898\u76ee1\uff1a\u4eca\u6709\u82e5\u5e72\u5806\u706b\u67f4\uff0c\u4e24\u4eba\u4f9d\u6b21\u4ece\u4e2d\u62ff\u53d6\uff0c\u89c4\u5b9a\u6bcf\u6b21\u53ea\u80fd\u4ece\u4e00\u5806\u4e2d\u53d6\u82e5\u5e72\u6839\uff0c
\n\u53ef\u5c06\u4e00\u5806\u5168\u53d6\u8d70\uff0c\u4f46\u4e0d\u53ef\u4e0d\u53d6\uff0c\u6700\u540e\u53d6\u5b8c\u8005\u4e3a\u80dc\uff0c\u6c42\u5fc5\u80dc\u7684\u65b9\u6cd5\u3002
\n\u9898\u76ee2\uff1a\u4eca\u6709\u82e5\u5e72\u5806\u706b\u67f4\uff0c\u4e24\u4eba\u4f9d\u6b21\u4ece\u4e2d\u62ff\u53d6\uff0c\u89c4\u5b9a\u6bcf\u6b21\u53ea\u80fd\u4ece\u4e00\u5806\u4e2d\u53d6\u82e5\u5e72\u6839\uff0c
\n\u53ef\u5c06\u4e00\u5806\u5168\u53d6\u8d70\uff0c\u4f46\u4e0d\u53ef\u4e0d\u53d6\uff0c\u6700\u540e\u53d6\u5b8c\u8005\u4e3a\u8d1f\uff0c\u6c42\u5fc5\u80dc\u7684\u65b9\u6cd5\u3002
\n\u563f\u563f\uff0c\u8fd9\u4e2a\u6e38\u620f\u6211\u65e9\u5c31\u89c1\u8bc6\u8fc7\u4e86\u3002\u5c0f\u65f6\u5019\u7528\u73e0\u7b97\u73a9\u8fd9\u4e2a\u6e38\u620f\uff1a\u7b2c\u4e00\u6863\u62e8\u4e00\u4e2a\uff0c\u7b2c\u4e8c\u6863\u62e8\u4e24\u4e2a\uff0c\u4f9d\u6b21\u76f4\u5230\u7b2c\u4e94\u6863\u62e8\u4e94\u4e2a\u3002\u7136\u540e\u4e24\u4e2a\u4eba\u5c31\u8f6e\u6d41\u518d\u628a\u68cb\u5b50\u62e8\u4e0b\u6765\uff0c\u8c01\u8981\u662f\u6700\u540e\u4e00\u4e2a\u62e8\u8c01\u5c31\u8d62\u3002\u6709\u4e00\u6b21\u6691\u5047\u770b\u89c1\u4e24\u4e2a\u5c0f\u5b69\u5b50\u5728\u73a9\u8fd9\u4e2a\u6e38\u620f\uff0c\u6211\u5c31\u5728\u60f3\u6709\u6ca1\u6709\u4e00\u4e2a\u5b9a\u8bba\u5462\u3002\u4e0b\u9762\u5c31\u6765\u8bd5\u7740\u8bc1\u660e\u4e00\u4e0b\u5427
\n\u5148\u89e3\u51b3\u7b2c\u4e00\u4e2a\u95ee\u9898\u5427\u3002
\n\u5b9a\u4e49\uff1a\u82e5\u6240\u6709\u706b\u67f4\u6570\u5f02\u6216\u4e3a0\uff0c\u5219\u8be5\u72b6\u6001\u88ab\u79f0\u4e3a\u5229\u4ed6\u6001\uff0c\u7528\u5b57\u6bcdT\u8868\u793a\uff1b\u5426\u5219\uff0c
\n\u4e3a\u5229\u5df1\u6001\uff0c\u7528S\u8868\u793a\u3002
\n[\u5b9a\u74061]\uff1a\u5bf9\u4e8e\u4efb\u4f55\u4e00\u4e2aS\u6001\uff0c\u603b\u80fd\u4ece\u4e00\u5806\u706b\u67f4\u4e2d\u53d6\u51fa\u82e5\u5e72\u4e2a\u4f7f\u4e4b\u6210\u4e3aT\u6001\u3002
\n\u8bc1\u660e\uff1a
\n\u82e5\u6709n\u5806\u706b\u67f4\uff0c\u6bcf\u5806\u706b\u67f4\u6709A(i)\u6839\u706b\u67f4\u6570\uff0c\u90a3\u4e48\u65e2\u7136\u73b0\u5728\u5904\u4e8eS\u6001\uff0c
\nc = A(1) xor A(2) xor \u2026 xor A(n) > 0;
\n\u628ac\u8868\u793a\u6210\u4e8c\u8fdb\u5236\uff0c\u8bb0\u5b83\u7684\u4e8c\u8fdb\u5236\u6570\u7684\u6700\u9ad8\u4f4d\u4e3a\u7b2cp\u4f4d\uff0c\u5219\u5fc5\u7136\u5b58\u5728\u4e00\u4e2aA(t),\u5b83\u4e8c\u8fdb\u5236\u7684\u7b2cp\u4f4d\u4e5f\u662f1\u3002\uff08\u5426\u5219\uff0c\u82e5\u6240\u6709\u7684A(i)\u7684\u7b2cp\u4f4d\u90fd\u662f0\uff0c\u8fd9\u4e0ec\u7684\u7b2cp\u4f4d\u5c31\u4e5f\u4e3a0\u77db\u76fe\uff09\u3002
\n\u90a3\u4e48\u6211\u4eec\u628ax = A(t) xor c,\u5219\u5f97\u5230x < A(t).\u8fd9\u662f\u56e0\u4e3a\u65e2\u7136A(t)\u7684\u7b2cp\u4f4d\u4e0ec\u7684\u7b2cp\u4f4d\u540c\u4e3a1,\u90a3\u4e48x\u7684\u7b2cp\u4f4d\u53d8\u4e3a0,\u800c\u9ad8\u4e8ep\u7684\u4f4d\u5e76\u6ca1\u6709\u6539\u53d8\u3002\u6240\u4ee5x < A(t).