POJ 3621 Sightseeing Cows

 

SPFA+0/1分数规划。

CODE:

 

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;

#define MAXN 1010
#define INF 0X3F3F3F3F
#define eps 1e-7

struct Edge
{
    int v, next;
    double w;
}edge[MAXN*5];

double d[MAXN], num[MAXN];
int first[MAXN];

int n, m, cnt;

void init()
{
    cnt = 0;
    memset(first, -1, sizeof(first));
}

void read_graph(int u, int v, double w)
{
    edge[cnt].v = v, edge[cnt].w = w;
    edge[cnt].next = first[u], first[u] = cnt++;
}

int spfa(int src, double mid)
{
    queue<int> q;
    bool inq[MAXN] = {0};
    int ct[MAXN] = {0};
    for(int i = 1; i <= n; i++) d[i] = (i == src)?0:INF;
    q.push(src);
    while(!q.empty())
    {
        int x = q.front(); q.pop();
        inq[x] = 0, ct[x]++;
        if(ct[x] >= n) return 0; //存在负环 
        for(int e = first[x]; e != -1; e = edge[e].next)
        {
            int v = edge[e].v;
            double w = -num[v] + mid*edge[e].w;
            if(d[v] > d[x] + w)
            {
                d[v] = d[x] + w;
                if(!inq[v])
                {
                    inq[v] = 1;
                    q.push(v);
                }
            }
        }
    }
    return 1;
}

double BSearch()
{
    double x = 0, y = 100.0, ans;
    while((y-x) > eps)
    {
        double mid = x+(y-x)/2;
        if(spfa(1, mid))
        {
            ans = mid;
            y = mid;
        }
        else x = mid;
    }
    return ans;
}

int main()
{
    scanf("%d%d", &n, &m);
    init();
    for(int i = 1; i <= n; i++)
    {
        scanf("%lf", &num[i]);
    }
    while(m--)
    {
        int u, v;
        double w;
        scanf("%d%d%lf", &u, &v, &w);
        read_graph(u, v, w);
    }
    double ans = BSearch();
    printf("%.2lf\n", ans);
    return 0;
}