\u9898\u662f\u674e\u79d1\u548c\u7f57\u8000\u71ca\u51fa\u7684\uff0c\u8fd8\u662f\u5f88\u4e0d\u9519\u7684\uff0c\u8f9b\u82e6\u4e8c\u4f4d\u4e86\uff5e
\n\u4e4b\u524d\u6211\u4e5f\u6ca1\u770b\u9898\uff0c4\u70b9\u5de6\u53f3\u4e0a\u6765\u79d2\u4e863\u4e2a\u6c34\u9898\uff0c\u5c31\u6ca1\u5f80\u4e0b\u770b\u3002B\u9898\u6570\u636e\u540e\u6765\u53d1\u73b0\u6709\u95ee\u9898\uff0c\u8d5b\u540erejudge\u6709\u4e24\u4e2a\u8fc7\u7684\u3002
\n\u606d\u559c\u5927\u5de5\u7684\u80e1\u9a8f\u83b7\u5f97NEUACM\u4e8c\u6708\u6708\u8d5b\u7b2c\u4e00\uff0c\u606d\u559c\u8f6f\u4fe11001\u6768\u9038\u98a2\u83b7\u5f97\u4e1c\u5927\u7b2c\u4e00\u3002\u4f46\u613f\u4e0b\u6b21\u6708\u8d5b\u4e1c\u5927\u7684\u53ef\u4ee5\u767b\u9876\u3002\u79ef\u5206\u548c\u65b0\u5b66\u671f\u96c6\u8bad\u961f\u540d\u5355\u9002\u65f6\u516c\u5e03\u3002<\/p>\n
\n1001. John\u2019s Problem I
\n\u89e3\u6cd5\uff1aDP
\n\u96be\u5ea6\uff1a\u4e2d\u7b49
\n\u867d\u7136\u53ea\u6709HIT\u7684\u5927\u725b\u8fc7\u4e86\u8fd9\u4e2a\u9898\uff0c\u4f46\u662f\u5176\u5b9e\u8fd9\u5e76\u4e0d\u662f\u4e00\u4e2a\u5f88\u96be\u7684dp\u3002
\n\u53ef\u4ee5\u5f00\u4e24\u4e2a900\u3000\u00d7\u30008100\u7684\u6570\u7ec4\u6765\u4fdd\u5b58\u72b6\u6001\u3002\u5206\u522b\u7528\u6765\u8bb0\u5f55\u548c\u4e3ai\u5e73\u65b9\u548c\u4e3aj\u65f6\u5f97\u5230\u7684\u6570\u7684\u6700\u5c0f\u4f4d\u6570\u548c\u8fd9\u4e2a\u6570\u7684\u7b2c\u4e00\u4f4d(\u4e0d\u662f\u6700\u540e\u4e00\u4f4d)\u3002
\n\u56e0\u4e3a\u53ef\u80fd\u5b58\u5728\u4f4d\u6570\u4e00\u6837\u4f46\u662f\u5927\u5c0f\u4e0d\u4e00\u6837\u7684\u60c5\u51b5\uff0c\u5982\u679c\u662f\u4ece\u524d\u5f80\u540e\u63a8\u7684\u8bdd\u90a3\u4e48\u6700\u540e\u4e00\u4f4d\u4e0d\u540c\u5e76\u4e0d\u80fd\u51b3\u5b9a\u51fa\u4e24\u4e2a\u6570\u8c01\u5927\u8c01\u5c0f\uff0c\u4f46\u662f\u7b2c\u4e00\u4f4d\u4e0d\u540c\u5219\u80af\u5b9a\u4e00\u4e2a\u5927\u4e00\u4e2a\u5c0f\u3002\u6240\u4ee5\u4ece\u540e\u5f80\u524d\u63a8\uff0c\u65f6\u95f4\u590d\u6742\u5ea6900*8100*9.
