poj 1273 Drainage Ditches(最大流入门)

题意:n个池塘，m条水渠，求从第一个池塘到第m个池塘能运送的最大流量；

思路：裸最大流dicnic算法。建分层图并不断找增广路，直到找不到增广路即为最大流。

邻接表实现：

#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;
#define MAXN 210
#define INF 0x3f3f3f3f
struct Edge
{
    int st, ed;
    int c;
    int next;
}edge[MAXN << 1];
int n, m;
int s, t;
int ans;
int e = 0; 
int head[MAXN];
int d[MAXN];
int min(int a, int b)
{
    return a < b ? a : b;
}
void init()
{
    int i, j;
    int a, b, c; 
    s = 1;   //源点
    t = m;   //汇点
    e = 0;   //边数
    ans = 0;
    memset(head, -1, sizeof(head));
    for(i = 1; i <= n; i++)
    {
        scanf("%d%d%d", &a, &b, &c);
        edge[e].st = a;
        edge[e].ed = b;
        edge[e].c = c;
        edge[e].next = head[a];
        head[a]= e++;
        edge[e].st = b;
        edge[e].ed = a;
        edge[e].next = head[b];
        head[b] = e++;
    }
}
int bfs()
{
    memset(d, -1, sizeof(d));
    queue<int> q;
    d[s] = 0;
    q.push(s);
    int i;
    int cur;
    while(!q.empty())
    {
        cur = q.front();
        q.pop();
        for(i = head[cur]; i != -1; i = edge[i].next)
        {
            if(d[edge[i].ed] == -1 && edge[i].c > 0)
            {
                d[edge[i].ed] = d[cur] + 1; 
                q.push(edge[i].ed);
            }    
        }
    }
    if(d[t] < 0)
        return 0;
    return 1;
}
int dinic(int x, int flow)
{
    if(x == t)
        return flow;
    int i, a;
    for(i = head[x]; i != -1; i = edge[i].next)
    {
        if(d[edge[i].ed] == d[x] + 1 && edge[i].c > 0 && (a = dinic(edge[i].ed, min(flow, edge[i].c))))
        {
            edge[i].c -= a;
            edge[i ^ 1].c += a;
            return a;    
        }
    }
    return 0;
}
void solve()
{
    while(scanf("%d%d", &n, &m) != EOF)
    {
        init();
        while(bfs()) //建图，增广
        {
            int increment;
            increment = dinic(1, INF);
                ans +=  increment; 
        }
        printf("%d\n", ans);
    }
}
int main()
{
    solve();
    return 0;
}

邻接矩阵实现：

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#define min(x,y) ((x<y)?(x):(y))
using namespace std;
const int MAX=0x5fffffff;//
int tab[250][250];//邻接矩阵
int dis[250];//距源点距离,分层图
int q[2000],h,r;//BFS队列 ,首,尾
int N,M,ANS;//N:点数;M,边数
int BFS()  //建分层图
{
     int i,j;
     memset(dis,0xff,sizeof(dis));//以-1填充
     dis[1]=0;
     h=0;r=1;
     q[1]=1;
     while (h<r)
     {
           j=q[++h];
           for (i=1;i<=N;i++)
               if (dis[i]<0 && tab[j][i]>0)
               {
                  dis[i]=dis[j]+1;
                  q[++r]=i;
               }
     }
     if (dis[N]>0)
        return 1;
     else
        return 0;//汇点的DIS小于零,表明BFS不到汇点
}
//Find代表一次增广,函数返回本次增广的流量,返回0表示无法增广
int find(int x,int low)//Low是源点到现在最窄的(剩余流量最小)的边的剩余流量
{
    int i,a=0;
    if (x==N)return low;//是汇点
    for (i=1;i<=N;i++)
    if (tab[x][i] >0 //联通
     && dis[i]==dis[x]+1 //是分层图的下一层
     &&(a=find(i,min(low,tab[x][i]))))//能到汇点(a !=  0)
    {
       tab[x][i]-=a;
       tab[i][x]+=a;
       return a;
    }
    return 0;

