UVA 11090 Going in Cycle!! 二分答案 + bellman-ford

求平均值最小的环，如果平均值最小为x，则如果把每条边的权值都减(x+1)，那么新图将会有负环，用bellman ford判断。

//#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<sstream>
#include<cmath>
#include<climits>
#include<string>
#include<map>
#include<queue>
#include<vector>
#include<stack>
#include<set>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
#define pb(a) push(a)
#define INF 0x1f1f1f1f
#define lson idx<<1,l,mid
#define rson idx<<1|1,mid+1,r
#define PI  3.1415926535898
template<class T> T min(const T& a,const T& b,const T& c) {
    return min(min(a,b),min(a,c));
}
template<class T> T max(const T& a,const T& b,const T& c) {
    return max(max(a,b),max(a,c));
}
void debug() {
#ifdef ONLINE_JUDGE
#else

    freopen("d:\\in1.txt","r",stdin);
    freopen("d:\\out1.txt","w",stdout);
#endif
}
int getch() {
    int ch;
    while((ch=getchar())!=EOF) {
        if(ch!=' '&&ch!='\n')return ch;
    }
    return EOF;
}

struct Edge
{
    int from,to;
    double dist;
};
const int maxn=55;
vector<int> g[maxn];
vector<Edge> edge;
double d[maxn];
int inq[maxn];
int inq_cnt[maxn];
int n,m;
void init()
{
    for(int i=1;i<=n;i++)g[i].clear();
    edge.clear();
}
void add(int u,int v,double w)
{
    Edge e=(Edge){u,v,w};
    edge.push_back(e);
    g[u].push_back(edge.size()-1);
}
bool negativeCycle(int s)
{
    queue<int> q;
    memset(inq,0,sizeof(inq));
    memset(inq_cnt,0,sizeof(inq_cnt));
    for(int i=1;i<=n;i++)
    {
        d[i]=0;
        inq[i]=1;
        q.push(i);
    }
    while(!q.empty())
    {
        int u=q.front();q.pop();
        inq[u]=0;
        for(int i=0;i<g[u].size();i++)
        {
            Edge &e=edge[g[u][i]];
            if(d[u]+e.dist<d[e.to])
            {
                d[e.to]=d[u]+e.dist;
                if(!inq[e.to])
                {
                    inq[e.to]=1;
                    q.push(e.to);
                    if(++inq_cnt[e.to]>n)return true;
                }
            }
        }
    }
    return false;
}
bool check(double x)
{
    for(int i=0;i<m;i++)
        edge[i].dist-=x;
    int flag=negativeCycle(1);
    for(int i=0;i<m;i++)
        edge[i].dist+=x;
    return flag;
}
int main()
{
    int t;
    scanf("%d",&t);
    for(int ca=1;ca<=t;ca++)
    {
        scanf("%d%d",&n,&m);
        init();
        for(int i=1;i<=m;i++)
        {
            int u,v;
            double w;
            scanf("%d%d%lf",&u,&v,&w);
            add(u,v,w);
        }

        double l=0,r=10000002;
        //printf("%d\n%d\n",10000000,INF);
        while(r-l>10e-4)
        {
            double mid=l+(r-l)/2;
            if(!check(mid))
                l=mid;
            else r=mid;
        }
        if(l>10000000)
            printf("Case #%d: No cycle found.\n",ca);
        else
            printf("Case #%d: %.2lf\n",ca,l);
    }
    return 0;
}