\u800c \u00a0 \u00a0 A(1) xor A(2) xor \u2026 xor x xor \u2026 xor A(n) \u00a0 = A(1) xor A(2) xor \u2026 xor A(t) xor c xor \u2026 xor A(n) \u00a0 = A(1) xor A(2) xor\u2026 xor A(n) xor A(1) xor A(2) xor \u2026 xor A(n) \u00a0 = 0 \u8fd9\u5c31\u662f\u8bf4\u4eceA(t)\u5806\u4e2d\u53d6\u51fa A(t) \u2013 x \u6839\u706b\u67f4\u540e\u72b6\u6001\u5c31\u4f1a\u4eceS\u6001\u53d8\u4e3aT\u6001\u3002\u8bc1\u6bd5 [\u5b9a\u74062]\uff1aT\u6001\uff0c\u53d6\u4efb\u4f55\u4e00\u5806\u7684\u82e5\u5e72\u6839\uff0c\u90fd\u5c06\u6210\u4e3aS\u6001\u3002 \u8bc1\u660e\uff1a\u7528\u53cd\u8bc1\u6cd5\u8bd5\u8bd5\u3002 \u00a0 \u00a0 \u00a0 \u82e5 \u00a0 \u00a0 \u00a0 c = A(1) xor A(2) xor \u2026 xor A(i) xor \u2026 xor A(n) = 0\uff1b \u00a0 \u00a0 \u00a0 c\u2019 = A(1) xor A(2) xor \u2026 xor A(i\u2019) xor c xor \u2026 xor A(n) = 0; \u00a0 \u00a0 \u00a0 \u5219\u6709 c xor c\u2019 = A(1) xor A(2) xor \u2026 xor A(i) xor \u2026 xor A(n) xor A(1) xor A(2) xor \u2026 xor A(i\u2019) xor c xor \u2026 xor A(n) = A(i) xor A(i\u2019) =0 \u00a0 \u00a0 \u00a0 \u8fdb\u800c\u63a8\u51faA(i) = A(i\u2019)\uff0c\u8fd9\u4e0e\u5df2\u77e5\u77db\u76fe\u3002\u6240\u4ee5\u547d\u9898\u5f97\u8bc1\u3002 [\u5b9a\u7406 3]\uff1aS\u6001\uff0c\u53ea\u8981\u65b9\u6cd5\u6b63\u786e\uff0c\u5fc5\u8d62\u3002\u00a0 \u00a0 \u6700\u7ec8\u80dc\u5229\u5373\u7531S\u6001\u8f6c\u53d8\u4e3aT\u6001\uff0c\u4efb\u4f55\u4e00\u4e2aS\u6001\uff0c\u53ea\u8981\u628a\u5b83\u53d8\u4e3aT\u6001\uff0c\uff08\u7531\u5b9a\u74061\uff0c\u53ef\u4ee5\u628a\u5b83\u53d8\u6210T\u6001\u3002\uff09\u5bf9\u65b9\u53ea\u80fd\u628aT\u6001\u8f6c\u53d8\u4e3aS\u6001(\u5b9a\u74062)\u3002\u8fd9\u6837\uff0c\u6240\u6709S\u6001\u5411T\u6001\u7684\u8f6c\u53d8\u90fd\u53ef\u4ee5\u6709\u5df1\u65b9\u63a7\u5236\uff0c\u5bf9\u65b9\u53ea\u80fd\u88ab\u52a8\u5730\u5b9e\u73b0\u7531T\u6001\u8f6c\u53d8\u4e3aS\u6001\u3002\u6545S\u6001\u5fc5\u8d62\u3002 [\u5b9a\u74064]\uff1aT\u6001\uff0c\u53ea\u8981\u5bf9\u65b9\u6cd5\u6b63\u786e\uff0c\u5fc5\u8d25\u3002\u00a0 \u00a0 \u7531\u5b9a\u74063\u6613\u5f97\u3002\u00a0 \u63a5\u7740\u6765\u89e3\u51b3\u7b2c\u4e8c\u4e2a\u95ee\u9898\u3002 \u5b9a\u4e49\uff1a\u82e5\u4e00\u5806\u4e2d\u4ec5\u67091\u6839\u706b\u67f4\uff0c\u5219\u88ab\u79f0\u4e3a\u5b64\u5355\u5806\u3002\u82e5\u5927\u4e8e1\u6839\uff0c\u5219\u79f0\u4e3a\u5145\u88d5\u5806\u3002 \u5b9a\u4e49\uff1aT\u6001\u4e2d\uff0c\u82e5\u5145\u88d5\u5806\u7684\u5806\u6570\u5927\u4e8e\u7b49\u4e8e2\uff0c\u5219\u79f0\u4e3a\u5b8c\u5168\u5229\u4ed6\u6001\uff0c\u7528T2\u8868\u793a\uff1b\u82e5\u5145\u88d5\u5806\u7684\u5806\u6570\u7b49\u4e8e0\uff0c\u5219\u79f0\u4e3a\u90e8\u5206\u5229\u4ed6\u6001\uff0c\u7528T0\u8868\u793a\u3002 \u00a0 \u5b64\u5355\u5806\u7684\u6839\u6570\u5f02\u6216\u53ea\u4f1a\u5f71\u54cd\u4e8c\u8fdb\u5236\u7684\u6700\u540e\u4e00\u4f4d\uff0c\u4f46\u5145\u88d5\u5806\u4f1a\u5f71\u54cd\u9ad8\u4f4d\uff08\u975e\u6700\u540e\u4e00\u4f4d\uff09\u3002\u4e00\u4e2a\u5145\u88d5\u5806\uff0c\u9ad8\u4f4d\u5fc5\u6709\u4e00\u4f4d\u4e0d\u4e3a0\uff0c\u5219\u6240\u6709\u6839\u6570\u5f02\u6216\u4e0d\u4e3a0\u3002\u6545\u4e0d\u4f1a\u662fT\u6001\u3002 [\u5b9a\u74065]\uff1aS0\u6001\uff0c\u5373\u4ec5\u6709\u5947\u6570\u4e2a\u5b64\u5355\u5806\uff0c\u5fc5\u8d25\u3002T0\u6001\u5fc5\u80dc\u3002\u00a0 \u8bc1\u660e\uff1a S0\u6001\uff0c\u5176\u5b9e\u5c31\u662f\u6bcf\u6b21\u53ea\u80fd\u53d6\u4e00\u6839\u3002\u6bcf\u6b21\u7b2c\u5947\u6570\u6839\u90fd\u7531\u5df1\u53d6\uff0c\u7b2c\u5076\u6570\u6839\u90fd\u7531\u5bf9\u00a0 \u65b9\u53d6\uff0c\u6240\u4ee5\u6700\u540e\u4e00\u6839\u5fc5\u5df1\u53d6\u3002\u8d25\u3002\u540c\u7406,\u00a0 