POJ3090：Visible Lattice Points——题解

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POJ3090 Visible Lattice Points

/* * 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…

POJ3090：Visible Lattice Points——题解

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/…

ACM学习历程—POJ3090 Visible Lattice Points（容斥原理 || 莫比乌斯）

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 from the origin if the line from (0, 0) to (x, y) does not pass through any other lattice point. For example…

POJ3090 Visible Lattice Points 欧拉函数

欧拉函数裸题,直接欧拉函数值乘二加一就行了.具体证明略,反正很简单. 题干: 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 from the origin if the line from (0, 0) to (x, y) does not pass throu…

POJ3090 Visible Lattice Points （数论：欧拉函数模板）

题目链接:传送门思路: 所有gcd(x, y) = 1的数对都满足题意,然后还有(1, 0) 和 (0, 1). #include <iostream> #include <cstring> using namespace std; ; ], phi[MAX_N+]; void getPrime_and_Phi() { memset(prime, , sizeof prime); phi[] = ; ; i <= MAX_N; i++) { ]] = i, phi[i] =…

[POJ3090]Visible Lattice Points（欧拉函数）

答案为3+2*∑φ(i),(i=2 to n) Code #include <cstdio> int T,n,A[1010]; void Init(){ for(int i=2;i<=1000;++i)A[i]=i; for(int i=2;i<=1000;++i) if(A[i]==i)for(int j=i;j<=1000;j+=i) A[j]=A[j]/i*(i-1); for(int i=3;i<=1000;++i)A[i]+=A[i-1]; } int mai…

POJ3090 Visible Lattice Points 欧拉筛

题目大意:给出范围为(0, 0)到(n, n)的整点,你站在原点处,问有多少个整点可见. 线y=x和坐标轴上的点都被(1,0)(0,1)(1,1)挡住了.除这三个钉子外,如果一个点(x,y)不互质,则它就会被点(x0, y0) (x0,y0互质,x/x0==y/y0)挡住.能看见的钉子关于线y=x对称.所以,求出x=2至n的所有与x互质的数的个数φ(x)的和(也就是线y=x右下角(因为φ(x)<x)所有能看见的点的个数)乘以2(对角线两旁的看见的点的个数)+3(那几个特殊点)即为所求. 求φ值时…