}
int main()
{
    //freopen("ditch.in" ,"r",stdin );
    //freopen("ditch.out","w",stdout);
    int i,j,f,t,flow,tans;
    while (scanf("%d%d",&M,&N)!=EOF){
    memset(tab,0,sizeof(tab));
    for (i=1;i<=M;i++)
    {
        scanf("%d%d%d",&f,&t,&flow);
        tab[f][t]+=flow;
    }
    //
    ANS=0;
    while (BFS())//要不停地建立分层图,如果BFS不到汇点才结束
    {
          while(tans=find(1,0x7fffffff))ANS+=tans;//一次BFS要不停地找增广路,直到找不到为止
    }
    printf("%d\n",ANS);
    }
}

 sap算法：（出现断链时直接退出；对当前弧优化）

#include<iostream>
#include<cstdio>
#include<memory.h>
#include<cmath>
using namespace std;
#define MAXN 500
#define MAXE 40000
#define INF 0x7fffffff
long ne,nv,tmp,s,t,index;
struct Edge{
    long next,pair;
    long v,cap,flow;
}edge[MAXE];
long net[MAXN];
long ISAP()
{
    long numb[MAXN],dist[MAXN],curedge[MAXN],pre[MAXN];
    long cur_flow,max_flow,u,tmp,neck,i;
    memset(dist,0,sizeof(dist));
    memset(numb,0,sizeof(numb));
    memset(pre,-1,sizeof(pre));
    for(i = 1 ; i <= nv ; ++i)
        curedge[i] = net[i];
    numb[nv] = nv;
    max_flow = 0;
    u = s;
    while(dist[s] < nv)
    {
        /* first , check if has augmemt flow */
        if(u == t)
        {
            cur_flow = INF;
            for(i = s; i != t;i = edge[curedge[i]].v) 
            {  
                if(cur_flow > edge[curedge[i]].cap)
                {
                    neck = i;
                    cur_flow = edge[curedge[i]].cap;
                }
            }
            for(i = s; i != t; i = edge[curedge[i]].v)
            {
                tmp = curedge[i];
                edge[tmp].cap -= cur_flow;
                edge[tmp].flow += cur_flow;
                tmp = edge[tmp].pair;
                edge[tmp].cap += cur_flow;
                edge[tmp].flow -= cur_flow;
            }
            max_flow += cur_flow;
            u = neck;
        }
        /* if .... else ... */
        for(i = curedge[u]; i != -1; i = edge[i].next)
            if(edge[i].cap > 0 && dist[u] == dist[edge[i].v]+1)
                break;
        if(i != -1)
        {
            curedge[u] = i;
            pre[edge[i].v] = u;
            u = edge[i].v;
        }else{
            if(0 == --numb[dist[u]]) break;
            curedge[u] = net[u];
            for(tmp = nv,i = net[u]; i != -1; i = edge[i].next)
                if(edge[i].cap > 0)
                    tmp = tmp<dist[edge[i].v]?tmp:dist[edge[i].v];
            dist[u] = tmp + 1;
            ++numb[dist[u]];
            if(u != s) u = pre[u];
        }
    }
    
    return max_flow;
}
int main() {
    long i,j,np,nc,m,n;
    long a,b,val;
    long g[MAXN][MAXN];
    while(scanf("%d%d",&ne,&nv)!=EOF)
    {
        s = 1;
        t = nv;
        memset(g,0,sizeof(g));
        memset(net,-1,sizeof(net));
        for(i=0;i<ne;++i)
        {
            scanf("%ld%ld%ld",&a,&b,&val);
            g[a][b] += val;
         }
         for(i=1;i<=nv;++i)
             for(j = i; j <= nv;++j)
                 if(g[i][j]||g[j][i])
                 {
                     edge[index].next = net[i];
                     edge[index].v = j;
                     edge[index].cap = g[i][j];
                     edge[index].flow = 0;
                     edge[index].pair = index+1;
                     net[i] = index++;
                     edge[index].next = net[j];
                     edge[index].v = i;
                     edge[index].cap = g[j][i];
                     edge[index].flow = 0;
                     edge[index].pair = index-1;
                     net[j] = index++;
                 }
        printf("%ld\n",ISAP());
    }
    return 0;
}