T0\u6001\u5fc5\u80dc# [\u5b9a\u74066]\uff1aS1\u6001\uff0c\u53ea\u8981\u65b9\u6cd5\u6b63\u786e\uff0c\u5fc5\u80dc\u3002\u00a0 \u8bc1\u660e\uff1a \u82e5\u6b64\u65f6\u5b64\u5355\u5806\u5806\u6570\u4e3a\u5947\u6570\uff0c\u628a\u5145\u88d5\u5806\u53d6\u5b8c\uff1b\u5426\u5219\uff0c\u53d6\u6210\u4e00\u6839\u3002\u8fd9\u6837\uff0c\u5c31\u53d8\u6210\u5947\u6570\u4e2a\u5b64\u5355\u5806\uff0c\u7531\u5bf9\u65b9\u53d6\u3002\u7531\u5b9a\u74065\uff0c\u5bf9\u65b9\u5fc5\u8f93\u3002\u5df1\u5fc5\u80dc\u3002\u00a0 #\u00a0 [\u5b9a\u74067]\uff1aS2\u6001\u4e0d\u53ef\u8f6c\u4e00\u6b21\u53d8\u4e3aT0\u6001\u3002\u00a0 \u8bc1\u660e\uff1a \u5145\u88d5\u5806\u6570\u4e0d\u53ef\u80fd\u4e00\u6b21\u75312\u53d8\u4e3a0\u3002\u5f97\u8bc1\u3002\u00a0 #\u00a0 [\u5b9a\u74068]\uff1aS2\u6001\u53ef\u4e00\u6b21\u8f6c\u53d8\u4e3aT2\u6001\u3002\u00a0 \u8bc1\u660e\uff1a \u7531\u5b9a\u74061\uff0cS\u6001\u53ef\u8f6c\u53d8\u4e3aT\u6001\uff0c\u6001\u53ef\u4e00\u6b21\u8f6c\u53d8\u4e3aT\u6001\uff0c\u53c8\u7531\u5b9a\u74066\uff0cS2\u6001\u4e0d\u53ef\u8f6c\u4e00\u6b21\u53d8\u4e3aT0\u6001\uff0c\u6240\u4ee5\u8f6c\u53d8\u7684T\u6001\u4e3aT2\u6001\u3002\u00a0 #\u00a0 [\u5b9a\u74069]\uff1aT2\u6001\uff0c\u53ea\u80fd\u8f6c\u53d8\u4e3aS2\u6001\u6216S1\u6001\u3002\u00a0 \u8bc1\u660e\uff1a \u7531\u5b9a\u74062\uff0cT\u6001\u5fc5\u7136\u53d8\u4e3aS\u6001\u3002\u7531\u4e8e\u5145\u88d5\u5806\u6570\u4e0d\u53ef\u80fd\u4e00\u6b21\u75312\u53d8\u4e3a0\uff0c\u6240\u4ee5\u6b64\u65f6\u7684S\u6001\u4e0d\u53ef\u80fd\u4e3aS0\u6001\u3002\u547d\u9898\u5f97\u8bc1\u3002\u00a0 [\u5b9a\u740610]\uff1aS2\u6001\uff0c\u53ea\u8981\u65b9\u6cd5\u6b63\u786e\uff0c\u5fc5\u80dc.\u00a0 \u8bc1\u660e\uff1a \u65b9\u6cd5\u5982\u4e0b\uff1a\u00a0 \u00a0 \u00a0 \u00a0 1\uff09\u00a0 S2\u6001\uff0c\u5c31\u628a\u5b83\u53d8\u4e3aT2\u6001\u3002\uff08\u7531\u5b9a\u74068\uff09\u00a0 \u00a0 \u00a0 \u00a0 2\uff09\u00a0 \u5bf9\u65b9\u53ea\u80fdT2\u8f6c\u53d8\u6210S2\u6001\u6216S1\u6001\uff08\u5b9a\u74069\uff09 \u00a0 \u00a0 \u82e5\u8f6c\u53d8\u4e3aS2,\u00a0 \u8f6c\u54111\uff09\u00a0 \u00a0 \u00a0 \u82e5\u8f6c\u53d8\u4e3aS1,\u00a0 \u8fd9\u5df1\u5fc5\u80dc\u3002\uff08\u5b9a\u74065\uff09\u00a0 [\u5b9a\u740611]\uff1aT2\u6001\u5fc5\u8f93\u3002\u00a0 \u8bc1\u660e\uff1a\u540c10\u3002\u00a0 \u7efc\u4e0a\u6240\u8ff0\uff0c\u5fc5\u8f93\u6001\u6709\uff1a\u00a0 T2,S0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u5fc5\u80dc\u6001\uff1a\u00a0 \u00a0 S2,S1,T0.\u00a0 \u4e24\u9898\u6bd4\u8f83\uff1a\u00a0 \u7b2c\u4e00\u9898\u7684\u5168\u8fc7\u7a0b\u5176\u5b9e\u5982\u4e0b\uff1a\u00a0 S2->T2->S2->T2->\u00a0 \u2026\u2026\u00a0 ->T2->S1->T0->S0->T0->\u2026\u2026->S0->T0(\u51680)
\n\u7b2c\u4e8c\u9898\u7684\u5168\u8fc7\u7a0b\u5176\u5b9e\u5982\u4e0b\uff1a
\nS2->T2->S2->T2->\u00a0 \u2026\u2026\u00a0 ->T2->S1->S0->T0->S0->\u2026\u2026->S0->T0(\u51680)
\n\u4e0b\u5212\u7ebf\u8868\u793a\u80dc\u5229\u4e00\u65b9\u7684\u53d6\u6cd5\u3002\u00a0 \u662f\u5426\u53d1\u73b0\u4e86\u4ed6\u4eec\u7684\u60ca\u4eba\u76f8\u4f3c\u4e4b\u5904\u3002
\n\u6211\u4eec\u4e0d\u96be\u53d1\u73b0(\u89c1\u52a0\u9ed1\u90e8\u5206)\uff0cS1\u6001\u53ef\u4ee5\u8f6c\u53d8\u4e3aS0\u6001\uff08\u7b2c\u4e8c\u9898\u505a\u6cd5\uff09\uff0c\u4e5f\u53ef\u4ee5\u8f6c\u53d8\u4e3a
\nT0\uff08\u7b2c\u4e00\u9898\u505a\u6cd5\uff09\u3002\u54ea\u4e00\u65b9\u63a7\u5236\u4e86S1\u6001\uff0c\u4ed6\u5373\u53ef\u4ee5\u6709\u529e\u6cd5\u4f7f\u81ea\u5df1\u5f97\u5230\u6700\u540e\u4e00\u6839\uff08\u8f6c\u53d8\u4e3a
