【POJ2242】The Circumference of the Circle（初等几何）

已知三点坐标，算圆面积。

使用初等几何知识，根据海伦公式s = sqrt(p(p - a)(p - b)(p - c)) 和 外接圆直径 d = a * b * c / (2s) 来直接计算。

 

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdlib>

 4 #include <cstdio>

 5 #include <numeric>

 6 #include <cctype>

 7 #include <cmath>

 8 #include <algorithm>

 9 

10 #define PI acos(-1)

11 using namespace std;

12 

13 double calc_dis (double x1, double y1, double x2, double y2) {

14     return sqrt ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));

15 }

16 

17 int main () {

18     ios :: sync_with_stdio(false);

19     double x[3], y[3];

20     while (cin >> x[0] >> y[0]) {

21         for (int i = 1; i < 3; ++ i) {

22             cin >> x[i] >> y[i];

23         }

24         double a, b, c;

25         a = calc_dis (x[0], y[0], x[1], y[1]);

26         b = calc_dis (x[0], y[0], x[2], y[2]);

27         c = calc_dis (x[2], y[2], x[1], y[1]);

28         //cout << a << " " << b << " " << c << endl;

29         double p = (a + b + c) / 2;

30         double s = sqrt (p * (p - a) * (p - b) * (p - c));

31         //cout << "s : " << s << endl;

32         double d = a * b * c / (2 * s);

33         printf ("%.2f\n", PI * d);

34     }

35     return 0;

36 }