题目描述:
124. Broken line
time limit per test: 0.5 sec.
memory limit per test: 4096 KB
There is a closed broken line on a plane with sides parallel to coordinate axes, without self-crossings and self-contacts. The broken line consists of K segments. You have to determine, whether a given point with coordinates (X0,Y0) is inside this closed broken line, outside or belongs to the broken line.
Input
The first line contains integer K (4 Ј K Ј 10000) - the number of broken line segments. Each of the following N lines contains coordinates of the beginning and end points of the segments (4 integer xi1,yi1,xi2,yi2; all numbers in a range from -10000 up to 10000 inclusive). Number separate by a space. The segments are given in random order. Last line contains 2 integers X0 and Y0 - the coordinates of the given point delimited by a space. (Numbers X0, Y0 in a range from -10000 up to 10000 inclusive).
Output
The first line should contain:
INSIDE - if the point is inside closed broken line,
OUTSIDE - if the point is outside,
BORDER - if the point belongs to broken line.
Sample Input
4
0 0 0 3
3 3 3 0
0 3 3 3
3 0 0 0
2 2
Sample Output
INSIDE
一道比较简单的计算几何,就是求给定点是否在一个多边形内部,我们可以从这个点引出一条射线,计算其与所有边的交点,如果是奇数个,说明在内部,否则在外部。
那么我们取怎样的射线比较合适?
因为题目告诉我们边平行与坐标轴,我们可以取与Y正方向平行大致向左偏一点的射线,就可以避免其和平行于Y轴的边相交,这就是代码中 if(p[i].a.x<P.x&&p[i].b.x>=P.x)k++; 左边取小于号的原因。
附上AC代码:
#include<iostream>
#include<cstring>
#include<cstdio>
#include<set>
#include<algorithm>
#include<vector>
#include<cstdlib>
#define inf 0xfffffff
#define CLR(a,b) memset((a),(b),sizeof((a)))
#define FOR(a,b) for(int a=1;a<=(b);(a)++)
using namespace std;
int const nMax = 10010;
int const base = 10;
typedef int LL;
typedef pair<LL,LL> pij;
struct point{
int x,y;
bool operator <(const point& b)const {
if(x==b.x)return y<b.y;
else return x<b.x;
}
} P;
struct seg{
point a,b;
};
seg p[nMax];
int n;
int main(){
scanf("%d",&n);
for(int i=0;i<n;i++){
scanf("%d%d%d%d",&p[i].a.x,&p[i].a.y,&p[i].b.x,&p[i].b.y);
if(p[i].b<p[i].a)swap(p[i].a,p[i].b);
}
scanf("%d%d",&P.x,&P.y);
int k=0;
for(int i=0;i<n;i++){
if(p[i].a.x==p[i].b.x){
if(P.x==p[i].a.x&&P.y>=p[i].a.y&&P.y<=p[i].b.y){
printf("BORDER\n");
return 0;
}
}else {
if(p[i].a.y==P.y&&p[i].a.x<=P.x&&p[i].b.x>=P.x){
printf("BORDER\n");
return 0;
}
}
}
for(int i=0;i<n;i++){
if(p[i].a.y==p[i].b.y&&p[i].a.y>P.y){
if(p[i].a.x<P.x&&p[i].b.x>=P.x)k++;
}
}
if(k&1)printf("INSIDE\n");
else printf("OUTSIDE\n");
return 0;
}