\n\u56e0\u4e3a\u4e0d\u53ef\u80fd\u51fa\u73b0\u542b0\u7684\u4f4d\u3002<\/p>\n
1002. John\u2019s problem II
\n\u89e3\u6cd5\uff1a\u6392\u5e8f
\n\u96be\u5ea6\uff1a\u96be(\u56e0\u4e3a\u9898\u76ee\u4e0d\u4ec5\u5f00\u59cb\u63cf\u8ff0\u6709\u7f3a\u9677\uff0c\u540e\u9762\u53d1\u73b0\u6570\u636e\u4e5f\u6709\u95ee\u9898)\u3002
\n\u7528\u57fa\u6570\u6392\u5e8f\u6216\u8005\u6309\u7167\u5750\u6807\u4e8c\u7ea7\u6392\u5e8f\u5c31\u53ef\u4ee5\u89e3\u51b3\u3002\u5047\u8bbe\u4e00\u4e2ax\u8f74\u4e0a\u7684\u70b9xi\uff0c\u5982\u679c\u5728xi\u5efa\u9020\u90ae\u5c40\u7684\u8bdd\uff0c\u90a3\u4e48x\u5750\u6807<=xi\u7684\u4eba\u7684\u6570\u76ee\u5e94\u8be5>=\u603b\u4eba\u6570\u7684\u4e00\u534a\u3002\u56e0\u4e3a\u5982\u679c\u518d\u5f80\u53f3\u8d70\u4e00\u6b65\uff0c\u90a3\u589e\u52a0\u7684\u8ddd\u79bb\u548c\u5c31\u662f\u5de6\u8fb9\u7684\u4eba\u6570\u51cf\u53bb\u53f3\u8fb9\u7684\u4eba\u6570\u3002\u6240\u4ee5\u53ea\u8981\u6309\u7167\u5750\u6807\u503c\u6392\u5e8f\uff0c\u7136\u540e\u4ece\u6700\u5de6\u8fb9\u5f80\u6700\u53f3\u8fb9\u7d2f\u52a0\u4eba\u6570\u5c31\u884c\uff0c\u5982\u679c\u4eba\u6570\u548c\u5927\u4e8e\u6216\u8005\u7b49\u4e8e\u603b\u4eba\u6570\u7684\u4e00\u534a\uff0c\u5c31\u53ef\u4ee5\u5728\u8fd9\u4e2a\u5730\u65b9\u5efa\u9020\u90ae\u5c40\u4e86\u3002\u6ce8\u610f\u603b\u4eba\u6570\u4e3a\u5947\u6570\u7684\u60c5\u51b5\u3002<\/p>\n
1003. A hard problem
\n\u89e3\u6cd5\uff1a\u6570\u8bba
\n\u96be\u5ea6\uff1a\u4f1a\u8005\u4e0d\u96be\uff0c\u96be\u8005\u4e0d\u4f1a
\n\u4f20\u8bf4\u4e2d\u6709\u4e2a\u53eb\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u7684\u4e1c\u897f\uff0c\u636e\u8bf4\u662f\u5c0f\u5b66\u77e5\u8bc6\uff0c\u4f46\u662f\u6211\u4e5f\u4e0d\u4f1a\u3002\u672c\u9898\u662fTop Coder div2\u67d0\u6b21\u6bd4\u8d5b\u7684\u7b2c\u4e00\u9898\u3002\u9648\u666f\u6da6\u8bc1\u660e\u7684\u201c1+2\u201d\u5c31\u662f\u201c\u4efb\u4e00\u5145\u5206\u5927\u7684\u5076\u6570\u90fd\u53ef\u4ee5\u8868\u793a\u6210\u4e8c\u4e2a\u7d20\u6570\u7684\u548c\u201d\u3002\u7531\u6b64\u4e5f\u53ef\u63a8\u51fa\u201c\u4efb\u4e00\u5927\u4e8e7\u7684\u5947\u6570\u90fd\u53ef\u5199\u6210\u4e09\u4e2a\u8d28\u6570\u4e4b\u548c\u201d\u3002<\/p>\n
