UVA - 11082 Matrix Decompressing （最大流，技巧）

很经典的网络流模型，行编号和列编号分别看成一个点，行和列和分别看出容量，一个点(x,y)看出是一条边，边的容量下界是1，所以先减去1，之后在加上就好了。

建图的时候注意分配好编号，解从残留网络中的边找。

前向星建图的话，打印解会比较麻烦。

#include<bits/stdc++.h>
using namespace std;

const int maxn = ;

struct Edge
{
    int v,cap,flow;
};

vector<Edge> edges;
#define PB push_back

vector<int> G[maxn];

void AddEdge(int u,int v,int c)
{
    G[u].PB(edges.size());
    edges.PB(Edge{v,c,});
    G[v].PB(edges.size());
    edges.PB(Edge{u,,});
}

const int INF = 0x3f3f3f3f;
int S,T;
int vcnt;
bool vis[maxn];
int d[maxn];
int q[maxn<<];

bool bfs()
{
    memset(vis,,sizeof(bool)*vcnt);
    int l = ,r = ;
    q[r++] = S; vis[S] = true;
    while(r>l){
        int u = q[l++];
        for(int i = ; i < G[u].size(); i++){
            Edge &e = edges[G[u][i]];
            if(!vis[e.v] && e.cap >e.flow){
                vis[e.v] = true;
                d[e.v] = d[u]+;
                q[r++] = e.v;
            }
        }
    }
    return vis[T];
}

int cur[maxn];
int dfs(int u,int a)
{
    if(u == T||!a) return a;
    int flow = , f;
    for(int &i = cur[u]; i < G[u].size(); i++){
        Edge &e = edges[G[u][i]];
        if(d[e.v] == d[u]+ && (f = dfs(e.v,min(a,e.cap-e.flow)))>){
            e.flow += f;
            edges[G[u][i]^].flow -= f;
            flow += f;
            a -= f;
            if(!a) break;
        }
    }
    return flow;
}

int MaxFlow()
{
    int flow = ;
    while(bfs()){
        memset(cur,,sizeof(int)*vcnt);
        flow += dfs(S,INF);
    }
    return flow;
}

const int N = ;
int rid[N],cid[N];

void init()
{
    vcnt = ;
    edges.clear();
}

int main()
{
    //freopen("in.txt","r",stdin);
    S = ; T = ;
    int testCase; scanf("%d",&testCase);
    int mcnt = ;
    while(testCase--){
        init();
        int R,C,cap,pre; scanf("%d%d",&R,&C);

        for(int i = , M = R+C+; i < M; i++) G[i].clear();
        pre = ;
        for(int i = ; i < R; i++) {
            rid[i] = vcnt++;
            scanf("%d",&cap);
            AddEdge(S,rid[i],cap-pre-C);
            pre = cap;
        }
        pre = ;
        for(int i = ; i < C; i++){
            cid[i] = vcnt++;
            scanf("%d",&cap);
            AddEdge(cid[i],T,cap-pre-R);
            pre = cap;
        }

        for(int i = ; i < R; i++)
        for(int j = ; j < C; j++){
            AddEdge(rid[i],cid[j],);
        }

        MaxFlow();

        printf("Matrix %d\n",++mcnt);
        for(int i = ; i < R; i++){
            int k = , u = rid[i];
            for(int j = ; j < G[u].size(); j++){
                Edge &e = edges[G[u][j]];
                if(e.v == cid[k]){
                    printf("%d%c",e.flow+,++k==C?'\n':' ');
                    if(k == C) break;
                }
            }
        }

        if(testCase) putchar('\n');
    }
    return ;
}