{"id":348,"date":"2013-03-08T22:42:00","date_gmt":"2013-03-08T14:42:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/252"},"modified":"2013-03-08T22:42:00","modified_gmt":"2013-03-08T14:42:00","slug":"poj_1091_fleas_-_extended_euclidean_solution_inference__inclusion_and_exclusion","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=348","title":{"rendered":"POJ 1091(\u8df3\u86a4-\u6269\u5c55\u6b27\u51e0\u91cc\u5fb7\u6709\u89e3\u63a8\u8bba+\u5bb9\u65a5\u539f\u7406)"},"content":{"rendered":"\n\n\n
\n
Language:\n\n\n\n
Time Limit:<\/strong> 1000MS<\/td>\n <\/td>\nMemory Limit:<\/strong> 10000K<\/td>\n<\/tr>\n
Total Submissions:<\/strong> 6911<\/td>\n <\/td>\nAccepted:<\/strong> 1951<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Description<\/p>\n

\nZ\u57ce\u5e02\u5c45\u4f4f\u7740\u5f88\u591a\u53ea\u8df3\u86a4\u3002\u5728Z\u57ce\u5e02\u5468\u516d\u751f\u6d3b\u9891\u9053\u6709\u4e00\u4e2a\u5a31\u4e50\u8282\u76ee\u3002\u4e00\u53ea\u8df3\u86a4\u5c06\u88ab\u8bf7\u4e0a\u4e00\u4e2a\u9ad8\u7a7a\u94a2\u4e1d\u7684\u6b63\u4e2d\u592e\u3002\u94a2\u4e1d\u5f88\u957f\uff0c\u53ef\u4ee5\u770b\u4f5c\u662f\u65e0\u9650\u957f\u3002\u8282\u76ee\u4e3b\u6301\u4eba\u4f1a\u7ed9\u8be5\u8df3\u86a4\u53d1\u4e00\u5f20\u5361\u7247\u3002\u5361\u7247\u4e0a\u5199\u6709N+1\u4e2a\u81ea\u7136\u6570\u3002\u5176\u4e2d\u6700\u540e\u4e00\u4e2a\u662fM\uff0c\u800c\u524dN\u4e2a\u6570\u90fd\u4e0d\u8d85\u8fc7M\uff0c\u5361\u7247\u4e0a\u5141\u8bb8\u6709\u76f8\u540c\u7684\u6570\u5b57\u3002\u8df3\u86a4\u6bcf\u6b21\u53ef\u4ee5\u4ece\u5361\u7247\u4e0a\u4efb\u610f\u9009\u62e9\u4e00\u4e2a\u81ea\u7136\u6570S\uff0c\u7136\u540e\u5411\u5de6\uff0c\u6216\u5411\u53f3\u8df3S\u4e2a\u5355\u4f4d\u957f\u5ea6\u3002\u800c\u4ed6\u6700\u7ec8\u7684\u4efb\u52a1\u662f\u8df3\u5230\u8ddd\u79bb\u4ed6\u5de6\u8fb9\u4e00\u4e2a\u5355\u4f4d\u957f\u5ea6\u7684\u5730\u65b9\uff0c\u5e76\u6361\u8d77\u4f4d\u4e8e\u90a3\u91cc\u7684礼\u7269\u3002 
\n\u6bd4\u5982\u5f53N=2\uff0cM=18\u65f6\uff0c\u6301\u6709\u5361\u7247(10, 15, 18)\u7684\u8df3\u86a4\uff0c\u5c31\u53ef\u4ee5\u5b8c\u6210\u4efb\u52a1\uff1a\u4ed6\u53ef\u4ee5\u5148\u5411\u5de6\u8df310\u4e2a\u5355\u4f4d\u957f\u5ea6\uff0c\u7136\u540e\u518d\u8fde\u5411\u5de6\u8df33\u6b21\uff0c\u6bcf\u6b2115\u4e2a\u5355\u4f4d\u957f\u5ea6\uff0c\u6700\u540e\u518d\u5411\u53f3\u8fde\u8df33\u6b21\uff0c\u6bcf\u6b2118\u4e2a\u5355\u4f4d\u957f\u5ea6\u3002\u800c\u6301\u6709\u5361\u7247(12, 15, 18)\u7684\u8df3\u86a4\uff0c\u5219\u600e\u4e48\u4e5f\u4e0d\u53ef\u80fd\u8df3\u5230\u8ddd\u4ed6\u5de6\u8fb9\u4e00\u4e2a\u5355\u4f4d\u957f\u5ea6\u7684\u5730\u65b9\u3002 
\n\u5f53\u786e\u5b9aN\u548cM\u540e\uff0c\u663e\u7136\u4e00\u5171\u6709M^N\u5f20\u4e0d\u540c\u7684\u5361\u7247\u3002\u73b0\u5728\u7684\u95ee\u9898\u662f\uff0c\u5728\u8fd9\u6240\u6709\u7684\u5361\u7247\u4e2d\uff0c\u6709\u591a\u5c11\u5f20\u53ef\u4ee5\u5b8c\u6210\u4efb\u52a1\u3002 \n<\/div>\n

