UVA 3905 计算几何<扫描法> <求一条线与矩形的交>

最新推荐文章于 2021-03-08 18:00:06 发布

点羽染墨

最新推荐文章于 2021-03-08 18:00:06 发布

阅读量480

点赞数

CC 4.0 BY-SA版权

本文链接：https://blog.youkuaiyun.com/qq_24667639/article/details/42172867

本文介绍了一个基于流星轨迹预测最大观测数目的算法。该算法通过计算流星进入和离开望远镜视野的时间来确定最佳观测时刻。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <climits>
#include <cstdlib>
#include <ctime>
using namespace std;
const int maxn = 100000 + 10;

struct event
{
	double x;
	int type;
	bool operator < (const event& a )const
	{
		return x < a.x || (x == a.x && type > a.type);
	}
}events[maxn*2];
void fun(int x,int a,int w,double& l,double& r)//求流星的在矩形里的时间。分别带入x和y这样求得两个区间的交集
{
	if(a == 0)
	{
		if(x <= 0 || x >= w) r = l - 1;
	}
	else if(a > 0) 
	{
		l = max(l,-(double) x / a);
		r = min(r,(double)(w - x)/a);
	}
	else 
	{
		l = max(l,(double)(w-x) / a);
		r = min(r,-(double)x / a);
	}
}
	
int main()
{
	int t;
	cin >> t;
	while(t--)
	{
		int w,h,n,e = 0;
		scanf("%d%d%d",&w,&h,&n);
		for(int i = 0; i < n; i++)
		{
			int x,y,vx,vy;
			scanf("%d%d%d%d",&x,&y,&vx,&vy);
			double l = 0, r = 1e9;
			fun(x,vx,w,l,r);
			fun(y,vy,h,l,r);
			if(r > l)
			{
				events[e++] = (event){l,0};
				events[e++] = (event){r,1};
			}
		}
		sort(events,events+e);
		int cnt = 0,ans = 0;//排序后扫描扫描的格点就是每一区间的开始和结尾
		for(int i = 0; i < e; i++)
		{
			if(events[i].type == 0) ans = max(ans,++cnt);
			else cnt --;

		}
		printf("%d\n",ans);
	}
	return 0;
}

UVALive - 3905

Meteor

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Submit Status

Description

The famous Korean internet company nhn has provided an internet-based photo service which allows The famous Korean internet company users to directly take a photo of an astronomical phenomenon in space by controlling a high-performance telescope owned by nhn. A few days later, a meteoric shower, known as the biggest one in this century, is expected. nhn has announced a photo competition which awards the user who takes a photo containing as many meteors as possible by using the photo service. For this competition, nhn provides the information on the trajectories of the meteors at their web page in advance. The best way to win is to compute the moment (the time) at which the telescope can catch the maximum number of meteors.

You have n meteors, each moving in uniform linear motion; the meteor m_i moves along the trajectory p_i + t×v_i over time t , where t is a non-negative real value, p_i is the starting point of m_i and v_i is the velocity ofm_i . The point p_i = (x_i, y_i) is represented by X -coordinate x_i and Y -coordinate y_i in the (X, Y) -plane, and the velocity v_i = (a_i, b_i) is a non-zero vector with two components a_i and b_i in the (X, Y) -plane. For example, if p_i = (1, 3) and v_i = (-2, 5) , then the meteor m_i will be at the position (0, 5.5) at time t = 0.5 because p_i + t×v_i = (1, 3) + 0.5×(-2, 5) = (0, 5.5) . The telescope has a rectangular frame with the lower-left corner (0, 0) and the upper-right corner (w, h) . Refer to Figure 1. A meteor is said to be in the telescope frame if the meteor is in the interior of the frame (not on the boundary of the frame). For exam! ple, in Figure 1, p₂, p₃, p₄, and p₅ cannot be taken by the telescope at any time because they do not pass the interior of the frame at all. You need to compute a time at which the number of meteors in the frame of the telescope is maximized, and then output the maximum number of meteors.

$\epsfbox{p3905.eps}$

Input

Your program is to read the input from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with a line containing two integers wand h(1 $\le$ w, h $\le$ 100, 000) , the width and height of the telescope frame, which are separated by single space. The second line contains an integer n , the number of input points (meteors), 1 $\le$ n $\le$ 100, 000 . Each of the next n lines contain four integers x_i, y_i, a_i , and b_i ; (x_i, y_i) is the starting point p_i and (a_i, b_i) is the nonzero velocity vector v_i of the i -th meteor; x_i and y_i are integer values between -200,000 and 200,000, and a_iand b_i are integer values between -10 and 10. Note that at least one of a_i and b_i is not zero. These four values are separated by single spaces. We assume that all starting points p_i are distinct.

Output

Your program is to write to standard output. Print the maximum number of meteors which can be in the telescope frame at some moment.

Sample Input

Sample Output

1 
2

FAQ | About Virtual Judge | Forum | Discuss | Open Source Project
All Copyright Reserved ©2010-2014 HUST ACM/ICPC TEAM
Anything about the OJ, please ask in the forum, or contact author: Isun
Server Time: