洛谷 P1337 [JSOI2004]平衡点 / 吊打XXX

题意简述

有n个重物，每个重物系在一条足够长的绳子上。每条绳子自上而下穿过桌面上的洞，然后系在一起。求绳结X最终平衡于何处。

题解思路

模拟退火
每次随机出一个now,和ans比较，若比ans好，则替换，否则一定概率替换

代码

#include <ctime>
#include <cmath>
#include <cstdio>
#include <cstdlib>
using namespace std;
const double eps = 1e-15;
struct Point
{
	double x, y;
};
struct Node
{
	Point p;
	int w;
} a[10010];
int n;
double T = 2000, delta;
Point ans, now;
double sqr(double x)
{
	return x * x;
}
double calc(Point pp)
{
	double s = 0;
	for (register int i = 1; i <= n; ++i)
		s += sqrt(sqr(pp.x - a[i].p.x) + sqr(pp.y - a[i].p.y)) * a[i].w;
	return s;
}
double sa()
{
	while (T > eps)
	{
		now.x = ans.x + (rand() * 2 - RAND_MAX) * T;
		now.y = ans.y + (rand() * 2 - RAND_MAX) * T;
		delta = calc(now) - calc(ans);
		if (delta < 0) ans = now;
		else if (exp(-delta / T) * RAND_MAX > rand()) ans = now;
		T *= 0.998;
	}
}
int main()
{
	srand(29);
	scanf("%d", &n);
	for (register int i = 1; i <= n; ++i)
	{
		scanf("%lf%lf%d", &a[i].p.x, &a[i].p.y, &a[i].w);
		ans.x += a[i].p.x;
		ans.y += a[i].p.y;
	}
	ans.x /= (double)n;
	ans.y /= (double)n;
	sa();
	printf("%.3lf %.3lf", ans.x, ans.y);
}