Input<\/p>\n

\n\u4e24\u4e2a\u6574\u6570N\u548cM(N <= 15 , M <= 100000000)\u3002<\/div>\n

Output<\/p>\n

\n\u53ef\u4ee5\u5b8c\u6210\u4efb\u52a1\u7684\u5361\u7247\u6570\u3002<\/div>\n

Sample Input<\/p>\n

2 4<\/pre>\n
Sample Output<\/p>\n
12<\/pre>\n
Hint<\/p>\n
\n\u8fd912\u5f20\u5361\u7247\u5206\u522b\u662f\uff1a 
\n(1, 1, 4), (1, 2, 4), (1, 3, 4), (1, 4, 4), (2, 1, 4), (2, 3, 4), 
\n(3, 1, 4), (3, 2, 4), (3, 3, 4), (3, 4, 4), (4, 1, 4), (4, 3, 4) \n<\/div>\n
Source<\/p>\n
\nHNOI 2001<\/a><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\u5047<\/span>\u8bbe<\/span><\/p>\n
a1x1+a2x2+--anxn+a(n+1)M=1<\/span><\/p>\n
\u5219(a1,a2,..an,M)=1<\/span><\/p>\n
\u6240\u4ee5\u7528\u5bb9\u65a5\u539f\u7406\u8ba1\u7b97\u51fagcd\u22601\u7684\u60c5\u51b5\u7684\u603b\u6570<\/span><\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<cmath>\n#include<algorithm>\n#include<iostream>\n#include<cstdlib>\n#include<functional>\nusing namespace std;\n#define MAXN (15)\n#define MAXM (100000000)\nint n,m;\nlong long ans=0,temp=0;\nint a[MAXM],tot=0;\nlong long pow2(long long a,int b)\n{\n\tif (b==1) return a;\n\telse if (b%2)\n\t{\n\t\tlong long p=pow2(a,b\/2);\n\t\treturn p*p*a;\n\t}\n\telse\n\t{\n\t\tlong long p=pow2(a,b\/2);\n\t\treturn p*p;\n\t}\n}\nvoid dfs(int j,int c,int cost,int l)\n{\n\tif (c==l)\n\t{\n\t\tint p=m\/cost;\n\t\tif (l&1) ans+=pow2(p,n);\n\t\telse ans-=pow2(p,n);\n\t\treturn;\n\t}\n\tfor (int i=j+1;i<=tot+1-l+c;i++)\n\t\tdfs(i,c+1,cost*a[i],l);\n\n\n\n}\nint main()\n{\n\tscanf("%d%d",&n,&m);\n\tint m2=m;\n\tfor (int i=2;i<=(int)sqrt((double)m2);i++)\n\t\tif (0==m2%i)\n\t\t{\n\t\t\ta[++tot]=i;\n\t\t\twhile (0==m2%i) m2\/=i;\n\t\t}\n\tif (m2^1) a[++tot]=m2;\n\/\/\tfor (int i=1;i<=tot;i++) cout<<a[i]<<' ';\n\tfor (int i=1;i<=tot;i++) dfs(0,0,1,i);\n\/\/\tans=pow(m,n)-ans;\n\tprintf("%lldn",(long long)pow2(m,n)-ans);\n\n\n\treturn 0;\n}<\/pre>\n<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
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