题目大意:求 \[\sum\limits_{i=2}^n\phi(i)\] 题解:利用与埃筛类似的操作,可在 \(O(nlogn)\) 时间求出结果. 代码如下 #include <cstdio> using namespace std; const int maxn=3010; int kase,n,phi[maxn]; int main(){ int T;scanf("%d",&T); while(T--){ scanf("%d",&…

[题目链接] http://poj.org/problem?id=3090 [算法] 通过观察发现,在这个平面直角坐标系中,除了(1,1),(1,0)和(0,1),所有可见点的横纵坐标互质 那么,问题就转化为了求 2 * (phi(1) + phi(2) + ... + phi(n)) + 3 预处理phi的前缀和,O(1)回答询问,即可 [代码] #include <algorithm> #include <bitset> #include <cctype> #inc…

题意:问从(0,0)到(x,y)(0≤x, y≤N)的线段没有与其他整数点相交的点数. 解法:只有 gcd(x,y)=1 时才满足条件,问 N 以前所有的合法点的和,就发现和上一题-- [poj 2478]Farey Sequence(数论--欧拉函数 找规律求前缀和) 求 x/y,gcd(x,y)=1 且 x<y 很像.   而由于这里 x可等于或大于y,于是就求 欧拉函数的前缀和*2+边缘2个点+对角线1个点. 1 #include<cstdio> 2 #include<cst…

http://poj.org/problem?id=3090 题目大意:你站在(0,0)的点上看向第一向限的点,点和点会互相阻挡,问最多看到多少点. 很容易想到,我们能看到的点,它的横纵坐标一定是互质的,那么怎么求呢? 首先我们要知道一个东西叫做法雷级数: F1:0/1 1/1 F2:0/1 1/2 1/1 F3:0/1 1/3 1/2 2/3 1/1 F4:0/1 1/4 1/3 1/2 2/3 3/4 1/1 F5:0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/…

Visible Lattice Points Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 7705   Accepted: 4707 Description A lattice point (x, y) in the first quadrant (x and y are integers greater than or equal to 0), other than the origin, is visible fr…

Visible Lattice Points 题目链接(点击) Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 9031   Accepted: 5490 Description A lattice point (x, y) in the first quadrant (x and y are integers greater than or equal to 0), other than the origin, is v…

/* * POJ3090 Visible Lattice Points * 欧拉函数 */ #include<cstdio> using namespace std; int C,N; //欧拉函数模板 int Euler(int n) { int num = n; for(int i = 2;i <= n;i++) { if(n % i == 0) { num = num / i * (i-1); } while(n % i == 0) { n /= i; } } return num…

Visible Lattice Points Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 5636   Accepted: 3317 Description A lattice point (x, y) in the first quadrant (x and y are integers greater than or equal to 0), other than the origin, is visible fr…

SPOJ Problem Set (classical) 7001. Visible Lattice Points Problem code: VLATTICE Consider a N*N*N lattice. One corner is at (0,0,0) and the opposite one is at (N,N,N). How many lattice points are visible from corner at (0,0,0) ? A point X is visible…

http://poj.org/problem?id=3090 Visible Lattice Points Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 6153   Accepted: 3662 Description A lattice point (x, y) in the first quadrant (x and y are integers greater than or equal to 0), other…