POJ 3304 Segments (直线和线段相交判断)

时间:2021-03-24 18:32:57
Segments
Time Limit: 1000MS   Memory Limit: 65536K
Total Submissions: 7739   Accepted: 2316

Description

Given n segments in the two dimensional space, write a program, which determines if there exists a line such that after projecting these segments on it, all projected segments have at least one point in common.

Input

Input begins with a number T showing the number of test cases and then, T test cases follow. Each test case begins with a line containing a positive integer n ≤ 100 showing the number of segments. After that, n lines containing four real numbers x1y1x2y2 follow, in which (x1, y1) and (x2, y2) are the coordinates of the two endpoints for one of the segments.

Output

For each test case, your program must output "Yes!", if a line with desired property exists and must output "No!" otherwise. You must assume that two floating point numbers a and b are equal if |a - b| < 10-8.

Sample Input

3
2
1.0 2.0 3.0 4.0
4.0 5.0 6.0 7.0
3
0.0 0.0 0.0 1.0
0.0 1.0 0.0 2.0
1.0 1.0 2.0 1.0
3
0.0 0.0 0.0 1.0
0.0 2.0 0.0 3.0
1.0 1.0 2.0 1.0

Sample Output

Yes!
Yes!
No!

Source

 
 
题目大意:给出n条线段两个端点的坐标,问所有线段投影到一条直线上,如果这些所有投影至少相交于一点就输出Yes!,否则输出No!。
解题思路:如果有存在这样的直线,过投影相交区域作直线的垂线,该垂线必定与每条线段相交,问题转化为问是否存在一条线和所有线段相交
 
直线肯定经过两个端点。
枚举端点,判断直线和线段是否相交。
 
细节要注意,判断重合点。
 
还有就是加入只有一条线段的话,刚好直线是过同一条直线的。
所以保险的做法是枚举所有的两个端点,包括同一条直线的。
 
/************************************************************
* Author : kuangbin
* Email : kuangbin2009@126.com
* Last modified : 2013-07-13 20:57
* Filename : POJ3304Segments.cpp
* Description :
* *********************************************************/ #include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#include <map>
#include <vector>
#include <set>
#include <string>
#include <math.h> using namespace std; const double eps = 1e-;
int sgn(double x)
{
if(fabs(x) < eps)return ;
if(x < ) return -;
return ;
}
struct Point
{
double x,y;
Point(){}
Point(double _x,double _y)
{
x = _x;y = _y;
}
Point operator -(const Point &b)const
{
return Point(x - b.x,y - b.y);
}
double operator ^(const Point &b)const
{
return x*b.y - y*b.x;
}
double operator *(const Point &b)const
{
return x*b.x + y*b.y;
}
};
struct Line
{
Point s,e;
Line(){}
Line(Point _s,Point _e)
{
s = _s;e = _e;
}
};
double xmult(Point p0,Point p1,Point p2) //p0p1 X p0p2
{
return (p1-p0)^(p2-p0);
}
bool Seg_inter_line(Line l1,Line l2) //判断直线l1和线段l2是否相交
{
return sgn(xmult(l2.s,l1.s,l1.e))*sgn(xmult(l2.e,l1.s,l1.e)) <= ;
}
double dist(Point a,Point b)
{
return sqrt( (b - a)*(b - a) );
}
const int MAXN = ;
Line line[MAXN];
bool check(Line l1,int n)
{
if(sgn(dist(l1.s,l1.e)) == )return false;
for(int i = ;i < n;i++)
if(Seg_inter_line(l1,line[i]) == false)
return false;
return true;
}
int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
int n;
int T;
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
double x1,y1,x2,y2;
for(int i = ; i < n;i++)
{
scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
line[i] = Line(Point(x1,y1),Point(x2,y2));
}
bool flag = false;
for(int i = ;i < n;i++)
for(int j = ; j < n;j++)
if(check(Line(line[i].s,line[j].s),n) || check(Line(line[i].s,line[j].e),n)
|| check(Line(line[i].e,line[j].s),n) || check(Line(line[i].e,line[j].e),n) )
{
flag = true;
break;
}
if(flag)
printf("Yes!\n");
else printf("No!\n");
}
return ;
}