1004. Choose a Way
\n\u89e3\u6cd5\uff1aFloyd
\n\u96be\u5ea6\uff1a\u57fa\u7840
\nFloyd\u7684\u4e09\u91cd\u5faa\u73af\u91cc\u9762\u6709\u4e00\u4e2adis[i][j] = min(d[i][j], d[i][k] + d[k][j])\uff0c
\n\u610f\u5373[i\uff0cj]\u4e4b\u95f4\u7684\u6700\u77ed\u8ddd\u79bb=min([i\uff0cj]\u5f53\u524d\u8ddd\u79bb\uff0c[I\uff0ck]\u4e4b\u95f4\u7684\u6700\u5c0f\u8ddd\u79bb+[k\uff0cj]\u4e4b\u95f4\u7684\u6700\u5c0f\u8ddd\u79bb)\u3002\u73b0\u5728\u53ea\u8981\u628adis[i][j]\u7684\u542b\u4e49\u6539\u6210[i\uff0cj]\u4e4b\u95f4\u7684\u8017\u8d39\u6700\u9ad8\u7684\u4e00\u6761\u8def\u7684\u8017\u8d39\uff0c\u6240\u4ee5\u53ef\u4ee5\u628a\u539f\u5f0f\u6539\u6210:
\ndis[i][j] = min(d[i][j], max(d[i][k], d[k][j]))
\n\u6211\u662f\u51fa\u540e4\u9898\u7684\u7f57\u8000\u71ca\uff08shen \u7b2c\u4e00\u58f0\uff09\u3002<\/p>\n
E\u9898\uff1a
\n\u9898\u610f\u662f\u4f60\u77e5\u9053\u67d0\u4e24\u4e2a\u672a\u77e5\u6b63\u6574\u6570\u7684\u548c\u4ee5\u53ca\u5b83\u4eec\u7684\u6700\u5c0f\u516c\u500d\u6570\uff0c\u6c42\u51fa\u8fd9\u4e24\u4e2a\u6570\u3002\u50bb\u50bb\u7684\u6211\u51fa\u7684\u6570\u636e\u91cf\u592aXX\u5f31\u667a\u4e86\u4ee5\u81f4\u6ca1\u8003\u51fa\u8fd9\u6761\u9898\u76ee\u7684\u7cbe\u7cb9\u6240\u5728\u3002\u7ed3\u679c\u771f\u53d8\u6210\u4e86\u201cAn Easy Problem\u201d\u3002
\n\u6211\u8d5b\u540e\u4f1a\u518d\u6362\u4e2a\u518d\u5927\u6570\u91cf\u7ea7\u522b\u7684\u6570\u636e\u529b\u6c42\u5927\u5bb6\u7528O(1)\u7684\u7b97\u6cd5\u6765\u505a\u51fa\u8fd9\u9898\u6765\uff0c\u800c\u4e0d\u662f\u6bd4\u8d5b\u4e2d\u5f88\u591a\u4eba\u7528\u5230\u7684\u679a\u4e3e\u7b49\u65b9\u6cd5\u6c34\u8fc7\u3002\u5982\u679c\u4f60\u60f3\u518d\u505a\u4e00\u904d\u7684\u53ef\u4ee5\u5148\u8df3\u8fc7\u4ee5\u4e0b\u7684\u9898\u89e3\uff0c\u8fd9\u9898\u60f3\u7740\u63a8\u5bfc\u8fc7\u7a0b\u662f\u5f88\u6709\u610f\u601d\u7684\u3002<\/p>\n
\u9996\u5148\u6211\u4eec\u77e5\u9053\u9898\u76ee\u662f\u53ef\u4ee5\u5217\u51fa\u4e24\u6761\u5f0f\u5b50 x+y=A \u548c x*y\/gcd(x,y)=B \u3002\u63a5\u7740\u6211\u4eec\u5c06\u7528 x0*gcd(x,y) \u5e26\u5165x\u4e2d\uff0c\u540c\u6837 y0*gcd(x,y)\u4ee3\u5165y\u4e2d\u90a3\u73b0\u5728 \u5f97\u5230\u65b0\u7684\u4e24\u6761\u5f0f\u5b50 gcd(x,y)*(x0+y0)=A \u548c gcd(x,y)*x0*y0=B \u3002\u5176\u5b9e\u5e94\u8be5\u9a6c\u4e0a\u80fd\u53cd\u5e94\u5230 gcd(A,B)==gcd(x,y) \uff0c\u56e0\u4e3a\u5982\u679c(x0+y0) \u548c x0*y0 \u8fd8\u80fd\u63d0\u51fa\u5927\u4e8e1\u7684\u516c\u56e0\u5b50\u7684\u8bdd \u90a3\u663e\u7136\u539f\u6765\u5047\u8bbegcd(x,y)\u5c31\u4e0d\u662fx\u548cy\u7684\u6700\u5927\u516c\u7ea6\u6570\u4e86\uff08\u4e5f\u5c31\u662f\u8bf4\u77db\u76fe\u4e86\uff09\u3002
\n\u7531\u6b64\u6211\u4eec\u518d\u80fd\u5f97\u5230 x0+y0=A0 x0*y0=B0 (A=gcd(A,B)*A0, B=gcd(A,B)*B0) \u7531\u6b64\u6211\u4eec\u80fd\u5f97\u5230\u4e00\u6761\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7ec4 (A0-x)*x=B0 x\u7684\u4e24\u4e2a\u89e3\u5c31\u662fx0\u548cy0\u4e86\u3002
\n\u6574\u7406\u5f97 x^2-A0*x+B0=0 \u7531\u6c42\u6839\u516c\u5f0f\u5f97 \u5f53\u0394=(-A0)^2-4*B0\uff1c0\u65f6\u81ea\u7136\u662f\u6ca1\u89e3\u54af\u3002 \u0394=(-A0)^2-4*B0\u22650\u65f6\uff0cx=[A0\u00b1(A0^2-4*B0)^(1\/2)]\/2 \u4f46\u8fd8\u8981\u6ce8\u610f\u4e00\u4e9b\u60c5\u51b5 \uff1a\u0394\u7684\u503c\u5fc5\u987b\u662f\u80fd\u5f00\u6839\u53f7\u7684\uff0c\u5426\u5219\u4e5f\u7b97\u65e0\u89e3\u3002\u6709\u4e9b\u7ec6\u5fc3\u7684\u540c\u5b66\u8fd8\u4f1a\u95ee\u9700\u4e0d\u9700\u8981\u5224\u65ad[A0\u00b1(A0^2-4*B0)^(1\/2)]\u80fd\u88ab2\u6574\u9664\u3002\u5206\u6790\u4e00\u4e0b\uff0c\u65e0\u8bbaA0\u662f\u5947\u6570\u8fd8\u662f\u5076\u6570\u5f0f\u5b50\u7ed3\u679c\u90fd\u662f\u5076\u6570\u7684\u3002\u6700\u540ex0*gcd(A,B) \u548c y0*gcd(A,B)\u5c31\u662f\u8fd9\u9898\u7684\u89e3\u4e86\u3002<\/p>\n
\u8fd9\u4ee5\u4e0a\u5c31\u662f\u6211\u5bf9\u8fd9\u9898\u7684\u8ba4\u8bc6\u3002\u6bd4\u8d5b\u4e2d\u7684\u9898\u76ee\u6570\u636e\u5f31\u662f\u6211\u7684\u95ee\u9898\uff0c\u6ca1\u6709\u8ba9\u8fd9\u9898\u53d1\u6325\u5230\u8ba9\u5927\u5bb6\u6df1\u5165\u53bb\u60f3\u8fd9\u4e2a\u95ee\u9898\u7684\u6548\u679c\uff0c\u771f\u7684\u5f88\u4e0d\u597d\u610f\u601d\u3002
\nF\u9898\uff1a
\n\u6709\u7c7b\u4f3c\u7684\u6570\u5b66\u9898\uff0c\u6211\u662f\u653e\u5927\u4e86\u6570\u636e\u8303\u56f4\uff0c\u56e0\u6b64\u9700\u8981\u7528\u5230\u8bb0\u5fc6\u5316\u641c\u7d22\u7684\u7684\u6280\u5de7\uff0c\u5f53\u7136\u4f60\u4e5f\u53ef\u4ee5\u9012\u63a8\u3002