\nT0\uff09,\u4e5f\u53ef\u4ee5\u4f7f\u5bf9\u65b9\u5f97\u5230\u6700\u540e\u4e00\u6839\uff08\u8f6c\u53d8\u4e3aS0\uff09\u3002
\n\u6240\u4ee5\uff0c\u62a2\u593aS1\u662f\u5236\u80dc\u7684\u5173\u952e\uff01
\n\u4e3a\u6b64\uff0c\u59cb\u7ec8\u628aT2\u6001\u8ba9\u7ed9\u5bf9\u65b9\uff0c\u5c06\u4f7f\u5bf9\u65b9\u5904\u4e8e\u88ab\u52a8\u72b6\u6001\uff0c\u4ed6\u65e9\u665a\u5c06\u628a\u72b6\u6001\u53d8\u4e3aS1.<\/p>\n

\u63a8\u8350HDOJ\u9898\u76ee
\nhttp:\/\/acm.hdu.edu.cn\/showproblem.php?pid=1907
\nhttp:\/\/acm.hdu.edu.cn\/showproblem.php?pid=2509
\n\u770b\u5b8c\u4e0a\u9762\u7684\u7ed3\u8bba\uff0c\u5c31\u80fd\u987a\u5229\u89e3\u51b3\u4e0a\u97622\u9053\u4e86<\/p>\n

S-Nim
\nhttp:\/\/acm.hdu.edu.cn\/showproblem.php?pid=1536
\nhttp:\/\/acm.hdu.edu.cn\/showproblem.php?pid=1944<\/p>\n

\u535a\u5f08\u7b97\u6cd5\u5165\u95e8\u5c0f\u8282 1536 1517 1907
\n\u5c0f\u5b50\u6700\u8fd1\u8ff7\u9014\u4e8e\u535a\u5f08\u4e4b\u4e2d\u3002\u3002\u3002\u611f\u89e6\u9887\u6df1\u3002
\n\u4e3a\u4e86\u8ba9\u5927\u5bb6\u80fd\u591f\u5728\u5b66\u4e60\u535a\u5f08\u7684\u65f6\u5019\u5c11\u8d70\u5f2f\u8def\uff0c\u6700\u91cd\u8981\u7684\u4e5f\u662f\u4e3a\u4e86\u52a0\u6df1\u81ea\u5df1\u7684\u5f71\u54cd\uff0c\u6e29\u6545\u800c\u77e5\u65b0\uff0c\u7279\u53d1\u6b64\u8d34\u4e0e\u5927\u5bb6\u5171\u52c9\u3002
\n\u5b66\u535a\u5f08\u5148\u4ece\u6982\u5ff5\u5f00\u59cb\uff1a
\n\u7279\u522b\u63a8\u8350LCY\u8001\u5e08\u7684\u8bfe\u4ef6\uff1a\u535a\u5f08\u5165\u95e8\u3002
\n\u4e0b\u8f7d\u5730\u5740\uff1ahttp:\/\/acm.hdu.edu.cn\/forum\/read.php?tid=6875
\n\u8fd9\u4e2a\u8bfe\u4ef6\u4e2a\u4eba\u8ba4\u4e3a\u4ece\u535a\u5f08\u7684\u57fa\u672c\u601d\u60f3\uff0c\u4e00\u76f4\u5230\u89e3\u535a\u5f08\u7684\u4e2d\u5fc3\u7b97\u6cd5\u505a\u4e86\u5f88\u597d\u7684\u8be0\u91ca\u3002\u4f46\u662f\u7279\u522b\u8981\u6ce8\u610f\u7684\u662f\u3002\u8bfe\u4ef6\u540e\u9762\u4e00\u90e8\u5206\u82f1\u8bed\u5199\u7684\u8bb2\u4e49\u662f\u91cd\u4e2d\u4e4b\u91cd\u3002\u5c0f\u5b50\u82f1\u8bed\u5f88\u5f31\uff0c\u5728\u8fd9\u56f0\u6270\u5f88\u4e45\u3002\u73b0\u5728\u4e3a\u5927\u5bb6\u5927\u6982\u4ecb\u7ecd\u4e00\u4e0b\u3002
\n\u4e3b\u8981\u662f\u540e\u7ee7\u70b9\u548cSG\u503c\u7684\u95ee\u9898:
\nSG\u503c\uff1a\u4e00\u4e2a\u70b9\u7684SG\u503c\u5c31\u662f\u4e00\u4e2a\u4e0d\u7b49\u4e8e\u5b83\u7684\u540e\u7ee7\u70b9\u7684SG\u7684\u4e14\u5927\u4e8e\u7b49\u4e8e\u96f6\u7684\u6700\u5c0f\u6574\u6570\u3002
\n\u540e\u7ee7\u70b9\uff1a\u4e5f\u5c31\u662f\u6309\u7167\u9898\u76ee\u8981\u6c42\u7684\u8d70\u6cd5\uff08\u6bd4\u5982\u53d6\u77f3\u5b50\u53ef\u4ee5\u53d6\u7684\u6570\u91cf\uff0c\u65b9\u6cd5\uff09\u80fd\u591f\u8d70\u4e00\u6b65\u8fbe\u5230\u7684\u90a3\u4e2a\u70b9\u3002
\n\u5177\u4f53\u7684\u6709\u5173SG\u503c\u662f\u600e\u4e48\u8fd0\u7528\u7684\u5e0c\u671b\u5927\u5bb6\u81ea\u5df1\u591a\u60f3\u60f3\u3002
\n\u8bfe\u4ef6\u540e\u9762\u6709\u4e00\u4e2a1536\u7684\u4ee3\u7801\u3002\u53ef\u4ee5\u653e\u5728\u540e\u9762\u505a\u505a
\n\u770b\u5230\u8fd9\u91cc\u63a8\u8350\u5927\u5bb6\u505a\u51e0\u9053\u9898\uff1a1846\uff08\u6700\u7b80\u5355\u7684\u535a\u5f08\u6c34\u9898\uff09
\n1847\uff08\u6c42SG\u503c\uff09
\n\u6709\u4e86\u4e0a\u9762\u7684\u77e5\u8bc6\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u770b\u770b\u7ec4\u5408\u535a\u5f08\uff08n\u5806\u77f3\u5b50\uff09
