网络流模板

/*
SAP算法（矩阵形式）
结点编号从0开始
*/
#include<iostream>
#include<stdio.h>
#include<string.h>
using namespace std;

const int MAXN=1100;
int maze[MAXN][MAXN];
int gap[MAXN],dis[MAXN],pre[MAXN],cur[MAXN];
int sap(int start,int end,int nodenum){
    memset(cur,0,sizeof(cur));
    memset(dis,0,sizeof(dis));
    memset(gap,0,sizeof(gap));
    int u=pre[start]=start,maxflow=0,aug=-1;
    gap[0]=nodenum;
    while(dis[start]<nodenum){
        loop:
            for(int v=cur[u];v<nodenum;v++)
                if(maze[u][v]&&dis[u]==dis[v]+1){
                    if(aug==-1||aug>maze[u][v])aug=maze[u][v];
                    pre[v]=u;
                    u=cur[u]=v;
                    if(v==end){
                        maxflow+=aug;
                        for(u=pre[u];v!=start;v=u,u=pre[u]){
                            maze[u][v]-=aug;
                            maze[v][u]+=aug;
                        }
                        aug=-1;
                    }
                    goto loop;
                }
            int mindis=nodenum-1;
            for(int v=0;v<nodenum;v++)
                if(maze[u][v]&&mindis>dis[v]){
                    cur[u]=v;
                    mindis=dis[v];
                }
            if((--gap[dis[u]])==0)break;
            gap[dis[u]=mindis+1]++;
            u=pre[u];
    }
    return maxflow;
}

int main(){
    return 0;
}

/*
保留原矩阵，可用于多次使用最大流
SAP邻接矩阵形式
点的编号从0开始
增加个flow数组，保留原矩阵maze，可用于多次使用最大流
*/
#include<iostream>
#include<stdio.h>
#include<string.h>
using namespace std;

const int MAXN=1100;
int maze[MAXN][MAXN];
int gap[MAXN],dis[MAXN],pre[MAXN],cur[MAXN];
int flow[MAXN][MAXN];//存最大流的容量
int sap(int start,int end,int nodenum){
    memset(cur,0,sizeof(cur));
    memset(dis,0,sizeof(dis));
    memset(gap,0,sizeof(gap));
    memset(flow,0,sizeof(flow));
    int u=pre[start]=start,maxflow=0,aug=-1;
    gap[0]=nodenum;
    while(dis[start]<nodenum){
        loop:
            for(int v=cur[u];v<nodenum;v++)
                if(maze[u][v]-flow[u][v]&&dis[u]==dis[v]+1){
                    if(aug==-1||aug>maze[u][v]-flow[u][v])aug=maze[u][v]-flow[u][v];
                    pre[v]=u;
                    u=cur[u]=v;
                    if(v==end){
                        maxflow+=aug;
                        for(u=pre[u];v!=start;v=u,u=pre[u]){
                            flow[u][v]+=aug;
                            flow[v][u]-=aug;
                        }
                        aug=-1;
                    }
                    goto loop;
                }
            int mindis=nodenum-1;
            for(int v=0;v<nodenum;v++)
            if(maze[u][v]-flow[u][v]&&mindis>dis[v]){
                cur[u]=v;
                mindis=dis[v];
            }
            if((--gap[dis[u]])==0)break;
            gap[dis[u]=mindis+1]++;
            u=pre[u];
    }
    return maxflow;
}

int main(){
    return 0;
}

#include<iostream>
#include<stdio.h>
#include<string.h>
using namespace std;

const int MAXN=100010;//点数的最大值
const int MAXM=400010;//边数的最大值
const int INF=0x3f3f3f3f;
struct Edge{
    int to,next,cap,flow;
}edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],pre[MAXN],cur[MAXN];
void init(){
    tol=0;
    memset(head,-1,sizeof(head));
}
//加边，单向图三个参数，双向图四个参数
void addedge(int u,int v,int w,int rw=0){
    edge[tol].to=v;edge[tol].cap=w;edge[tol].next=head[u];
    edge[tol].flow=0;head[u]=tol++;
    edge[tol].to=u;edge[tol].cap=rw;edge[tol].next=head[v];
    edge[tol].flow=0;head[v]=tol++;
}
//输入参数：起点、终点、点的总数
//点的编号没有影响，只要输入点的总数
int sap(int start,int end,int N){
    memset(gap,0,sizeof(gap));
    memset(dep,0,sizeof(dep));
    memcpy(cur,head,sizeof(head));
    int u=start;
    pre[u]=-1;
    gap[0]=N;
    int ans=0;
    while(dep[start]<N){
        if(u==end){
            int Min=INF;
            for(int i=pre[u];i!=-1;i=pre[edge[i^1].to])
                if(Min>edge[i].cap-edge[i].flow)
                    Min=edge[i].cap-edge[i].flow;
            for(int i=pre[u];i!=-1;i=pre[edge[i^1].to]){
                edge[i].flow+=Min;
                edge[i^1].flow-=Min;
            }
            u=start;
            ans+=Min;
            continue;
        }
        bool flag=false;
        int v;
        for(int i=cur[u];i!=-1;i=edge[i].next){
            v=edge[i].to;
            if(edge[i].cap-edge[i].flow&&dep[v]+1==dep[u]){
                flag=true;
                cur[u]=pre[v]=i;
                break;
            }
        }
        if(flag){
            u=v;
            continue;
        }
        int Min=N;
        for(int i=head[u];i!=-1;i=edge[i].next)
            if(edge[i].cap-edge[i].flow&&dep[edge[i].to]<Min){
                Min=dep[edge[i].to];
                cur[u]=i;
            }
        gap[dep[u]]--;
        if(!gap[dep[u]])return ans;
        dep[u]=Min+1;
        gap[dep[u]]++;
        if(u!=start)u=edge[pre[u]^1].to;
    }
    return ans;
}

