先放知识点: 莫比乌斯反演 卢卡斯定理求组合数 乘法逆元 快速幂取模 GCD of Sequence Alice is playing a game with Bob. Alice shows N integers a 1, a 2, -, a N, and M, K. She says each integers 1 ≤ a i ≤ M. And now Alice wants to ask for each d = 1 to M, how many different sequences b…

GCD of Sequence Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)Total Submission(s): 46    Accepted Submission(s): 14 Problem Description Alice is playing a game with Bob.Alice shows N integers a1, a2, …, aN, and M,…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=4675 题意:给出n,m,K,一个长度为n的数列A(1<=A[i]<=m).对于d(1<=d<=m),有多少个长度为n的数列B满足: (1)1<=B[i]<=m; (2)Gcd(B[1],B[2],……,B[n])=d: (3)恰有K个位置满足A[i]!=B[i]. 思路: i64 p[N]; void init(){    p[0]=1;    int i;    FOR1…

题意:给出序列[a1..aN],整数M和k,求对1-M中的每个整数d,构建新的序列[b1...bN],使其满足: 1. \(1 \le bi \le M\) 2. \(gcd(b 1, b 2, -, b N) = d\) 3. 恰好有k个位置 \(bi!=ai\) 求对每个d,有多少种满足条件的序列 分析:对于前两个条件,就是单纯的莫比乌斯反演. 令\(F(d) = [d|gcd(b1...bN)]\) \(f(d) = [gcd(b1...bN)]=d]\) 则$f(n) = \sum_{x…

题意: 给出\(M\)和\(a数组\),询问每一个\(d\in[1,M]\),有多少组数组满足:正好修改\(k\)个\(a\)数组里的数使得和原来不同,并且要\(\leq M\),并且\(gcd(a_1,a_2,\dots,a_n)=d\). 思路: 对于每一个\(d\),即求\(f(d)\):修改\(k\)个后\(gcd(a_1,a_2,\dots,a_n)=d\)的对数. 那么假设\(F(d)\):修改\(k\)个后\(gcd(a_1,a_2,\dots,a_n)\)是\(d\)倍数的对数.…

数学题! 从M到1计算,在计算i的时候,算出原序列是i的倍数的个数cnt: 也就是将cnt个数中的cnt-(n-k)个数变掉,n-cnt个数变为i的倍数. 且i的倍数为t=m/i; 则符合的数为:c[cnt][n-k]*t^(n-cnt)*(t-1)*(cnt-(n-k)). 这样得到的是所有i的倍数,还要减去2*i,3*i…… 代码如下: #include<stdio.h> #include<cstring> #define M 1000000007 #define MM 300…

 HDU 5288 OO’s Sequence http://acm.hdu.edu.cn/showproblem.php?pid=5288 OO has got a array A of size n ,defined a function f(l,r) represent the number of i (l<=i<=r) , that there’s no j(l<=j<=r,j<>i) satisfy a i mod a j=0,now OO want to k…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=4675 题意:给一个大小为N的数列a[i],然后一个数M以及一个数K,要你求得一个数列b[i],其中b[i]有K个数与a[i]中的不相同,使得gcd(b[i])=j.对于每个 j ,求出满足的b[i]的个数.. 首先我们统计数列a[i]每个数的个数,假设现在求gcd(b[i])=j,那么可以在t=M/j的时间内求出 j 的倍数的个数cnt.那么就相当于在cnt个中选择N-K个不变C(cnt,N-K),…

GCD is Funny 题目连接: http://acm.hdu.edu.cn/showproblem.php?pid=5902 Description Alex has invented a new game for fun. There are n integers at a board and he performs the following moves repeatedly: He chooses three numbers a, b and c written at the boa…

GCD and LCM Time Limit: 20 Sec Memory Limit: 256 MB 题目连接 http://acm.hdu.edu.cn/showproblem.php?pid=4497 Description Given two positive integers G and L, could you tell me how many solutions of (x, y, z) there are, satisfying that gcd(x, y, z) = G and…