\n\u63a8\u8350\u5927\u5bb6\u770b\u4e2a\u8d44\u6599\uff1a
\n\u535a\u5f08-\u53d6\u77f3\u5b50\u6e38\u620f(\u63a8\u8350\u7b49\u7ea7\u4e94\u661f\u7ea7)
\nhttp:\/\/acm.hdu.edu.cn\/forum\/read.php?fid=20&tid=5748
\nhttp:\/\/hi.baidu.com\/netnode\/blog\/item\/30932c2edc7384514fc226ea.html
\n\u8fd9\u91cc\u63d0\u51fa\u4e86\u4e00\u4e2a\u5947\u5f02\u72b6\u6001\u7684\u95ee\u9898\u3002\u770b\u4e86\u8fd9\u7bc7\u6587\u7ae0\u4f60\u4f1a\u53d1\u73b0\u5f02\u6216\u8fd0\u7b97\u5728\u535a\u5f08\u4e2d\u4f7f\u7528\u7684\u5999\u5904\u3002\u5f53\u7136\u8fd9\u91cc\u6307\u51fa\u7684\u53ea\u662f\u7ec4\u5408\u535a\u5f08\u4e2d\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\u3002
\n\u738b\u9053\u8fd8\u662f\u5bf9SG\u503c\u7684\u6c42\u89e3\uff0c\u4f46\u662f\u77e5\u9053\u8fd9\u4e48\u4e00\u79cd\u601d\u8def\u65e0\u7591\u5bf9\u601d\u7ef4\u7684\u5e7f\u5ea6\u548c\u6df1\u5ea6\u6269\u5c55\u662f\u5f88\u6709\u5e2e\u52a9\u7684\u3002
\nZZ\u535a\u5f08
\nhttp:\/\/acm.hdu.edu.cn\/forum\/read.php?fid=9&tid=10617
\n\u8fd9\u91cc\u4ecb\u7ecd\u4e86\u7ec4\u548c\u535a\u5f08\u7684\u4e24\u79cd\u5927\u7684\u7c7b\u578b\uff0c\u4e00\u79cd\u662f\u6700\u540e\u53d6\u7684\u662fN\u72b6\u6001\u4e00\u79cd\u662f\u6700\u540e\u53d6\u7684\u662fP\u72b6\u6001\uff0c\u4e24\u4e2a\u72b6\u6001\u7684\u89e3\u9898\u65b9\u6cd5\u80fd\u770b\u61c2\u5f88\u6709\u5e2e\u52a9\u3002\u5f53\u7136\uff0c\u80fd\u591f\u628a\u63a8\u5bfc\u8fc7\u7a0b\u7406\u89e3\uff0c\u5403\u900f\u65e0\u7591\u662f\u5927\u725b\u7ea7\u7684\u505a\u6cd5~\u5c0f\u5b50\u4e5f\u4f69\u670d\u7684\u7d27~
\n1536\u9898\u63a8\u8350\u505a\u505a\u8fd9\u9898\uff0c\u8fd9\u9898\u524d\u9762\u63d0\u9192\u5927\u5bb6\u662f\u4e00\u4e2a\u6c42SG\u503c\u7684\u9898\u76ee\uff0c\u9898\u76ee\u524d\u9762\u662f\u5bf9\u5f02\u6216\u8fd0\u7b97\u8fd0\u7528\u5728\u7ec4\u5408\u535a\u5f08\u95ee\u9898\u4e2d\u7684\u5f88\u597d\u7684\u89e3\u91ca\u3002\u5f53\u7136\u9898\u76ee\u672c\u8eab\u662f\u6709\u6240\u4e0d\u540c\u7684\u3002\u56e0\u4e3a\u5728\u8fd9\u91cc\u9762\u5bf9\u53d6\u6cd5\u6709\u6240\u8981\u6c42\u3002\u90a3\u4e48\u8fd9\u6837\u5c31\u56de\u5f52\u5230\u4e86\u89e3\u51b3\u535a\u5f08\u95ee\u9898\u7684\u738b\u9053\u7b97\u6cd5\u2014\u2014\u6c42SG\u503c\u4e0a\u3002
\n\u6709\u5173\u8fd0\u7528\u6c42SG\u503c\u7684\u535a\u5f08\u9898\u76ee\u6709\uff1a 1850\uff08\u4e5f\u53ef\u57fa\u4e8e\u5947\u5f02\u72b6\u6001\u5f02\u6216\uff09
\n1848\uff08\u4e2d\u548c\u7684\u5927\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u5178\u578b\u6c42SG\u503c\u9898\uff09
\n1517\uff08\u4e2a\u4eba\u8ba4\u4e3a\u6709\u70b9\u7325\u7410\u7684\u9898\u76ee\u3002\u3002\u3002\u3002\u5728\u6b64\u9898\u4e0a\u56f0\u6270\u5f88\u4e45\u3002\u5f53\u7136\u641e\u51fa\u6765\u5f88\u5f00\u5fc3\u3002\u5c0f\u5b50\u662f\u7528\u6bd4\u8f83\u89c4\u77e9\u7684\u6c42SG\u503c\u7684\u65b9\u6cd5\u6c42\u51fa\u6765\u7684\uff0c\u4f46\u662f\u8bba\u575b\u6709\u4eba\u5bf9\u5176\u63a8\u51fa\u6765\u4e86\u89c4\u5f8b\uff0c\u8fd9\u91cc\u4f69\u670d\u4e00\u4e0b\uff0c\u5927\u5bb6\u53ef\u4ee5\u5b66\u4e60\u4e00\u4e0b\uff09
\n1079\uff08\u66f4\u7325\u7410\u7684\u9898\u76ee\uff0c\u5bf9\u65b0\u624b\u8981\u6c42\u8f83\u9ad8\uff0c\u56e0\u4e3a\u6309\u4f20\u7edf\u65b9\u6cd5\u9700\u8981\u6bd4\u8f83\u7ec6\u81f4\u7684\u6a21\u62df\u52a0\u5bf9\u8fb9\u89d2\u72b6\u6001\u7684\u8003\u8651\uff0c\u540c\u6837\u6709\u4eba\u63a8\u51fa\u6765\u4e86\u516c\u5f0f\uff09
