Codeforces 793C Mice Problem 几何(模拟)
2017-06-01 12:33
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题意:n个点(x,y),速度(vx,vy),n<=1e5,问n个点第一次同时落在矩形内时间?
某个点落在矩形内的时间t为:x1<=x+t1*vx<=x2,(x1-x)/vx<=t1<=(x2-x)/vx,y1<=y+t2*vy<=y2 (y1-y)/vy<=t2<=(y2-y)/vy
max(t1,t2)<=t<=min(t1,t2) 每个点落在矩形内的时间看成一条线段,则求n条线段公共部分的左端点即可
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> ii;
const int N=1e3+20;
const int inf=2e8;
const double eps=1e-11;
int n;
int main()
{
double x1,y1,x2,y2;
double x,y,vx,vy;
double L=0,R=1e9;
while(cin>>n)
{
bool flag=true;
scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
for(int i=0;i<n;i++)
{
double lx,rx,ly,ry,l,r;
scanf("%lf%lf%lf%lf",&x,&y,&vx,&vy);
if(vx==0)
lx=0,rx=(x>x1&&x<x2)?inf:-1;
else
{
lx=(x1-x)/vx,rx=(x2-x)/vx;
if(vx<0)
swap(lx,rx);
}
if(vy==0)
ly=0,ry=(y>y1&&y<y2)?inf:-1;
else
{
ly=(y1-y)/vy,ry=(y2-y)/vy;
if(vy<0)
swap(ly,ry);
}
if(ly>ry||lx>rx)
flag=false;//
else
{
l=max(lx,ly);
r=min(rx,ry);
//l<=t<=r
L=max(l,L);
R=min(r,R);
}
if(L>R)
flag=false;
}
if(R-L>=eps&&flag)
printf("%.10lf\n",L);
else
puts("-1");
}
return 0;
}
题意:n个点(x,y),速度(vx,vy),n<=1e5,问n个点第一次同时落在矩形内时间?
某个点落在矩形内的时间t为:x1<=x+t1*vx<=x2,(x1-x)/vx<=t1<=(x2-x)/vx,y1<=y+t2*vy<=y2 (y1-y)/vy<=t2<=(y2-y)/vy
max(t1,t2)<=t<=min(t1,t2) 每个点落在矩形内的时间看成一条线段,则求n条线段公共部分的左端点即可
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> ii;
const int N=1e3+20;
const int inf=2e8;
const double eps=1e-11;
int n;
int main()
{
double x1,y1,x2,y2;
double x,y,vx,vy;
double L=0,R=1e9;
while(cin>>n)
{
bool flag=true;
scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
for(int i=0;i<n;i++)
{
double lx,rx,ly,ry,l,r;
scanf("%lf%lf%lf%lf",&x,&y,&vx,&vy);
if(vx==0)
lx=0,rx=(x>x1&&x<x2)?inf:-1;
else
{
lx=(x1-x)/vx,rx=(x2-x)/vx;
if(vx<0)
swap(lx,rx);
}
if(vy==0)
ly=0,ry=(y>y1&&y<y2)?inf:-1;
else
{
ly=(y1-y)/vy,ry=(y2-y)/vy;
if(vy<0)
swap(ly,ry);
}
if(ly>ry||lx>rx)
flag=false;//
else
{
l=max(lx,ly);
r=min(rx,ry);
//l<=t<=r
L=max(l,L);
R=min(r,R);
}
if(L>R)
flag=false;
}
if(R-L>=eps&&flag)
printf("%.10lf\n",L);
else
puts("-1");
}
return 0;
}
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