2017 多校2 hdu 6053 TrickGCD 题目: You are given an array \(A\) , and Zhu wants to know there are how many different array \(B\) satisfy the following conditions? \(1≤B_i≤A_i\) For each pair(\(l , r) (1≤l≤r≤n) , gcd(bl,bl+1...br)≥2\) Input The first line…

/* HDU 6053 - TrickGCD [ 莫比乌斯函数,筛法分块 ] | 2017 Multi-University Training Contest 2 题意: 给出数列 A[N],问满足: 1 <= B[i] <= A[i] ; 对任意(l, r) (1<=l<=r<=n) ,使得 gcd(bl,...br) >= 2 ; 的 B[N] 数列的个数 分析: 设 gcd(b1,...bn) = k (k >= 2),此时 k 对答案的贡献为 (a1/k)…

Frogs Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 1315    Accepted Submission(s): 443 Problem Description There are m stones lying on a circle, and n frogs are jumping over them.The stones a…

给出n个数,给出m个询问,询问 区间[l,r] [u,v],在两个区间内分别取一个数,两个的和为k的对数数量. $k<=2*N$,$n <= 30000$ 发现可以容斥简化一个询问.一个询问的答案为 $[l,v]+(r,u)-[l,u)-(r,v]$,那么我们离线询问,将一个询问分成四个,分块暴力就行了. 然后就是注意细节,不要发生越界,访问错位置之类比较蠢的问题了. /** @Date : 2017-09-24 19:54:55 * @FileName: HDU 5213 分块 容斥.cpp…

求满足$1<=X<=N ,(X,N)>=M$的个数,其中$N, M (2<=N<=1000000000, 1<=M<=N)$. 首先,假定$(x, n)=m$,那么 $(\frac{x}{n},\frac{n}{m})=1$,故$$ans=\sum_{i=m}^{n}\varphi(\frac{n}{i})$$ ん?遅い! $$\sum_{i=m}^{n}\varphi(\frac{n}{i})=\sum\limits_{d|n}{\varphi(\frac{n}…

题意:给出n个数$a[i]$,每个数可以变成不大于它的数,现问所有数的gcd大于1的方案数.其中$(n,a[i]<=1e5)$ 思路:鉴于a[i]不大,可以想到枚举gcd的值.考虑一个$gcd(a_1,a_2,a_3…a_n)=d$,显然每个$a_i$的倍数都满足,有$\frac{a_i}{d}$种方案 那么一个d对答案的贡献为\[\prod_{i=1}^{min(a)}{\lfloor\frac{a_i}{d}\rfloor}    \] 但是所有的d计入会有重复情况,考虑容斥,对d进行素数分…

TrickGCD Time Limit: 5000/2500 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)Total Submission(s): 2649    Accepted Submission(s): 1007 Problem Description You are given an array A , and Zhu wants to know there are how many different…

TrickGCD Time Limit: 5000/2500 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)Total Submission(s): 3401    Accepted Submission(s): 1268 Problem Description You are given an array A , and Zhu wants to know there are how many different…

Online Judge:Hdu6053 Label:容斥,前缀和 题面: 题目描述 给你一个长度为\(N\)的序列A,现在让你构造一个长度同样为\(N\)的序列B,并满足如下条件,问有多少种方案数?答案对\(1e9+7\)取模. \(1≤Bi≤Ai\) 对于任意(l,r) \((1≤l≤r≤N)\),有\(gcd(b_l,b_{l+1}...b_r)>=2\) 输入 The first line is an integer T(1≤T≤10) describe the number of te…

[题目链接] http://acm.hdu.edu.cn/showproblem.php?pid=6053 [题目大意] 给出一个数列每个位置可以取到的最大值, 问这个可以构造多少个数列,使得他们的最大公约数大于1 [题解] 我们可以枚举最大公约数k,对于k来说, 他对答案的贡献为∏[ai/k],我们将数列中的数字转化为权值数组 ∏_{i=1}^{100000}[i/k],对于求解i/k的部分我们可以进行数值分块, j*k-1~j*k+k-1的数值除k得到的结果都是相同的,因此可以直接求这个结果…