洛谷 [P1337] 平衡点

模拟退火练手

一道模拟退火的好题

结果一定势能最小

与模拟退火思路高度一致

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <ctime>
using namespace std;
const int MAXN = 1005;
struct point {
	double x, y, wei;
}poor[MAXN];
int n;
const double delta = 0.993;
const double eps = 1e-14;
double xans, yans, ans = 1e15, best = 1e15;
double energy(double x, double y) {
	double tot = 0.0;
	for(int i = 1; i <= n; i++) {
		tot += sqrt((poor[i].x - x) * (poor[i].x - x) + (poor[i].y - y) * (poor[i].y - y)) * poor[i].wei;
	}
	return tot;
}
double RAND(double T) {
	return (rand() * 2 - RAND_MAX) * T;
}
void solve() {
	double T = 10000.0;
	best = ans = energy(xans, yans);
	double xx = xans, yy = yans;
	while(T > eps) {
		double xt = xx + RAND(T);
		double yt = yy + RAND(T);
		double anst = energy(xt, yt);
		double DE = ans - anst;
		if(DE > 0.0) {
			xx = xt; yy = yt;
			ans = anst;
			if(ans < best) {
				xans = xx; yans = yy;
				best = ans;
			}
		} else if(exp(DE / T) * RAND_MAX > (double)rand()) {
			xx = xt; yy = yt;ans = anst;
		}
		T *= delta;
	}
}
int main() {
	srand(time(NULL));
	cin >> n;
	for(int i = 1; i <= n; i++) {
		cin >> poor[i].x >> poor[i].y >> poor[i].wei;
		xans += poor[i].x; yans += poor[i].y;
	}
	xans /= (double)n; yans /= (double)n;
	solve();
	solve();
	solve();
	printf("%.3f %.3f\n", xans, yans);
	return 0;
}