White Bird

Angry Birds is a mobile game of a big craze all over the world. You were convinced that it was a waste of time to play the game, so you decided to create an automatic solver.

You are describing a routine that optimizes the white bird's strategy to defeat a pig (enemy) by hitting an egg bomb. The white bird follows a parabolic trajectory from the initial position, and it can vertically drop egg bombs on the way.

In order to make it easy to solve, the following conditions hold for the stages.

N obstacles are put on the stage.
Each obstacle is a rectangle whose sides are parallel to the coordinate axes.
The pig is put on the point (X,Y).
You can launch the white bird in any direction at an initial velocity V from the origin.
If the white bird collides with an obstacle, it becomes unable to drop egg bombs.
If the egg bomb collides with an obstacle, the egg bomb is vanished.

The acceleration of gravity is 9.8m⁄s2. Gravity exerts a force on the objects in the decreasing direction of y-coordinate.

Input

A dataset follows the format shown below:

N V X Y
L1 B1 R1 T1
…
LN BN RN TN

All inputs are integer.

N: the number of obstacles
V: the initial speed of the white bird
X, Y: the position of the pig

(0≤N≤50, 0≤V≤50, 0≤X,Y≤300, X≠0)

for 1≤i≤N,

Li: the x-coordinate of the left side of the i-th obstacle
Bi: the y-coordinate of the bottom side of the i-th obstacle
Ri: the x-coordinate of the right side of the i-th obstacle
Ti: the y-coordinate of the top side of the i-th obstacle

(0≤Li,Bi,Ri,Ti≤300)

It is guaranteed that the answer remains unaffected by a change of Li, Bi, Ri and Ti in 10−6.

Output

Yes/No

You should answer whether the white bird can drop an egg bomb toward the pig.

Sample Input 1

0 7 3 1

Output for the Sample Input 1

Yes

Sample Input 2

1 7 3 1
1 1 2 2

Output for the Sample Input 2

No

Sample Input 3

1 7 2 2
0 1 1 2

Output for the Sample Input 3

No

题意：给n个障碍物和一个猪的位置坐标一个初速度的小鸟，小鸟可以在飞行的过程中任意位置下一个蛋问蛋能否击中猪，小鸟撞到障碍物就会停下；

题解：我们分析不能被砸中的情况

当小鸟不能飞行到猪的上方在这之前就碰到障碍物了
当小鸟能飞到猪的正上方

小鸟向上飞行的过程中可以从一个障碍物的左上角飞过也可以从一个障碍物的右下角飞过对于每一种我们都考虑这个极限不断更改小鸟的发射角度然后枚举每一个在猪之前的障碍物判断其是否能击中

#include<bits/stdc++.h>
using namespace std;
#define clr(a,b) memset(a,b,sizeof(a))
#define rep(a,b) for(int a=0;a<b;a++)
#define pre(a,b) for(int a=b,a>0;a--)
const int maxn=1e8+7;
const int minn=100+7;
const double g=9.8;
const double eps=1e-10;
struct Barr
{
    int l,b,r,t;
} q[minn];
int n,v,ex,ey;
int cmp(Barr a,Barr b)
{
    if(a.l==b.l){return a.b<b.b;}
    return a.l<b.l;
}
//判断t秒后y的位置
double calc(double vy,double t)
{
    return vy*t-g*t*t/2;
}
int judge(double lb,double ub,double a)
{
    return a<lb+eps?-1:a>ub-eps?1:0;
}
int check(double qx,double qy)
{
    double a=g*g/4,b=g*qy-v*v,c=qx*qx+qy*qy;
    double D=b*b-4*a*c;
    if(D<0&&D>-eps)D=0;
    if(D<0)return 0;
    for(int d=-1;d<=1;d+=2){
        double t2=(-b+d*sqrt(D))/(2*a);
        if(t2<=0){continue;}
        double t=sqrt(t2);
        double vx=qx/t,vy=(qy+g*t*t/2)/t;
        double yt=calc(vy,ex/vx);
        if(yt<ey-eps){continue;}
        int ok=1;
        for(int i=0;i<n;i++)
        {
            if(q[i].l>=ex){break;}
            if(q[i].r==ex&&ey<=q[i].t&&q[i].b<=yt)ok=0;
            int yl=judge(q[i].b,q[i].t,calc(vy,q[i].l/vx));
            int yr=judge(q[i].b,q[i].t,calc(vy,q[i].r/vx));
            int xh=judge(q[i].l,q[i].r,vx*(vy/g));
            int yh=judge(q[i].b,q[i].t,calc(vy,vy/g));
            if(xh==0&&yh>=0&&yl<0)ok=0;
            if(yl*yr<=0)ok=0;
        }
        if(ok)return 1;
    }
    return 0;
}
void slove()
{
    sort(q,q+n,cmp);
    int ok=check(ex,ey);//直接撞上的情况
    for(int i=0;i<n;i++)
    {
        if(q[i].l>=ex){break;}
        ok|=check(q[i].l,q[i].t)|check(q[i].r,q[i].t);
    }
    puts(ok?"Yes":"No");
    return ;
}
int main()
{
    scanf("%d%d%d%d",&n,&v,&ex,&ey);
    rep(i,n)
    {
        scanf("%d%d%d%d",&q[i].l,&q[i].b,&q[i].r,&q[i].t);
        q[i].r=min(ex,q[i].r);
    }
    slove();
    return 0;
}

AOJ2308-White Bird