HDU 3549 Flow Problem【网络流入门题】

来源：互联网发布：win7美化mac 编辑：程序博客网时间：2024/05/30 23:37

没找到比较好的博客介绍网络流，可以看下白书（电子书的224页）

Edmonds-Karp（EK）算法 O(V*E*E) 124ms

#include <cstdio>#include <cmath>#include <cstring>#include <set>#include <stack>#include <queue>#include <vector>#include <iostream>#include <algorithm>using namespace std;#define ll long long#define INF 0x7FFFFFFF#define INT_MIN -(1<<31)#define eps 10^(-6)#define Q_CIN ios::sync_with_stdio(false)#define REP( i , n ) for ( int i = 0 ; i < n ; ++ i )#define REV( i , n ) for ( int i = n - 1 ; i >= 0 ; -- i )#define FOR( i , a , b ) for ( int i = a ; i <= b ; ++ i )#define FOV( i , a , b ) for ( int i = a ; i >= b ; -- i )#define CLR( a , x ) memset ( a , x , sizeof (a) )#define RE freopen("in.txt","r",stdin)#define WE freopen("out.txt","w",stdout)#define NMAX 1002#define min(a,b) ((a)>(b)?(b):(a))#define Dian_NAX 21int flow[Dian_NAX][Dian_NAX];   //边实际流量int cap[Dian_NAX][Dian_NAX];    //边容量int pre[NMAX];  //增广路径int res[NMAX];  //残余网络int n;          //点int EK(int s,int t){    queue<int>q;    int ans = 0;    CLR(flow,0);    while(true)    {        CLR(res,0);        res[s] = INF; //源点无限大        q.push(s);        while(!q.empty())        {            int u = q.front();            q.pop();            for(int v=1;v<=n;v++)                if(!res[v] && flow[u][v] < cap[u][v])                {                    pre[v] = u;                    q.push(v);                    res[v] = min(res[u],cap[u][v] - flow[u][v]);                }        }        if(res[t] == 0) //找不到增广路就退出            break;        for(int u = t;u != s; u=pre[u])        {            flow[pre[u]][u] += res[t];            flow[u][pre[u]] -= res[t];      //反向边        }        ans += res[t];    }    return ans;}int main(){    int a,b,c,t,m;    int test = 1;  //  RE;    scanf("%d",&t);    while(t--)    {        CLR(cap,0);        scanf("%d%d",&n,&m);        while(m--)        {            scanf("%d%d%d",&a,&b,&c);            cap[a][b] +=c;        }        printf("Case %d: %d\n",test++,EK(1,n));    }    return 0;}

Dinic 124ms

#include <string.h>#include <iostream>#include <cstdio>using namespace std;#define REP( i , n ) for ( int i = 0 ; i < n ; ++ i )#define FOR( i , a , b ) for ( int i = a ; i <= b ; ++ i )#define CLR( a , x ) memset ( a , x , sizeof (a) );#define RE freopen("1.in","r",stdin);#define WE freopen("output.txt","w",stdout);#define debug(x) cout<<#x<<":"<<(x)<<endl;const int maxn=16;int tab[maxn][maxn],dis[maxn],n,m;  //tab为流量,dis为层次//bfs找层次图int bfs(int s,int t){    int q[maxn],head=0,tail=0;    q[tail++]=s;    memset(dis,-1,sizeof(dis));    dis[s]=0;    while(head<tail)    {        int cur=q[head++];        for(int i=1;i<=n;i++)        {            if(dis[i]<0&&tab[cur][i]>0)            {                dis[i]=dis[cur]+1;                q[tail++]=i;            }        }    }    if(dis[t]>0)    return 1;    return 0;   //dis[t]=-1：路不通}//dfs为一次增广,s->tint dfs(int s,int t,int low)//Low为增广路径上的最小流量{    int flow=0;    if(s==t)    return low; //到汇点直接返回目前为止的最小流量    for(int i=1;i<=n;i++)    {       //在下一层里找        if(tab[s][i]>0           &&dis[i]==dis[s]+1           &&(flow=dfs(i,t,min(low,tab[s][i]))))        {            tab[s][i]-=flow;    //不断的减流量            tab[i][s]+=flow;            return flow;        //能到汇点        }    }    return 0;}int main() {//    RE    int a,b,c,t;    scanf("%d",&t);    for(int te=1;te<=t;te++)    {        scanf("%d%d",&n,&m);        CLR(tab,0); //流量初始化为0        while(m--)        {            scanf("%d%d%d",&a,&b,&c);            tab[a][b]+=c;        }        int ans=0,tans=0;        while(bfs(1,n))         //直到源点不能到汇点为止            while(tans=dfs(1,n,0x7FFFFFFF))     //在同一个层次图里尽量找增广路                ans+=tans;         printf("Case %d: %d\n",te,ans);    }    return 0;}

邻接表 436MS

#include <string.h>#include <iostream>#include <cstdio>#include <queue>using namespace std;#define REP( i , n ) for ( int i = 0 ; i < n ; ++ i )#define FOR( i , a , b ) for ( int i = a ; i <= b ; ++ i )#define CLR( a , x ) memset ( a , x , sizeof (a) );#define RE freopen("1.in","r",stdin);#define WE freopen("output.txt","w",stdout);#define debug(x) cout<<#x<<":"<<(x)<<endl;const int maxm=1005;const int maxn=20;const int inf = 0x3f3f3f3f;struct Edge{    int v,w,next;}edge[maxm*2];int head[maxn],dis[maxn];int tol;void addEdge(int u,int v,int w){    edge[tol].v=v,edge[tol].w=w,edge[tol].next=head[u];head[u]=tol++;    edge[tol].v=u,edge[tol].w=0,edge[tol].next=head[v];head[v]=tol++;}void init(){    tol=0;    CLR(head,-1);}bool bfs(int s,int t){    queue<int>q;    q.push(s);    CLR(dis,-1);    dis[s]=0;    while(!q.empty())    {        int u=q.front();q.pop();        for(int i=head[u];i!=-1;i=edge[i].next)        {            int v=edge[i].v;            if( dis[v]<0 && edge[i].w)            {                dis[v]=dis[u]+1;                q.push(v);            }        }    }    return dis[t]!=-1;}int dfs(int s,int t,int low){    int flow;    if(t==s)   return low;    for(int i=head[s];i!=-1;i=edge[i].next)    {        int v=edge[i].v;        if(edge[i].w && (dis[v]==dis[s]+1) &&            (flow = dfs(v,t,min(low,edge[i].w))))        {            edge[i].w -= flow;            edge[i^1].w += flow;            return flow;        }    }    return 0;}int maxFlow(int s,int t){    int ans=0,tmp;    while(bfs(s,t))        while(tmp=dfs(s,t,inf))            ans+=tmp;    return ans;}int main(){    int t,m,n,a,b,c;//    RE    scanf("%d",&t);    for(int te=1;te<=t;te++)    {        init();        scanf("%d%d",&n,&m);        while(m--)        {            scanf("%d%d%d",&a,&b,&c);            addEdge(a,b,c);        }        printf("Case %d: %d\n",te,maxFlow(1,n));    }    return 0;}

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