# largest circle define _CRT_SECURE_NO_WARNI NGS include iostream includ

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116``` ```//largest circle// #define _CRT_SECURE_NO_WARNINGS #include #include #include #include #include #include #define ll long long #define eps 1e-8 #define all(x) x.begin(), x.end() #define Cout cout << fixed << setprecision(6) const double pi = acos(-1.0); using namespace std; int I1 = 38; int I2 = 38; struct v2 { double x, y; v2() {} v2(double _x, double _y) : x(_x), y(_y) {} v2 operator -(const v2 &a) const { return v2(x - a.x, y - a.y); } v2 operator +(const v2 &a) const { return v2(x + a.x, y + a.y); } v2 operator *(double a) const { return v2(a * x, a * y); } inline double sqlen() const { return x * x + y * y; } bool operator <(const v2 a) const { if (std::abs(x - a.x) < eps) return y < a.y; else return x < a.x; } }; double dot(const v2& a, const v2& b) { return a.x * b.x + a.y * b.y; } double cross(const v2& a, const v2& b) { return a.x * b.y - a.y * b.x; } double dist2(const v2&a, const v2& b) { return dot(a - b, a - b); } double w, h; vector g(4); double dist(const v2& a) { v2 p = g[0] + (g[3] - g[0]) * (a.x / w); v2 q = g[1] + (g[2] - g[1]) * (a.x / w); v2 b = p + (q - p) * (a.y / h); //Cout << b.x << " " << b.y << endl; //cout << endl; return dist2(a, b); } double f(double x) { double l = 0.0, r = h; for (int q = 0; q < 30; ++q) { double y1 = l + (r - l) / 3; double y2 = r - (r - l) / 3; //Cout << "ololo " << y1 << " " << y2 << endl << dist(v2(x, y1)) << " " << dist(v2(x, y2)) << endl << endl; if (dist(v2(x, y1)) > dist(v2(x, y2))) l = y1; else r = y2; } return dist(v2(x, l)); } double final_f(double x) { double l = 0.0, r = h; for (int q = 0; q < 40; ++q) { double y1 = l + (r - l) * 0.49; double y2 = l + (r - l) * 0.51; if (dist(v2(x, y1)) > dist(v2(x, y2))) l = y1; else r = y2; } return l; } int main(){ #ifdef _DEBUG freopen("input.txt", "r", stdin); //freopen( "output.txt", "w", stdout); #endif int n; cin >> w >> h; for (int i = 0; i < 4; ++i) cin >> g[i].x >> g[i].y; double l = 0.0, r = w; for (int q = 0; q < 40; ++q) { double x1 = l + (r - l) * 0.49; double x2 = l + (r - l) * 0.51; if (f(x1) > f(x2)) l = x1; else r = x2; } double x = l; double y = final_f(x); double ans = dist(v2(x, y)); if (dist(v2(x, y)) < 1e-6) Cout << x << " " << y << endl; else cout << "NONE" << endl; return 0; } ```