Ellipsoid HDU-5017 模拟退火

Ellipsoid

solution

存在最优解，模拟退火

$a{x}^2+b{y}^2+c{z}^2+dyz+exz+fxy=1$

$c{z}^2+(ex+dy)z+(a{x}^2+b{y}^2+fxy-1)=0$

$A=c$

$B=ex+dy$

$C=a{x}^2+b{y}^2+fxy-1$

$\Delta =B^2-4AC$

$z=\frac{-b+\sqrt{\Delta }}{2A},\frac{-b-\sqrt{\Delta }}{2A}$

$dis=x\ast x+y\ast y+min(z_1\ast z_1,z_2\ast z_2)$

code

/*Siberian Squirrel*/
/*Cute JinFish*/
#include<bits/stdc++.h>

#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define ACM_LOCAL

using namespace std;
typedef long long ll;

const double PI = acos(-1);
const double eps = 1e-8;
/*const int MOD = 998244353, r = 119, k = 23, g = 3;
const int MOD = 1004535809, r = 479, k = 21, g = 3;*/
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const int M = 1e7 + 10;
const int N = 4e5 + 10;

int fx[5] = {
    
    0, 0, 1, -1};
int fy[5] = {
    
    1, -1, 0, 0};

int dcmp(double x) {
    
    
    if(fabs(x) < eps) return 0;
    else return x < 0? -1: 1;
}
//inline int rnd(){static int seed=2333;return seed=(((seed*666666ll+20050818)%998244353)^1000000007)%1004535809;}

double a, b, c, d, e, f;

double func(double x, double y) {
    
    
    double A = c, B = e * x + d * y, C = a * x * x + b * y * y + f * x * y - 1;
    double dleta = B * B - 4 * A * C;
    if(dleta < 0) return INF;
    double z1 = (-B + sqrt(dleta)) / (2 * A);
    double z2 = (-B - sqrt(dleta)) / (2 * A);
    return sqrt(x * x + y * y + min(z1 * z1, z2 * z2));
}

inline void solve(double res = 0, bool flag = false) {
    
    
    double x = sqrt(1.0 / a), y = 0;
    double t = 1.0, xx, yy;
    while(t > eps) {
    
    
        res = func(x, y);
        flag = false;
        for(int i = 0; i < 4; ++ i) {
    
    
            xx = x + t * fx[i];
            yy = y + t * fy[i];
            if(func(xx, yy) + eps < res) {
    
    
                flag = true;
                break;
            }
        }
        if(flag) x = xx, y = yy;
        else t *= 0.618;
    }
    res = func(x, y);
    cout << fixed << setprecision(10) << res << endl;
}


int main() {
    
    
    IO;
#ifdef ACM_LOCAL
    freopen("input", "r", stdin);
	freopen("output", "w", stdout);
#endif
    int o = 1;
//	cin >> o;
    while(o --) {
    
    
        while(cin >> a >> b >> c >> d >> e >> f)
            solve();
    }
    return 0;
}