简介
就是模拟退火的物理过程,每次随机逼近乘上温度,以\(e^{\Delta/T}\)的概率接受答案,随机一个概率比较
然后就是调参+乱搞
题目
# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(1005);
IL int Input(){
RG int x = 0, z = 1; RG char c = getchar();
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
return x * z;
}
const double EPS(1e-15);
const double dt(0.99);
double x[_], y[_], w[_], ans, ansx, ansy;
int n;
# define Sqr(x) ((x) * (x))
IL double Dis(RG double x1, RG double y1, RG double x2, RG double y2){
return sqrt(Sqr(x1 - x2) + Sqr(y1 - y2));
}
IL double Sum(RG double x0, RG double y0){
RG double ret = 0;
for(RG int i = 1; i <= n; ++i) ret += Dis(x[i], y[i], x0, y0) * w[i];
return ret;
}
IL double SA(RG double T){
RG double x0 = ansx, y0 = ansy, cnt = 1e18;
for(; T > EPS; T *= dt){
RG double dx = rand() * 2 - RAND_MAX, dy = rand() * 2 - RAND_MAX;
RG double xx = x0 + T * dx;
RG double yy = y0 + T * dy;
RG double ret = Sum(xx, yy);
if(ret < ans) ans = ret, ansx = xx, ansy = yy;
if(ret < cnt || exp((ret - ans) / T) * RAND_MAX < rand()){
cnt = ret;
x0 = xx, y0 = yy;
}
}
}
int main(RG int argc, RG char* argv[]){
n = Input();
srand(n + 19260817); RG double x0 = 0, y0 = 0;
for(RG int i = 1; i <= n; ++i) x[i] = Input(), y[i] = Input(), w[i] = Input();
for(RG int i = 1; i <= n; ++i) x0 += x[i], y0 += y[i];
x0 /= n; y0 /= n; ansx = x0; ansy = y0;
ans = Sum(x0, y0);
for(RG int i = 1; i <= 10; ++i) SA(1000000);
printf("%.3lf %.3lf\n", ansx, ansy);
return 0;
}