【POJ】2069.Super Star

题解

求一个最小的半径的球，包括三维平面上所有的点，输出半径

随机移动球心，半径即为距离最远的点，移动的方式是向离的最远的那个点移动一点，之后模拟退火就好

代码

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
//#define ivorysi
#define MAXN 105
#define eps 1e-8
#define pb push_back
using namespace std;
typedef long long int64;
typedef unsigned int u32;
typedef double db;
struct Point {
    db x,y,z;
    Point(db _x = 0,db _y = 0,db _z = 0) {
	x = _x;y = _y;z = _z;
    }
}P[35];
int N;
u32 Rand() {
    static u32 x = 1736382156;
    return x += x << 2 | 1;
}
db Rand_p() {
    return (db) (Rand() % 10000) / 10000;
}
inline db o(db x) {return x * x;}
db dist(Point a,Point b) {
    return sqrt(o(a.x - b.x) + o(a.y - b.y) + o(a.z - b.z));
}
db get_radius(Point a) {
    db res = dist(a,P[1]);
    for(int i = 2 ; i <= N ; ++i) res = max(res,dist(P[i],a));
    return res;
}
int get_farthest(Point a) {
    int r = 1;
    for(int i = 2 ; i <= N ; ++i) {
	if(dist(a,P[i]) > dist(a,P[r])) r = i;
    }
    return r;
}
void Solve() {
    db delta = 0.99,T = 1000;
    db now = get_radius(P[1]),ans = now;
    Point s = P[1];
    while(T > eps) {
	ans = min(ans,now);
	int c = get_farthest(s);
	db d = dist(P[c],s);
	Point t = Point(s.x + (P[c].x - s.x) / d * T,s.y + (P[c].y - s.y) / d * T,s.z + (P[c].z - s.z) / d * T);
	db r = get_radius(t);
	if(r <= now) {
	    now = r,s = t;
	}
	else {
	    if(exp((now - r) / T) > Rand_p()) {
		now = r,s = t;
	    }
	}
	T *= delta;
    }
    printf("%.5f\n",ans);
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    while(scanf("%d",&N) != EOF && N) {
	for(int i = 1 ; i <= N ; ++i) {
	    scanf("%lf%lf%lf",&P[i].x,&P[i].y,&P[i].z);
	}
	Solve();
    }
}