poj 2069 Super Star 最小求覆蓋【爬山演算法】
阿新 • • 發佈:2018-11-30
題意:給定幾個點,要求覆蓋這些點的最小球半徑。(求到n個點的最大距離最小化的點
因為是單峰的所以可以用爬山演算法
主要是我的退火演算法板子精度達不到?
//#include<bits/stdc++.h> #include <iostream> #include <cmath> #include <cstdio> #include <stdlib.h> #include <ctime> using namespace std; typedef long long ll; typedef pair<int,int> PII; const int inf = 0x3f3f3f3f; const int mod = 1e9 + 7; const int maxn = 1e4 + 5; int n; double X,Y; struct point { double x,y,z; } p[maxn],pp; double ans=1e10; double dis(point a,point b) { return ((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)+(a.z-b.z)*(a.z-b.z)); } int get(point x) { double res=-1; int k; for(int i=1; i<=n; ++i) { double m=dis(p[i],x); if(m>res) res=m,k=i; } ans=min(ans,dis(x,p[k])); return k; } void hc() { double T=1,eps=1e-10; while(T>eps) { //if(pp.x<=X&&pp.y<=Y&&pp.x>=0&&pp.y>=0) // { int k=get(pp); pp.x=pp.x+(p[k].x-pp.x)*T; pp.y=pp.y+(p[k].y-pp.y)*T; pp.z=pp.z+(p[k].z-pp.z)*T; // } T*=0.9996; } } int main() { double X,Y; while(scanf("%d",&n)!=EOF) { if(n==0)break; pp.x=pp.y=pp.z=0; for(int i=1; i<=n; ++i) { cin>>p[i].x>>p[i].y>>p[i].z; pp.x+=p[i].x,pp.y+=p[i].y,pp.z+=p[i].z; } pp.x/=n;pp.y/=n;pp.z/=n; ans=1e10; hc(); // printf("(%.1f,%.1f).\n",pp.x,pp.y,pp.z); printf("%.5f\n",sqrt(ans)); } return 0; }
退火沒有A掉:
///退火演算法 #include <iostream> #include <cmath> #include <algorithm> #include <cstdio> #include <stdlib.h> #include <ctime> #define mp make_pair #define io ios::sync_with_stdio(0),cin.tie(0) using namespace std; typedef long long ll; typedef pair<int, int> PII; const int inf = 0x3f3f3f3f; const int mod = 1e9 + 7; const int maxn = 1e6 + 5; int n, x, y; struct point { double x, y, z; } p[maxn], now, nex, ansp; double dis(point a, point b) { return ((a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y) + (a.z - b.z)*(a.z - b.z)); } double f(point x) { //評估函式 double res = 0; for (int i = 1;i <= n;i++) res = max(res, dis(x, p[i])); return res; } long double ans = 1e20;//最開始的能量值,初始很大就可以,不用修改 void sa() { ans = 1e22; double T = 100; //初始溫度, (可以適當修改,最好和給的資料最大範圍相同,或者縮小其原來0.1) double d = 0.9999; //降溫係數 (可以適當修改,影響結果的精度和迴圈的次數,) double eps = 1e-10; //最終溫度 (要是因為精度問題,可以適當減小最終溫度) double TT = 1.0; //採納新解的初始概率 double dd = 0.999; //(可以適當修改,採納新解變更的概率)(這個概率下面新解更新的時候,最好和未採納的新解更新的次數是一半一半) double res = f(now); //傳入的初始預設解(now)下得到的評估能量值 if (res < ans) ans = res, ansp = now;//ansp終解 int cnt=0; while (T > eps) { for (int i = -1;i <= 1;++i) for (int j = -1;j <= 1;++j) if ((now.x+T*i<=100)&&(now.x+T*i>=0)&&(now.y+T*j<=100)&&(now.y+T*j>=0)) { nex.x = now.x + T * i, nex.y = now.y + T * j;//新解 double tmp = f(nex);//新解下的評估能量值 if (tmp < ans) ans = tmp, ansp = nex;//降溫成功,更新當前最優解 if (tmp < res) res = tmp, now = nex;// 降溫成功,採納新解 else if (TT > rand() % 10000 / 10000.0) res = tmp, now = nex;//,cout<<"======"<<endl;//沒有 降溫成功,但是以一定的概率採納新解 //else cout<<"="<<endl;//用於測試,設定的採納新解的概率,是否為一半一半,可以適當修改降溫引數dd }cnt++; T *= d; TT *= dd; } //cout<<cnt<<endl; } int main() { srand(time(0)); while (scanf("%d", &n)!=EOF) { if (n == 0)break; now.x = now.y = 0, now.z = 0; for (int i = 1;i <= n;++i) { cin >> p[i].x >> p[i].y >> p[i].z;//scanf("%lf%lf%lf",&p[i].x,&p[i].y), now.x += p[i].x, now.y += p[i].y, now.z += p[i].z; }now.x = now.y = 55, now.z = 55;sa(); //now.x /= n, now.y /= n, now.z /= n;sa(); //now.x = now.y = 20, now.z = 20;sa(); printf("%.5Lf\n", sqrt(ans));//cout<<ans<<endl; } return 0; }