int main(){
    return 0;
}

#include<iostream>
#include<stdio.h>
#include<string.h>
using namespace std;

const int MAXN=100010;//点数的最大值
const int MAXM=400010;//边数的最大值
const int INF=0x3f3f3f3f;
struct Edge{
    int to,next,cap,flow;
}edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],cur[MAXN];
void init(){
    tol=0;
    memset(head,-1,sizeof(head));
}
void addedge(int u,int v,int w,int rw=0){
    edge[tol].to=v;edge[tol].cap=w;edge[tol].flow=0;
    edge[tol].next=head[u];head[u]=tol++;
    edge[tol].to=u;edge[tol].cap=rw;edge[tol].flow=0;
    edge[tol].next=head[v];head[v]=tol++;
}
int Q[MAXN];
void BFS(int start,int end){
    memset(dep,-1,sizeof(dep));
    memset(gap,0,sizeof(gap));
    gap[0]=1;
    int front=0,rear=0;
    dep[end]=0;
    Q[rear++]=end;
    while(front!=rear){
        int u=Q[front++];
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if(dep[v]!=-1)continue;
            Q[rear++]=v;
            dep[v]=dep[u]+1;
            gap[dep[v]]++;
        }
    }
}
int S[MAXN];
int sap(int start,int end,int N){
    BFS(start,end);
    memcpy(cur,head,sizeof(head));
    int top=0;
    int u=start;
    int ans=0;
    while(dep[start]<N){
        if(u==end){
            int Min=INF;
            int inser;
            for(int i=0;i<top;i++)
                if(Min>edge[S[i]].cap-edge[S[i]].flow){
                    Min=edge[S[i]].cap-edge[S[i]].flow;
                    inser=i;
                }
            for(int i=0;i<top;i++){
                edge[S[i]].flow+=Min;
                edge[S[i]^1].flow-=Min;
            }
            ans+=Min;
            top=inser;
            u=edge[S[top]^1].to;
            continue;
        }
        bool flag=false;
        int v;
        for(int i=cur[u];i!=-1;i=edge[i].next){
            v=edge[i].to;
            if(edge[i].cap-edge[i].flow&&dep[v]+1==dep[u]){
                flag=true;
                cur[u]=i;
                break;
            }
        }
        if(flag){
            S[top++]=cur[u];
            u=v;
            continue;
        }
        int Min=N;
        for(int i=head[u];i!=-1;i=edge[i].next)
            if(edge[i].cap-edge[i].flow&&dep[edge[i].to]<Min){
                Min=dep[edge[i].to];
                cur[u]=i;
            }
        gap[dep[u]]--;
        if(!gap[dep[u]])return ans;
        dep[u]=Min+1;
        gap[dep[u]]++;
        if(u!=start)u=edge[S[--top]^1].to;
    }
    return ans;
}

int main(){
    return 0;
}

#include<iostream>
#include<stdio.h>
#include<string.h>
using namespace std;

const int MAXN=2010;//点数的最大值
const int MAXM=1200010;//边数的最大值
const int INF=0x3f3f3f3f;
struct Edge{
    int to,next,cap,flow;
}edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
void init(){
    tol=2;
    memset(head,-1,sizeof(head));
}
void addedge(int u,int v,int w,int rw=0){
    edge[tol].to=v;edge[tol].cap=w;edge[tol].flow=0;
    edge[tol].next=head[u];head[u]=tol++;
    edge[tol].to=u;edge[tol].cap=rw;edge[tol].flow=0;
    edge[tol].next=head[v];head[v]=tol++;
}
int Q[MAXN];
int dep[MAXN],cur[MAXN],sta[MAXN];
bool bfs(int s,int t,int n){
    int front=0,tail=0;
    memset(dep,-1,sizeof(dep[0])*(n+1));
    dep[s]=0;
    Q[tail++]=s;
    while(front<tail){
        int u=Q[front++];
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if(edge[i].cap>edge[i].flow&&dep[v]==-1){
                dep[v]=dep[u]+1;
                if(v==t)return true;
                Q[tail++]=v;
            }
        }
    }
    return false;
}
int dinic(int s,int t,int n){
    int maxflow=0;
    while(bfs(s,t,n)){
        for(int i=0;i<n;i++)cur[i]=head[i];
        int u=s,tail=0;
        while(cur[s]!=-1){
            if(u==t){
                int tp=INF;
                for(int i=tail-1;i>=0;i--)
                    tp=min(tp,edge[sta[i]].cap-edge[sta[i]].flow);
                maxflow+=tp;
                for(int i=tail-1;i>=0;i--){
                    edge[sta[i]].flow+=tp;
                    edge[sta[i]^1].flow-=tp;
                    if(edge[sta[i]].cap-edge[sta[i]].flow==0)
                        tail=i;
                }
                u=edge[sta[tail]^1].to;
            }
            else if(cur[u]!=-1&&edge[cur[u]].cap>edge[cur[u]].flow&&dep[u]+1==dep[edge[cur[u]].to]){
                sta[tail++]=cur[u];
                u=edge[cur[u]].to;
            }
            else{
                while(u!=s&&cur[u]==-1)
                    u=edge[sta[--tail]^1].to;
                cur[u]=edge[cur[u]].next;
            }
        }
    }
    return maxflow;
}

int main(){
    return 0;
}