HDU 3400 Line belt （三分法）

Line belt

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1820    Accepted Submission(s): 683

Problem Description

In a two-dimensional plane there are two line belts, there are two segments AB and CD, lxhgww's speed on AB is P and on CD is Q, he can move with the speed R on other area on the plane.
How long must he take to travel from A to D?

 

 

Input

The first line is the case number T.
For each case, there are three lines.
The first line, four integers, the coordinates of A and B: Ax Ay Bx By.
The second line , four integers, the coordinates of C and D:Cx Cy Dx Dy.
The third line, three integers, P Q R.
0<= Ax，Ay，Bx，By，Cx，Cy，Dx，Dy<=1000
1<=P，Q，R<=10

 

 

Output

The minimum time to travel from A to D, round to two decimals.

 

 

Sample Input

1 0 0 0 100 100 0 100 100 2 2 1

 

 

Sample Output

136.60

 

 

Author

lxhgww&&momodi

 

 

Source

HDOJ Monthly Contest – 2010.05.01

 

 

Recommend

lcy

 

 

 

神奇的三分法。

就是利用凸性。

#include<stdio.h>

#include<iostream>

#include<math.h>

#include<iostream>

#include<algorithm>

#include<string.h>

using namespace std;

const double eps=1e-5;

struct point

{

    double x,y;

};

double dis(point a,point b)

{

    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));

}



double p,q,r;



double find2(point a,point c,point d)

{

    point left,right;

    point mid,midmid;

    double t1,t2;

    left=c;right=d;

    do

    {

        mid.x=(left.x+right.x)/2;

        mid.y=(left.y+right.y)/2;

        midmid.x=(mid.x+right.x)/2;

        midmid.y=(mid.y+right.y)/2;

        t1=dis(a,mid)/r+dis(mid,d)/q;

        t2=dis(a,midmid)/r+dis(midmid,d)/q;

        if(t1>t2)left=mid;

        else right=midmid;

    }

    while(dis(left,right)>=eps);

    return t1;

}

double find(point a,point b,point c,point d)

{

    point left,right;

    point mid,midmid;

    double t1,t2;

    left=a;

    right=b;

    do

    {

        mid.x=(left.x+right.x)/2;

        mid.y=(left.y+right.y)/2;

        midmid.x=(mid.x+right.x)/2;

        midmid.y=(mid.y+right.y)/2;

        t1=dis(a,mid)/p+find2(mid,c,d);

        t2=dis(a,midmid)/p+find2(midmid,c,d);

        if(t1>t2)left=mid;

        else right=midmid;

    }while(dis(right,left)>=eps);

    return t1;

}

int main()

{

    int T;

    point a,b,c,d;

    scanf("%d",&T);

    while(T--)

    {

        scanf("%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y);

        scanf("%lf%lf%lf%lf",&c.x,&c.y,&d.x,&d.y);

        scanf("%lf%lf%lf",&p,&q,&r);

        printf("%.2lf\n",find(a,b,c,d));

    }

    return 0;

}