\n\u5f53\u4f60\u5168\u90e8\u770b\u5b8c\u4ee5\u4e0a\u7684\u4e1c\u897f\u3002\u505a\u5b8c\u4ee5\u4e0a\u7684\u9898\u76ee\u7684\u8bdd\u3002\u3002\u3002\u5c0f\u5b50\u606d\u559c\u4f60~\u4f60\u535a\u5f08\u5165\u95e8\u4e86~~~~
\n\u8fd9\u91cc\u5c0f\u5b50\u544a\u8bc9\u5927\u5bb6\u3002\u535a\u5f08\u5f88\u5f3a\u5927\u3002\u5b66\u4e60\u8981\u8010\u5fc3~\u8c22\u8c22
\nCurrent System Time : 2008-12-11 19:16:03
\nACM\u8bfe\u4f5c\u4e1a\uff1a
\n1001 Brave Game
\n1002 Good Luck in CET-4 Everybody!
\n1003 Fibonacci again and again
\n1004 Rabbit and Grass
\n1005 Being a Good Boy in Spring Festival
\n1006 Public Sale
\n1007 \u60bc\u5ff5512\u6c76\u5ddd\u5927\u5730\u9707\u9047\u96be\u540c\u80de\u2014\u2014\u9009\u62d4\u5fd7\u613f\u8005
\n1008 kiki\u2019s game
\n1009 Calendar Game
\n1010 A Multiplication Game
\n1011 Digital Deletions
\n1012 S-Nim
\nhttp:\/\/acm.hdu.edu.cn\/forum\/read.php?tid=11339&fpage=0&toread=&page=1<\/p>\n

1536\u7684\u53c2\u8003\u4ee3\u7801
\n\u672c\u90e8\u5206\u8bbe\u5b9a\u4e86\u9690\u85cf,\u60a8\u5df2\u56de\u590d\u8fc7\u4e86,\u4ee5\u4e0b\u662f\u9690\u85cf\u7684\u5185\u5bb9
\nCopy code<\/p>\n

\/\/\u535a\u5f08-\u57fa\u4e8e\u6c42SG\u503c\n \/\/Accepted 1536 578MS 416K 904 B\n #include\u201diostream\u201d\n using namespace std;\n int f[101],sg[10001],k;\n int mex(int b)\n {\n     int a[101]={0},i;\n     for(i=0;i     {\n         if(b-f             break;\n         if(sg[b-f]==-1)\n         {\n             sg[b-f]=mex(b-f);\n         }\n         a[sg[b-f]]=1;\n     }\n     for(i=0;i> k,k)\n     {\n         for(i=0;i> f;\n         }\n         memset(sg,-1,sizeof(sg));\n         for(i=0;i             for(j=i+1;jf[j])\n                 {\n                     f+=f[j];\n                     f[j]=f-f[j];\n                     f-=f[j];\n                 }\n         sg[0]=0;\n         cin >> t;\n         while(t\u2013)\n         {\n             cin >> n;\n             s=0;\n             while(n\u2013)\n             {\n                 cin >> bead;\/\/\u8be5\u5806\u7684\u6210\u5458\u4e2a\u6570\n                 if(sg[bead]==-1)\n                     sg[bead]=mex(bead);\n                 s=s^sg[bead];\n             }\n             if(s==0)\n                 cout << \u201cL\u201d;\n             else\n                 cout << \u201cW\u201d;\n         }\n         cout << endl;\n     }\n     return 0;\n }<\/pre>\n
1517\u53c2\u8003\u4ee3\u7801
\n\u672c\u90e8\u5206\u8bbe\u5b9a\u4e86\u9690\u85cf,\u60a8\u5df2\u56de\u590d\u8fc7\u4e86,\u4ee5\u4e0b\u662f\u9690\u85cf\u7684\u5185\u5bb9
\nCopy code<\/p>\n
\/\/\u535a\u5f08-\u57fa\u4e8e\u6c42SG\u503c\n \/\/Accepted 1517 234MS 0K 837 B\n #include\u201diostream\u201d\n using namespace std;\n int main()\n {\n \u00a0 \u00a0 __int64 a[7000]={1},min,n;\n \u00a0 \u00a0 int p[10],sg[7000],i,j,k;\n \u00a0 \u00a0 for(i=2;i \u00a0 \u00a0 for(i=1;i \u00a0 \u00a0 {\n \u00a0 \u00a0 \u00a0 \u00a0 for(j=2,min=-1;j \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if(min==-1||a[p[j]]*j=5000000000)\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 break;\n \u00a0 \u00a0 \u00a0 \u00a0 for(j=2;j \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if(a[p[j]]*j==min)\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 p[j]++;\n \u00a0 \u00a0 }\/\/\u4ece\u5c0f\u5230\u5927\u6c42\u51fa\u6240\u6709\u4e58\u79ef\n \u00a0 \u00a0 while(scanf(\u201c%I64d\u201d,&n)!