UVA11090-Going in Cycle!!-最短路/图判环/二分

UVA11090-Going in Cycle!!-最短路

Description

You are given a weighted directed graph with n vertices and m edges. Each cycle in the graph has a
weight, which equals to sum of its edges. There are so many cycles in the graph with different weights.
In this problem we want to find a cycle with the minimum mean.

Input

The first line of input gives the number of cases, N. N test cases follow. Each one starts with two
numbers n and m. m lines follow, each has three positive number a, b, c which means there is an edge
from vertex a to b with weight of c.
O#utput
For each test case output one line containing Case #x: followed by a number that is the lowest mean
cycle in graph with 2 digits after decimal place, if there is a cycle. Otherwise print No cycle found..
Constraints

• n ≤ 50
• a, b ≤ n
• c ≤ 10000000

Sample Input

22 11 2 12 21 2 22 1 3

Sample Output

Case #1: No cycle found.Case #2: 2.50

---

思路

存在一个边数为a的大小为m的圈 –> 边和-am<=0 –> 每个边都-m，判断有没有负环

AC代码

/************************************** *Source            : UVA11090 *Knowledge Point   : SSSP *Author            : CSUzick**************************************/#include <cstdio>#include <cstdlib>#include <iomanip>#include <cstring>#include <iostream>#include <stack>#include <vector>#include <queue>#include <cctype>#include <cmath>#include <string>#include <algorithm>#include <set>#include <bitset>#include <map>#define INF 0x3f3f3f3f3f3fLL#define ULL unsigned long long#define LL long long#define N 100100#define eps 10e-9#define MOD 100000000#define mem(a,n) memset(a,n,sizeof(a))#define fread freopen("in.txt","r",stdin)#define fwrite freopen("out.txt","w",stdout)using namespace std;const double PI=acos(-1.0);struct Edge{    int from,to,dist;    Edge(int u,int v,int d):from(u),to(v),dist(d){};};struct SPFA{    vector<Edge> edges;    vector<int> G[N];    bool inque[N];    double d[N];    int cnt[N];    int n,m;    void init(int n){        this->n=n;        for(int i=0;i<=n;++i){            G[i].clear();        }        edges.clear();    }    void AddEdge(int from,int to,int dist){        edges.push_back(Edge(from,to,dist));        m=edges.size();        G[from].push_back(m-1);    }    bool spfa(double mid){        queue<int> que;        memset(inque,0,sizeof(inque));        memset(cnt,0,sizeof(cnt));        for(int i=1;i<=n;++i){            que.push(i);            d[i]=0;        }        while(!que.empty()){            int temp=que.front();            if(cnt[temp]==n){                return true;            }            que.pop();            inque[temp]=false;            for(int i=0;i<G[temp].size();++i){                Edge &e=edges[G[temp][i]];                if(d[e.to]>d[temp]+e.dist-mid){                    d[e.to]=d[temp]+e.dist-mid;                    if(!inque[e.to]){                        que.push(e.to);                        inque[e.to]=true;                        if(++cnt[e.to]>=n)  return true;                    }                }            }        }        return false;    }};SPFA SMF;int main(){    int t,kase=0,n,m,u,c,v;    double maxl,high,low,mid;    scanf("%d",&t);    while(kase<t){        maxl=0;        scanf("%d%d",&n,&m);        SMF.init(n);        while(m--){            scanf("%d%d%d",&u,&v,&c);            maxl=max(maxl,(double)c);            SMF.AddEdge(u,v,c);        }        high=maxl+1,low=0;        if(!SMF.spfa(high)){            printf("Case #%d: No cycle found.\n",++kase);            continue;        }        while(high-low>eps){            mid=(low+high)/2;            if(SMF.spfa(mid)){                high=mid;            }else{                low=mid;            }        }        printf("Case #%d: %.2f\n",++kase,mid);    }    return 0;}