[hdu2899]Strange fuction

题目链接

[hdu2899Strange fuction]

题解

发现这个东西是个凸的，直接三分
但我想写模拟退火...

代码

#include<cmath> 
#include<cstdio> 
#include<algorithm> 
inline int read() { 
	int x = 0,f = 1; 
	char c = getchar(); 
	while(c < '0' || c > '9')c = getchar(); 
	while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = getchar(); 
	return x * f; 
} 
#define INF 1e18 
#define eps 1e-10 
int n; 
struct Node {
	double x,y; 
} p[101]; 
double dis(Node a,Node b) {
	return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)); 
} 
double calc(Node a) { 
	double sum = 0; 
	for(int i = 1;i <= n;++ i)	
		sum += dis(a,p[i]); 
	return sum; 
} 
#define T 100 
#define delta 0.98 

double Rand() { 
	return (double) rand() / (double)RAND_MAX;  
} 
#define IT 5 
double dx[7] = {1,0,-1,0,1}; 
double solve() { 
	Node x = p[1]; 
	double res = calc(x); 
	double t = T; 
	while(t > eps) { 
		for(int i = 1;i < IT; ++ i) {
			for(int i = 0;i <= 4;++ i) { 
				Node nx = x; 
				nx.x += dx[i] * Rand() * t; 
				nx.y += dx[i + 1] * Rand() * t; 
				double nxres = calc(nx); 
				if(nxres < res || Rand() >= exp((nxres - res) / res)) res = nxres,x = nx; 
			} 
		} 
		t *= delta; 
	} 
	return res; 
} 
int main() { 
	srand(20010901); 
	n = read(); 
	for(int i = 1;i <= n;++ i) 
		scanf("%lf%lf",&p[i].x,&p[i].y); 
	double ans = INF; 
	for(int i = 1;i <= 10;++ i) { 
		ans = std:: min(ans,solve()); 
	} 
	printf("%.0lf\n",ans); 
}