Here is the link to the question:
Http://acm.zju.edu.cn/onlinejudge/showProblem.do? ProblemCode = 1090 the topic description is very simple. The coordinates of the three points are given, which are set to A (x1, y1), B (x2, y2), C (x3, y3 ), then obtain the circumference of the circle through these three points (retain two decimal places ). However, it is troublesome to deduce the formula. I did this. First, it is difficult to obtain the diameter of the circumference d = BC/sin a = AC/sin B = AB/sin c according to the same center angle of the same string; therefore, calculate the circumference = BC/sin (a) * PI; where BC is the side length of angle a = sqrt (x2-x3) ^ 2 + (y2-y3) ^ 2 ); as for sin (a), we must calculate by three coordinate, more troublesome, you can use the trigonometric formula: sin (a) = sin (a1-a2) = sin (a1) cos (a2)-cos (a1) sin (a2). a1 and a2 are the angle between the X-ray AC and the X-ray AB respectively. If B, cpoints are all in the First quadrant, apparently there is sin (a1) = (y3-y1)/AC; cos (a1) = (x3-x1)/AC; sin (a2) = (x2-x1)/AB; cos (a2) = (y2-y1)/AB; simplified formula: Perimeter = BC/sin (a) * PI = (AC * AB * BC) /(y3-y1) (x2-x1)-(x3-x1) (y2-y1) * PI; so we can write The following code (in c): the Circumference of The Circle
# Include <stdio. h>
# Include <math. h>
# Define PI 3.141592653589793
# Define DISTANCE (x1, y1, x2, y2) sqrt (x2)-(x1) * (x2)-(x1) + (y2) -(y1) * (y2)-(y1 )))
Void main ()
{
Double x1, x2, x3, y1, y2, y3;
Double d12, d23, d31, k, result;
While (scanf ("% lf", & x1, & y1, & x2, & y2, & x3, & y3 )! = EOF)
{
D12 = DISTANCE (x1, y1, x2, y2 );
D23 = DISTANCE (x2, y2, x3, y3 );
D31 = DISTANCE (x3, y3, x1, y1 );
K = fabs (y3-y1) * (x2-x1)-(x3-x1) * (y2-y1 ));
Result = d12 * d23 * d31/k * PI;
Printf ("%. 2lf \ n", result );
}
}
There are only 18 lines of code and one-time smooth AC, and I found that my solution was ranked first among all solutions.
| AC |
WA |
PE |
FPE |
SF |
TLE |
MLE |
CE |
Total |
| 1926 (54%) |
864 (24%) |
8 (0%) |
1 (0%) |
85 (2%) |
275 (7%) |
0 (0%) |
354 (10%) |
3517 |
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