=EOF)\n \u00a0 \u00a0 {\n \u00a0 \u00a0 \u00a0 \u00a0 for(i=0;i=n)\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 break;\n \u00a0 \u00a0 \u00a0 \u00a0 }\n \u00a0 \u00a0 \u00a0 \u00a0 for(j=i-1;a[j]*9>=n&&j>=0;j\u2013)\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 sg[j]=1;\n \u00a0 \u00a0 \u00a0 \u00a0 while(j>=0)\n \u00a0 \u00a0 \u00a0 \u00a0 {\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 for(k=j+1;k=a[k];k++)\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if(a[k]%a[j]==0&&sg[k]==0)\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 {\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 sg[j]=1;\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 break;\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 j\u2013;\n \u00a0 \u00a0 \u00a0 \u00a0 }\n \u00a0 \u00a0 \u00a0 \u00a0 puts(sg[0]?\u201dStan wins.\u201d:\u201dOllie wins.\u201d);\n \u00a0 \u00a0 }\n \u00a0 \u00a0 return 0;\n }<\/pre>\n
\u8fd9\u91cc\u611f\u8c22sh\u01ce\u5d3d\u540c\u5b66\u7684\u4e00\u6bb5\u4ee3\u7801\u8ba9\u5c0f\u5b50\u5b66\u4f1a\u4e86puts\u7684\u5999\u7528<\/p>\n
1907\u53c2\u8003\u4ee3\u7801
\n\u672c\u90e8\u5206\u8bbe\u5b9a\u4e86\u9690\u85cf,\u60a8\u5df2\u56de\u590d\u8fc7\u4e86,\u4ee5\u4e0b\u662f\u9690\u85cf\u7684\u5185\u5bb9
\n<\/code><\/p>\n
#include\u201diostream\u201d\n using namespace std;\n int main()\n {\n \u00a0 \u00a0 int temp,t,n,s,x,i;\n \u00a0 \u00a0 cin >> t;\n \u00a0 \u00a0 while(t\u2013)\n \u00a0 \u00a0 {\n \u00a0 \u00a0 \u00a0 \u00a0 cin >> n;\n \u00a0 \u00a0 \u00a0 \u00a0 for(i=s=temp=0;i> x;\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if(x>1)\u00a0 \u00a0 temp=1;\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 s^=x;\n \u00a0 \u00a0 \u00a0 \u00a0 }\n \u00a0 \u00a0 \u00a0 \u00a0 if((s&&temp)||(!s&&!temp))\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 cout << \u201cJohn\u201d << endl;\n \u00a0 \u00a0 \u00a0 \u00a0 else\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 cout << \u201cBrother\u201d << endl;\n \u00a0 \u00a0 }\n \u00a0 \u00a0 return 0;\n }<\/pre>\n
Tanky Woo\u539f\u521b\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1a \u8f6c\u8f7d\u81eaTanky Woo<\/p>\n","protected":false},"excerpt":{"rendered":"
\u4ee5\u4e0b\u662f\u6211\u4ece\u7f51\u4e0a\u6536\u96c6\u7684\u5173\u4e8e\u7ec4\u5408\u535a\u5f08\u7684\u8d44\u6599\u6c47\u603b\uff1a \u6709\u4e00\u79cd\u5f88\u6709\u610f\u601d\u7684\u6e38\u620f\uff0c\u5c31\u662f\u6709\u7269\u4f53\u82e5\u5e72\u5806\uff0c\u53ef\u4ee5\u662f\u706b\u67f4\u68cd\u6216\u662f\u56f4\u68cb\u5b50\u7b49\u7b49\u5747\u53ef\u3002\u4e24\u4e2a \u4eba\u8f6e\u6d41\u4ece\u5806\u4e2d\u53d6\u7269\u4f53\u82e5\u5e72\uff0c\u89c4\u5b9a\u6700\u540e\u53d6\u5149\u7269\u4f53\u8005\u53d6\u80dc\u3002\u8fd9\u662f\u6211\u56fd\u6c11\u95f4\u5f88\u53e4\u8001\u7684\u4e00\u4e2a\u6e38\u620f \uff0c\u522b\u770b\u8fd9\u6e38\u620f\u6781\u5176\u7b80\u5355\uff0c\u5374\u8574\u542b\u7740\u6df1\u523b\u7684\u6570\u5b66\u539f\u7406\u3002\u4e0b\u9762\u6211\u4eec\u6765\u5206\u6790\u4e00\u4e0b\u8981\u5982\u4f55\u624d\u80fd\u591f \u53d6\u80dc\u3002 \uff08\u4e00\uff09\u5df4\u4ec0\u535a\u5955\uff08Bash 