\n\u53ef\u4ee5\u5047\u8bbe\u4e00\u4e2a\u51fd\u6570f(m,n) \u4ee3\u8868\u7684\u610f\u601d\u662f m\u4e2a\u6a59\u5b50 n\u4e2a\u76d8\uff0c\u8fd9n\u4e2a\u76d8\u91cc\u7684\u7403\u6570\u662f\u4ece\u5c0f\u5230\u5927\u6765\u653e\u7684\u3002\u90a3\u73b0\u5728 \u80fd\u63a8\u51fa f(m,n)=f(m-n,n)+f(m,n-1) \u5bf9\u4e8e\u7b2c\u4e00\u4e2a\u76d8\u5b50\u8981\u653e\u5c31\u4e00\u6392\u5730\u653e\uff0c\u8981\u4e48\u4e0d\u653e\u5c31\u5bf9\u5269\u4e0b\u7684n-1\u76d8\u5b50\u7ee7\u7eed\u3002\u5f53\u7136\u8981\u5bf9\u8fb9\u754c\u6709\u4e9b\u754c\u5b9a\u3002n<=0\u65f6 \u5f53\u7136\u662f0 \uff0c\u800cm<0\u65f6\u540c\u6837\u4e5f\u662f\u3002\u4f46m=0\u65f6\u5e94\u8be5\u662f\u4e00\u79cd\u3002
\nG\u9898\uff1a
\n\u539f\u672c\u662f\u8981\u8003\u5bdf\u4e00\u4e0bgcd(|x1-x2|,|y1-y2|)+1\u8fd9\u6761\u5f0f\u5b50\u7684\u3002\u4f46\u540e\u6765\u60f3\u4f1a\u4e0d\u4f1a\u8bf4\u592a\u504f\u4e86\uff0c\u5c31\u6539\u6210\u76f4\u63a5\u7ed9\u51fa\u4e86\u3002gcd(|x1-x2|,|y1-y2|)+1\u662f(x1,y1)\u4e0e(x2,y2)\u4e24\u70b9\u95f4\uff08\u5305\u62ec\u4e24\u7aef\u6574\u6570\u70b9\uff09\u6574\u6570\u70b9\u7684\u6570\u76ee\u3002\u63a5\u7740\u5c31\u8d64\u88f8\u88f8\u7684MST\u4e86\u3002\u5e94\u8be5\u662fprim\u7684\u7b97\u6cd5\u6bd4\u8f83\u597d\u70b9\u3002kruskal\u7684\u4e0d\u77e5\u9053\u4f1a\u4e0d\u4f1a\u8d85\u65f6\u3002
\nH\u9898\uff1a
\n\u662f\u300a\u7b97\u6cd5\u5bfc\u8bba\u300b352 353 \u4e60\u9898\u7684\u6a21\u578b\u3002\u5f53\u4e00\u4e2a\u6700\u5c0f\u751f\u6210\u6811\u642d\u597d\u540e\u6dfb\u52a0\u4e00\u6761\u65b0\u8fb9\uff08\u6ca1\u65b0\u7aef\u70b9\u7684\uff09\u8fdb\u53bb\u540e\u5c31\u662f\u591a\u4e86\u4e00\u4e2a\u73af\uff0c\u53bb\u6389\u8fd9\u73af\u4e0a\u6700\u957f\u7684\u8fb9\uff0c\u5c31\u53c8\u4fdd\u6301\u6700\u5c0f\u751f\u6210\u6811\u4e86\u3002\u80fd\u53bb\u627e\u627e\u6b21\u5c0f\u751f\u6210\u6811\u7684\u8d44\u6599\u3002\u5728\u7528prim\u7684\u8fc7\u7a0b\u4e2d\u80fd\u5efa\u4e2a\u8868Max_Edge[i][j]\u8bb0\u5f55\u70b9i\u5230\u70b9j\u7684\u6700\u957f\u8fb9\uff0c\u6bcf\u6b21\u67e5\u8be2\u662f\u5c31\u7528\u65b0\u8fb9\u548c\u8fd9\u8868\u91cc\u5934\u5bf9\u5e94\u7684\u503c\u6bd4\u8f83\u4e00\u4e0b\uff0c\u6bd4\u539f\u6765\u6700\u