POJ 2728 Desert King 最优比例生成树

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题目链接:http://poj.org/problem?id=2728

二分版代码:

#include <iostream>#include <cstdio>#include <algorithm>#include <cstring>#include <cmath>#define sf scanf#define pf printf#define dpow(x) ((x) * (x))#define esp 1e-5#define INF 1e10using namespace std;const int maxn = 1000 + 5;double A[maxn][maxn],B[maxn][maxn],D[maxn][maxn];double x[maxn],y[maxn],h[maxn];double dis[maxn];bool vis[maxn];double PRIME(int n,double l){    memset(vis,0,sizeof vis);    for(int i = 0;i < n;++i)        for(int j = 0;j < n;++j) D[i][j] = D[j][i] = A[i][j] - l * B[i][j];    for(int i = 0;i < n;++i) dis[i] = D[0][i];    dis[0] = 0;vis[0] = 1;dis[n] = INF;    int p;double tmp = 0;    for(int i = 0;i < n - 1;++i){        p = n;        for(int j = 0;j < n;++j)            if(!vis[j] && dis[j] < dis[p]) p = j;        vis[p] = 1;tmp += dis[p];        for(int j = 0;j < n;++j)            if(!vis[j] && dis[j] > D[p][j]) dis[j] = D[p][j];    }    return tmp;}int main(){    int n;    while( sf("%d",&n) && n ){        for(int i = 0;i < n;++i) sf("%lf %lf %lf",&x[i],&y[i],&h[i]);        for(int i = 0;i < n;++i){            for(int j = i;j < n;++j){                A[i][j] = A[j][i] = fabs(h[i] - h[j]);                B[i][j] = B[j][i] = sqrt( dpow(x[i] - x[j]) + dpow(y[i] - y[j]) );            }        }        double l = 0,r = 100,mid;        while(l + esp < r){            mid = (l + r) / 2.0;            if(PRIME(n,mid) < 0)  r = mid;            else l = mid;        }        pf("%.3f\n",mid);    }}

迭代版
代码:

#include <iostream>#include <cstdio>#include <algorithm>#include <cstring>#include <cmath>#define sf scanf#define pf printf#define dpow(x) ((x) * (x))#define esp 1e-5#define INF 1e10using namespace std;const int maxn = 1000 + 5;double A[maxn][maxn],B[maxn][maxn],D[maxn][maxn];double x[maxn],y[maxn],h[maxn];double dis[maxn];int fa[maxn];bool vis[maxn];double PRIME(int n,double l){    memset(vis,0,sizeof vis);    for(int i = 0;i < n;++i)        for(int j = 0;j < n;++j) D[i][j] = D[j][i] = A[i][j] - l * B[i][j];    for(int i = 0;i < n;++i) dis[i] = D[0][i],fa[i] = 0;    vis[0] = 1;dis[n] = INF;    int p;double up = 0,low = 0;    for(int i = 0;i < n - 1;++i){        p = n;        for(int j = 0;j < n;++j)            if(!vis[j] && dis[j] < dis[p]) p = j;        vis[p] = 1;up += A[fa[p]][p],low += B[fa[p]][p];        for(int j = 0;j < n;++j)            if(!vis[j] && dis[j] > D[p][j]) dis[j] = D[p][j],fa[j] = p;    }    return up / low;}int main(){    int n;    while( sf("%d",&n) && n ){        for(int i = 0;i < n;++i) sf("%lf %lf %lf",&x[i],&y[i],&h[i]);        for(int i = 0;i < n;++i){            for(int j = i;j < n;++j){                A[i][j] = A[j][i] = fabs(h[i] - h[j]);                B[i][j] = B[j][i] = sqrt( dpow(x[i] - x[j]) + dpow(y[i] - y[j]) );            }        }        double ans = 0,tmp = 10;        while(fabs(ans - tmp) > esp){            ans = tmp;            tmp = PRIME(n,tmp);        }        pf("%.3f\n",ans);    }}

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