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  1. #include "bits/stdc++.h"
  2.  
  3. #define int long long
  4. using namespace std;
  5. const int N = 1e5 + 5, mod = 1e9 + 7;
  6. typedef complex<double> point;
  7. #define INF 1e18
  8. #define ld long double
  9. #define eps 1e-4
  10. #define PI acos(-1)
  11. #define X real()
  12. #define Y imag()
  13. #define polar(r, t)          ((r)*exp(point(0,(t))))
  14. #define angle(a)            (atan2l((a).Y,(a).X))
  15. #define vec(a, b)           ((b)-(a))
  16. #define length(a)           (hypot((a).Y,(a).X))
  17. #define normalize(a)        ((a)/length(a))
  18. #define dp(a, b)          ((conj(a)*(b)).X)
  19. #define cp(a, b)            ((conj(a)*(b)).Y)
  20. #define length2(a)          (dot(a,a))
  21. #define rotate0(a, ang)     (polar(a,ang))
  22. #define rotateA(a, ang, A)  (rotate0(vec(A,a),ang)+(A))
  23. #define reflect(v, m)       (conj((v)/(m))*(m))
  24.  
  25. int dcmp(ld a, ld b) {
  26.     if (fabs(a - b) <= eps)return 0;
  27.  
  28.     return a < b ? -1 : 1;
  29. }
  30.  
  31.  
  32. double fixAngle(double A) {
  33.     return A > 1 ? 1 : (A < -1 ? -1 : A);
  34. }
  35.  
  36. double getAngle_A_abc(double a, double b, double c) {
  37.     return acos(fixAngle((b * b + c * c - a * a) / (2 * b * c)));
  38. }
  39.  
  40. // norm(a)  // return x^2 + y^2 //a is point //can use dp(a,a)
  41. bool same(point p1, point p2) {// check to points same or not
  42.     return dp(vec(p1, p2), vec(p1, p2)) < eps;
  43. }
  44.  
  45. vector<point> intersectCircleCircle(point c1, double r1, point c2, double r2) {
  46.     // Handle infinity case first: same center/radius and r > 0
  47.     if (same(c1, c2) && dcmp(r1, r2) == 0 && dcmp(r1, 0) > 0)
  48.         return vector<point>(3, c1);    // infinity 2 same circles (not points)
  49.  
  50.     // Compute 2 intersection case and handle 0, 1, 2 cases
  51.     double ang1 = angle(vec(c1, c2)), ang2 = getAngle_A_abc(r2, r1, length(vec(c1, c2)));
  52.     if (::isnan(ang2)) ang2 = 0; // if r1 or d = 0 => nan in getAngle_A_abc (/0)
  53.  
  54.     vector<point> v(1, polar(r1, ang1 + ang2) + c1);
  55.     // if point NOT on the 2 circles = no intersection
  56.     if (dcmp(dp(vec(c1, v[0]), vec(c1, v[0])), r1 * r1) != 0 ||
  57.         dcmp(dp(vec(c2, v[0]), vec(c2, v[0])), r2 * r2) != 0)
  58.         return vector<point>();
  59.     v.push_back(polar(r1, ang1 - ang2) + c1);
  60.     if (same(v[0], v[1]))  // if same, then 1 intersection only
  61.         v.pop_back();
  62.     return v;
  63. }
  64.  
  65. ld circleCircleIntersectionArea(point cen1, ld r1, point cen2, ld r2) {
  66.     ld dis = hypot(cen1.X - cen2.X, cen1.Y - cen2.Y);
  67.     if (dis > r1 + r2)return 0;
  68.     if (dis <= fabs(r2 - r1) && r1 >= r2)
  69.         return PI * r2 * r2;
  70.     if (dis <= fabs(r2 - r1) && r1 < r2)
  71.         return PI * r1 * r1;
  72.     ld a = r1 * r1, b = r2 * r2;
  73.     ld ang1 = acos((a + dis * dis - b) / (2 * r1 * dis)) * 2;
  74.     ld ang2 = acos((b + dis * dis - a) / (2 * r2 * dis)) * 2;
  75.     ld ret1 = .5 * b * (ang2 - sin(ang2));
  76.     ld ret2 = .5 * a * (ang1 - sin(ang1));
  77.     return ret1 + ret2;
  78. }
  79.  
  80. signed main() {
  81.     ios_base::sync_with_stdio(false);
  82.     cin.tie(nullptr);
  83.     cout.tie(nullptr);
  84.     ld x1, y1, x2, y2, r1, r2;
  85.     cin >> x1 >> y1 >> r1 >> x2 >> y2 >> r2;
  86.     point a(x1, y1), b(x2, y2);
  87.     auto v = intersectCircleCircle(a, r1, b, r2);
  88.     if (v.size() == 3 || v.empty() || dcmp(circleCircleIntersectionArea(a, r1, b, r2),0) == 0) {
  89.         cout << -1;
  90.         return 0;
  91.     }
  92.     int x = r1, y = r2;
  93.     if (v.size() == 1) {
  94.         if (norm(a - b) == (x + y) * (x + y)) {
  95.             cout << -1;
  96.             return 0;
  97.         }
  98.         ld R = max(r1, r2);
  99.         ld area = R * R * PI - circleCircleIntersectionArea(a, r1, b, r2);
  100.         cout << fixed << setprecision(8) << area;
  101.         return 0;
  102.     }
  103.     ld area = circleCircleIntersectionArea(a, r1, b, r2);
  104.     ld ans = r1 * r1 * PI;
  105.     ans = max(ans, r2 * r2 * PI);
  106.     cout << fixed << setprecision(8) << ans - area;
  107.     return 0;
  108. }
Success #stdin #stdout 0s 5284KB
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https://ideone.com/yfMRGD
language:
C++14 (gcc 8.3)
created:
49 days ago
visibility:
public

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