poj3621 Sightseeing Cows

Posted 2021-01-01 akcqhzdy

01分数规划

二分+spfa负环（SLF优化）

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

int n,m;
double p[1100];
struct edge{int x,y;double d;}e[5100];
struct node
{
    int x,y,next;double d;
}a[11000];int len,last[1100];
void ins(int x,int y,double d)
{
    len++;
    a[len].x=x;a[len].y=y;a[len].d=d;
    a[len].next=last[x];last[x]=len;
}

double d[1100];
int list[1100000],inq[1100];
bool v[1100];
bool check(double mid)
{
    len=0;memset(last,0,sizeof(last));
    for(int i=1;i<=m;i++)
        ins(e[i].x,e[i].y,mid*e[i].d-p[e[i].x]);
    
    memset(d,0,sizeof(0));
    memset(v,true,sizeof(v));
    memset(inq,0,sizeof(inq));
    int head=500000,tail=500000;
    for(int i=1;i<=n;i++)list[tail++]=i;
    while(head!=tail)
    {
        int x=list[head];head++;
        for(int k=last[x];k;k=a[k].next)
        {
            int y=a[k].y;
            if(d[y]>d[x]+a[k].d)
            {
                d[y]=d[x]+a[k].d;
                inq[y]++;if(inq[y]==n)return true;
                if(v[y]==false)
                {
                    v[y]=true;
                    if(d[y]>d[list[head]])list[tail++]=y;
                    else list[--head]=y;
                }
            }
        }
        v[x]=false;
    }
    return false;
}

int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)scanf("%lf",&p[i]);
    for(int i=1;i<=m;i++)
        scanf("%d%d%lf",&e[i].x,&e[i].y,&e[i].d);
    
    double l=0,r=100000.0;
    while(r-l>1e-5)
    {
        double mid=(l+r)/2;
        if(check(mid))l=mid;
        else r=mid;
    }
    printf("%.2lf
",l);
    return 0;
}