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k\uff08\u2264m)\u4e2a\uff0c\u90a3\u4e48\u5148\u53d6\u8005\u518d\u62ff\u8d70m+1-k\u4e2a\uff0c\u7ed3\u679c\u5269\u4e0b\uff08m+1\uff09\uff08r-1\uff09\u4e2a\uff0c\u4ee5\u540e\u4fdd\u6301\u8fd9\u6837\u7684 \u53d6\u6cd5\uff0c\u90a3\u4e48\u5148\u53d6\u8005\u80af\u5b9a\u83b7\u80dc\u3002\u603b\u4e4b\uff0c\u8981\u4fdd\u6301\u7ed9\u5bf9\u624b\u7559\u4e0b\uff08m+1\uff09\u7684\u500d\u6570\uff0c\u5c31\u80fd\u6700\u540e\u83b7\u80dc\u3002 \u8fd9\u4e2a\u6e38\u620f\u8fd8\u53ef\u4ee5\u6709\u4e00\u79cd\u53d8\u76f8\u7684\u73a9\u6cd5\uff1a\u4e24\u4e2a\u4eba\u8f6e\u6d41\u62a5\u6570\uff0c\u6bcf\u6b21\u81f3\u5c11\u62a5\u4e00\u4e2a\uff0c\u6700\u591a\u62a5\u5341 \u4e2a\uff0c\u8c01\u80fd\u62a5\u5230100\u8005\u80dc\u3002 \uff08\u4e8c\uff09\u5a01\u4f50\u592b\u535a\u5955\uff08Wythoff Game\uff09\uff1a\u6709\u4e24\u5806\u5404\u82e5\u5e72\u4e2a\u7269\u54c1\uff0c\u4e24\u4e2a\u4eba\u8f6e\u6d41\u4ece\u67d0\u4e00\u5806\u6216\u540c \u65f6\u4ece\u4e24\u5806\u4e2d\u53d6\u540c\u6837\u591a\u7684\u7269\u54c1\uff0c\u89c4\u5b9a\u6bcf\u6b21\u81f3\u5c11\u53d6\u4e00\u4e2a\uff0c\u591a\u8005\u4e0d\u9650\uff0c\u6700\u540e\u53d6\u5149\u8005\u5f97\u80dc\u3002 \u8fd9\u79cd\u60c5\u51b5\u4e0b\u662f\u9887\u4e3a\u590d\u6742\u7684\u3002\u6211\u4eec\u7528\uff08ak\uff0cbk\uff09\uff08ak \u2264 bk ,k=0\uff0c1\uff0c2\uff0c\u2026,n)\u8868\u793a \u4e24\u5806\u7269\u54c1\u7684\u6570\u91cf\u5e76\u79f0\u5176\u4e3a\u5c40\u52bf\uff0c\u5982\u679c\u7532\u9762\u5bf9\uff080\uff0c0\uff09\uff0c\u90a3\u4e48\u7532\u5df2\u7ecf\u8f93\u4e86\uff0c\u8fd9\u79cd\u5c40\u52bf\u6211\u4eec \u79f0\u4e3a\u5947\u5f02\u5c40\u52bf\u3002\u524d\u51e0\u4e2a\u5947\u5f02\u5c40\u52bf\u662f\uff1a\uff080\uff0c0\uff09\u3001\uff081\uff0c2\uff09\u3001\uff083\uff0c5\uff09\u3001\uff084\uff0c7\uff09\u3001\uff086\uff0c 10\uff09\u3001\uff088\uff0c13\uff09\u3001\uff089\uff0c15\uff09\u3001\uff0811\uff0c18\uff09\u3001\uff0812\uff0c20\uff09\u3002 \u53ef\u4ee5\u770b\u51fa,a0=b0=0,ak\u662f\u672a\u5728\u524d\u9762\u51fa\u73b0\u8fc7\u7684\u6700\u5c0f\u81ea\u7136\u6570,\u800c bk= ak + k\uff0c\u5947\u5f02\u5c40\u52bf\u6709 \u5982\u4e0b\u4e09\u6761\u6027\u8d28\uff1a 1\u3002\u4efb\u4f55\u81ea\u7136\u6570\u90fd\u5305\u542b\u5728\u4e00\u4e2a\u4e14\u4ec5\u6709\u4e00\u4e2a\u5947\u5f02\u5c40\u52bf\u4e2d\u3002 \u7531\u4e8eak\u662f\u672a\u5728\u524d\u9762\u51fa\u73b0\u8fc7\u7684\u6700\u5c0f\u81ea\u7136\u6570\uff0c\u6240\u4ee5\u6709ak > ak-1 \uff0c\u800c bk= ak + k … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":47,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[24],"tags":[207],"class_list":["post-199","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-24","tag-acm"],"jetpack_featured_media_url":"https:\/\/static.rexdf.org\/uploads\/2011\/10\/1280wallpaperQLY2.jpg","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/posts\/199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/comments?post=199"}],"version-history":[{"count":0,"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/posts\/199\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/media\/47"}],"wp:attachment":[{"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/media?parent=199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/categories?post=199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.rexdf.org\/en\/wp-json\/wp\/v2\/tags?post=199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}