loj#2076. 「JSOI2016」炸弹攻击 模拟退火

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目录

• [TOC]

题目链接

loj#2076. 「JSOI2016」炸弹攻击

题解

模拟退火
退火时，由于答案比较小，但是温度比较高
所以在算exp时最好把相差的点数乘以一个常数让选取更差的的概率降低

代码

#include<ctime> 
#include<cmath> 
#include<cstdio>  
#include<cstring> 
#include<algorithm>
#define gc getchar() 
#define pc putchar 
inline int read() {
	 int x = 0,f = 1; 
	 char c = gc; 
	 while(c < '0' || c > '9') c  =gc; 
	 while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = gc; 
	 return x * f; 
} 
void print(int x) {
	if(x < 0) { 
		pc('-'); 
		x = -x; 
	} 
	if(x >= 10) print(x / 10); 
	pc(x % 10 + '0'); 
} 
const int maxn = 100007;  
int n,m; double R; 
double X[maxn],Y[maxn],r[maxn],p[maxn],q[maxn]; 
double rd() { 
	return (double) rand() / RAND_MAX; 
} 
void randpos(double &x,double & y){ 
	x = 2 * R * rd() - R; 
	y = 2 * R * rd() - R; 
}  
#define dt 0.998 
#define eps 1e-2 
double dis(double x,double y,double x1,double y1) { 
	return std::sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1)); 
} 
int calc(double x,double y) { 
	int ret = 0; 
	double tr = R; 
	for(int i = 1;i <= n;++ i) { 
		tr = std::min(tr,dis(X[i],Y[i],x,y) - r[i]); 
	} 
	if(r < 0) return 0; 
	for(int i = 1;i <= m;++ i) 
		if(dis(x,y,p[i],q[i]) <= tr) ret ++; 
	return ret; 
} 
int solve(double x,double y) {
	int mx = calc(x,y); 
	int now = mx; 
	double T = R; 
	for(;T > eps;T *= dt) { 
		double nt = T + 0.1; 
		double nx = x + (2.0 * nt) * rd() - nt,ny = y + (2 * nt) * rd() - nt; 
		int nans = calc(nx,ny); 
		if(nans > mx || exp(1e4 * (nans - now) / T) > rd()) x = nx,y = ny,now = nans; 
		mx = std::max(mx,now);  
	} 
	return mx; 
} 
int main() { 
	srand(19991206); 
	scanf("%d%d%lf",&n,&m,&R); 
	for(int i = 1;i <= n;++ i) 
		scanf("%lf%lf%lf",&X[i],&Y[i],&r[i]); 
	for(int i = 1;i <= m;++ i)
		scanf("%lf%lf",p + i,q + i); 
	int ans = 0 ;
	double px,py; 
	for(int i = 1;i <= 20;++ i) { 
		randpos(px,py); 
		ans = std::max(ans,solve(px,py)); 
	} 
	print(ans); 
	pc('
'); 
}