5927\u8fb9\u5927\u7684\u8bdd\u5c31\u8fd8\u662f\u539f\u6765\u6700\u5c0f\u751f\u6210\u6811\u7684\u503c\u5426\u5219\u5c31\u662f\u539f\u6570\u503c\u51cf\u53bb\u539f\u8fb9\u52a0\u4e0a\u65b0\u8fb9\u7684\u503c\u4e86\u3002\u89e3\u51fa\u8fd9\u9898\u5e94\u8be5\u6ca1\u4ec0\u4e48\u95ee\u9898\u7684\u4e86\u3002\uff08\u5176\u5b9e\u5f53\u521d\u6700\u62c5\u5fc3\u7684\u6570\u636e\u662f\u8fd9\u9898\u7684\u6570\u636e\uff0c\u4f46\u88ab\u5927\u5de5\u7684\u5927\u795e\u7b2c\u4e00\u9053\u79d2\u6389\u7684\u5c31\u662f\u8fd9\u9898\u3002\u5b9e\u5728\u662f\u51fa\u4e8e\u610f\u5916\uff0c\u4f46\u4e5f\u5e2e\u6211\u957f\u6292\u4e00\u6c14\uff09
\n\u5c0f\u5f1f\u7b2c\u4e00\u6b21\u51fa\u9898\uff0c\u8bf8\u591a\u7f3a\u6f0f\u6073\u8bf7\u539f\u8c05\u3002\u8fd8\u6709\u5c31\u591a\u52a0\u4e00\u53e5\uff1a\u9898\u76ee\u7684\u6a21\u578b\u662f\u5b66\u4e60\u4e86\u5404\u5927oj\u6216\u662f\u4e66\u4e0a\u6a21\u578b\uff0c\u4ec5\u7528\u4e8e\u5b66\u4e60\u548c\u4ea4\u6d41\u7528\u9014\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u9898\u662f\u674e\u79d1\u548c\u7f57\u8000\u71ca\u51fa\u7684\uff0c\u8fd8\u662f\u5f88\u4e0d\u9519\u7684\uff0c\u8f9b\u82e6\u4e8c\u4f4d\u4e86\uff5e \u4e4b\u524d\u6211\u4e5f\u6ca1\u770b\u9898\uff0c4\u70b9\u5de6\u53f3\u4e0a\u6765\u79d2\u4e863\u4e2a\u6c34\u9898\uff0c\u5c31\u6ca1\u5f80\u4e0b\u770b\u3002B\u9898\u6570 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[9],"_links":{"self":[{"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/posts\/223739"}],"collection":[{"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/comments?post=223739"}],"version-history":[{"count":1,"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/posts\/223739\/revisions"}],"predecessor-version":[{"id":224633,"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/posts\/223739\/revisions\/224633"}],"wp:attachment":[{"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/media?parent=223739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/categories?post=223739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/yangzhe1991.org\/blog\/wp-json\/wp\/v2\/tags?post=223739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}