UVA 11248 Frequency Hopping

来源：互联网发布：unity 角色模型优化编辑：程序博客网时间：2024/06/05 06:01

题意：给定一个流量网络，问是否存在一个流量为C的流，如果不存在，是否可以恰好修改一个弧的容量，让这个流存在。

思路：先求个最大流，如果大于C，则说明存在这样的流，否则，对于每个最小割的弧，将这个弧的容量添加到C，再求最大流，看最大流是否大于等于C。

代码：

#include <iostream>#include<cstdio>#include<cstring>#include<string>#include<algorithm>#include<map>#include<queue>#include<stack>#include<cmath>#include<vector>#define inf 2139062143#define Inf 0x3FFFFFFFFFFFFFFFLL#define eps 1e-9#define pi acos(-1.0)using namespace std;const int maxn=100+10;struct Edge{    int from,to,cap,flow;    bool operator < (const Edge a) const    {        return (from==a.from&&to<a.to)||from<a.from;    }};struct Dinic{    vector<Edge>edges;    vector<int>G[maxn];    int n,m,s,t;    int d[maxn],cur[maxn];    bool vis[maxn];    void clearAll(int n)    {        for(int i=0;i<=n;++i) G[i].clear();        edges.clear();    }    void AddEdges(int from,int to,int cap)    {        edges.push_back((Edge){from,to,cap,0});        edges.push_back((Edge){to,from,0,0});        m=edges.size();        G[from].push_back(m-2);        G[to].push_back(m-1);    }    bool BFS()    {        queue<int>q;        memset(vis,0,sizeof(vis));        q.push(s);        d[s]=0;vis[s]=true;        while(!q.empty())        {            int x=q.front();q.pop();            for(int i=0;i<G[x].size();++i)            {                Edge e=edges[G[x][i]];                if(!vis[e.to]&&e.cap>e.flow)                {                    vis[e.to]=true;                    d[e.to]=d[x]+1;                    q.push(e.to);                }            }        }        return vis[t];    }    int DFS(int x,int a)    {        if(x==t||a==0) return a;        int flow=0,f;        for(int& i=cur[x];i<G[x].size();++i)        {            Edge e=edges[G[x][i]];            if(d[e.to]==d[x]+1&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0)            {                flow+=f;                edges[G[x][i]].flow+=f;                edges[G[x][i]^1].flow-=f;                a-=f;                if(a==0) break;            }        }        return flow;    }    int Maxflow(int s,int t)    {        this->s=s;this->t=t;        int flow=0;        while(BFS())        {            memset(cur,0,sizeof(cur));            flow+=DFS(s,inf);        }        return flow;    }    void clearFlow()    {        for(int i=0;i<edges.size();++i)           edges[i].flow=0;    }    void Reduce()    {        for(int i=0;i<edges.size();++i)           edges[i].cap-=edges[i].flow;    }    vector<int> Mincut()    {        vector<int>ans;        for(int i=0;i<edges.size();++i)        {            Edge e=edges[i];            if(vis[e.from]&&!vis[e.to]&&e.cap>0) ans.push_back(i);        }        return ans;    }}dinic;Edge ans[10010];int main(){    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);    int N,E,C;    int tcase=0;    while(~scanf("%d%d%d",&N,&E,&C))    {        if(N==0&&E==0&&C==0) break;        tcase++;        dinic.clearAll(N);        int from,to,cap;        for(int i=0;i<E;++i)        {            scanf("%d%d%d",&from,&to,&cap);            dinic.AddEdges(from,to,cap);        }        printf("Case %d: ",tcase);        int maxflow=dinic.Maxflow(1,N);        if(maxflow>=C)           printf("possible\n");        else        {            int ss=0;            vector<int>cut=dinic.Mincut();            dinic.Reduce();            for(int i=0;i<cut.size();++i)            {                Edge &e=dinic.edges[cut[i]];                dinic.clearFlow();                e.cap=C;                int res=dinic.Maxflow(1,N);                if(res+maxflow>=C) ans[ss++]=e;                e.cap=0;            }            if(ss==0) printf("not possible\n");            else            {                sort(ans,ans+ss);                printf("possible option:(%d,%d)",ans[0].from,ans[0].to);                for(int i=1;i<ss;++i)                  printf(",(%d,%d)",ans[i].from,ans[i].to);                printf("\n");            }        }    }    return 0;}