山东省第四届ACM程序设计大赛 Problem A:Rescue The Princess (计算几何)

Problem A:Rescue The Princess

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 153  Solved: 66

[Submit][Status][Discuss]

Description

Several days ago, a beast caught a beautiful princess and the princess was put in prison. To rescue the princess, a prince who wanted to marry  the princess set out immediately. Yet,
the beast set a maze. Only if the prince find out the maze’s exit can he save the princess.
Now, here comes the problem. The maze is a dimensional plane. The beast is smart, and he hidden the princess snugly. He marked two coordinates
of an equilateral triangle in the maze. The two marked coordinates are A(x1,y1) and B(x2,y2). The third coordinate C(x3,y3) is the maze’s exit. If the prince can find out the exit, he can save the princess. After the prince comes into the maze, he finds out
the A(x1,y1) and B(x2,y2), but he doesn’t know where the C(x3,y3) is. The prince need your help. Can you calculate the C(x3,y3) and tell him?

Input

The first line is an integer T(1 <= T <= 100) which is the number of test cases. T test cases follow. Each test case contains two coordinates A(x1,y1) and B(x2,y2), described by four
floating-point numbers x1, y1, x2, y2 ( |x1|, |y1|, |x2|, |y2| <= 1000.0). 
        Please notice that A(x1,y1) and B(x2,y2) and C(x3,y3) are in an anticlockwise direction from the equilateral triangle. And coordinates A(x1,y1) and B(x2,y2) are given by
anticlockwise.

Output

For each test case, you should output the coordinate of C(x3,y3), the result should be rounded to 2 decimal places in a line.

Sample Input

4
-100.00 0.00 0.00 0.00
0.00 0.00 0.00 100.00
0.00 0.00 100.00 100.00
1.00 0.00 1.866 0.50

Sample Output

(-50.00,86.60)
(-86.60,50.00)
(-36.60,136.60)
(1.00,1.00)

HINT

Source

山东省第四届ACM程序设计大赛2013.6.9

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 153  Solved: 66

[Submit][Status][Discuss]

Description

Several days ago, a beast caught a beautiful princess and the princess was put in prison. To rescue the princess, a prince who wanted to marry  the princess set out immediately. Yet,
the beast set a maze. Only if the prince find out the maze’s exit can he save the princess.
Now, here comes the problem. The maze is a dimensional plane. The beast is smart, and he hidden the princess snugly. He marked two coordinates
of an equilateral triangle in the maze. The two marked coordinates are A(x1,y1) and B(x2,y2). The third coordinate C(x3,y3) is the maze’s exit. If the prince can find out the exit, he can save the princess. After the prince comes into the maze, he finds out
the A(x1,y1) and B(x2,y2), but he doesn’t know where the C(x3,y3) is. The prince need your help. Can you calculate the C(x3,y3) and tell him?

Input

The first line is an integer T(1 <= T <= 100) which is the number of test cases. T test cases follow. Each test case contains two coordinates A(x1,y1) and B(x2,y2), described by four
floating-point numbers x1, y1, x2, y2 ( |x1|, |y1|, |x2|, |y2| <= 1000.0). 
        Please notice that A(x1,y1) and B(x2,y2) and C(x3,y3) are in an anticlockwise direction from the equilateral triangle. And coordinates A(x1,y1) and B(x2,y2) are given by
anticlockwise.

Output

For each test case, you should output the coordinate of C(x3,y3), the result should be rounded to 2 decimal places in a line.

Sample Input

4
-100.00 0.00 0.00 0.00
0.00 0.00 0.00 100.00
0.00 0.00 100.00 100.00
1.00 0.00 1.866 0.50

Sample Output

(-50.00,86.60)
(-86.60,50.00)
(-36.60,136.60)
(1.00,1.00)

HINT

Source

山东省第四届ACM程序设计大赛2013.6.9

求夹角。 double a_a=atan2(b.y-a.y,b.x-a.x);
求边长  double l=sqrt((b.y-a.y)*(b.y-a.y)+(b.x-a.x)*(b.x-a.x));#include<stdio.h>
#include<string.h>
#include<math.h>
#define pi acos(-1.0)
#include<algorithm>
using namespace std;
struct{
double x,y;
}a,b,c;
int main()
{
int T;
scanf("%d",&T);
while(T--)
{
scanf("%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y);
double a_a=atan2(b.y-a.y,b.x-a.x);
double l=sqrt((b.y-a.y)*(b.y-a.y)+(b.x-a.x)*(b.x-a.x));
c.x=a.x+l*cos((1.0/3)*pi+a_a);
c.y=a.y+l*sin((1.0/3)*pi+a_a);
printf("(%.2f,%.2f)\n",c.x,c.y);
}
}