[POJ 3621] Sightseeing Cows

[题目链接]

          http://poj.org/problem?id=3621

[算法]

        01分数规划（最优比率环）

[代码]

        

#include <algorithm>  
#include <bitset>  
#include <cctype>  
#include <cerrno>  
#include <clocale>  
#include <cmath>  
#include <complex>  
#include <cstdio>  
#include <cstdlib>  
#include <cstring>  
#include <ctime>  
#include <deque>  
#include <exception>  
#include <fstream>  
#include <functional>  
#include <limits>  
#include <list>  
#include <map>  
#include <iomanip>  
#include <ios>  
#include <iosfwd>  
#include <iostream>  
#include <istream>  
#include <ostream>  
#include <queue>  
#include <set>  
#include <sstream>  
#include <stdexcept>  
#include <streambuf>  
#include <string>  
#include <utility>  
#include <vector>  
#include <cwchar>  
#include <cwctype>  
#include <stack>  
#include <limits.h>
using namespace std;
#define MAXL 1010
#define MAXP 5010 
const double eps = 1e-4;
const int T = 1e5;
const int INF = 2e9;

struct edge
{
        int to,w,nxt;
} e[MAXP];

int i,L,P,a,b,w,tot;
int f[MAXL],head[MAXL];
double l,r,mid,ans;

inline void addedge(int u,int v,int w)
{
        tot++;
        e[tot] = (edge){v,w,head[u]};
        head[u] = tot;
}
inline bool spfa(double mid)
{
        int i,cur,v;
        double w;
        static int cnt[MAXL];        
        static bool inq[MAXL];
        static double dist[MAXL];
        queue< int > q;
        memset(cnt,0,sizeof(cnt));
        memset(inq,false,sizeof(inq));
        while (!q.empty()) q.pop();
        for (i = 1; i <= L; i++)
        {
                q.push(i);
                cnt[i] = 1;
                inq[i] = true;
                dist[i] = -INF;
        }
        while (!q.empty())
        {
                cur = q.front();
                q.pop();
                inq[cur] = false;
                for (i = head[cur]; i; i = e[i].nxt)
                {
                        v = e[i].to;
                        w = 1.0 * f[cur] - 1.0 * mid * e[i].w;
                        if (dist[cur] + w > dist[v])
                        {
                                dist[v] = dist[cur] + w;
                                if (!inq[v])
                                {
                                        inq[v] = true;
                                        cnt[v]++;
                                        if (cnt[v] > L) return true;
                                        q.push(v);
                                }
                        }
                }
        }
        return false;
}

int main() 
{
        
        scanf("%d%d",&L,&P);
        for (i = 1; i <= L; i++) scanf("%d",&f[i]);
        for (i = 1; i <= P; i++)
        {
                scanf("%d%d%d",&a,&b,&w);
                addedge(a,b,w);    
        }         
        l = 0; r = T;
        while (r - l > eps)
        {
                mid = (l + r) / 2.0;
                if (spfa(mid))
                {
                        ans = mid;
                        l = mid;        
                }    else r = mid;
        }    
        printf("%.2f\n",ans);
        
        return 0;
    
}