cf976f Minimal k-covering

枚举 \(k\)，对于每个点 \(i\) 我们最多删 \(deg_i-k\) 条边，就源点向第一部、第二部向汇点连边，容量是 \(deg_i-k\)，原边连上，容量是 \(1\)，这样每流过一条原边在网络流图中的边时，就代表这条边可以删掉。也即没有流过的边就是 \(k\) 时的答案

#include <iostream>
#include <cstring>
#include <cstdio>
#include <vector>
#include <queue>
using namespace std;
int nu, nv, n, m, ss, tt, hea[4005], deg[4005], cnt, maxFlow, lev[4005], cur[4005];
const int oo=0x3f3f3f3f;
queue<int> d;
vector<int> vec[4005];
struct Edge{
    int too, nxt, val;
}edge[50005], orz[2005];
void add_edge(int fro, int too, int val){
    edge[cnt].nxt = hea[fro];
    edge[cnt].too = too;
    edge[cnt].val = val;
    hea[fro] = cnt++;
}
void addEdge(int fro, int too, int val){
    add_edge(fro, too, val);
    add_edge(too, fro, 0);
}
bool bfs(){
    memset(lev, 0, sizeof(lev));
    lev[ss] = 1;
    d.push(ss);
    while(!d.empty()){
        int x=d.front();
        d.pop();
        for(int i=hea[x]; i!=-1; i=edge[i].nxt){
            int t=edge[i].too;
            if(!lev[t] && edge[i].val>0){
                lev[t] = lev[x] + 1;
                d.push(t);
            }
        }
    }
    return lev[tt]!=0;
}
int dfs(int x, int lim){
    if(x==tt)   return lim;
    int addFlow=0;
    for(int &i=cur[x]; i!=-1; i=edge[i].nxt){
        int t=edge[i].too;
        if(lev[t]==lev[x]+1 && edge[i].val){
            int tmp=dfs(t, min(lim-addFlow, edge[i].val));
            edge[i].val -= tmp;
            edge[i^1].val += tmp;
            addFlow += tmp;
            if(addFlow==lim)    break;
        }
    }
    return addFlow;
}
void dinic(){
    while(bfs()){
        for(int i=ss; i<=tt; i++)   cur[i] = hea[i];
        maxFlow += dfs(ss, oo);
    }
}
int main(){
    memset(hea, -1, sizeof(hea));
    cin>>nu>>nv>>m;
    n = nu + nv;
    ss = 0; tt = n + 1;
    int minDeg=0x3f3f3f3f;
    for(int i=1; i<=m; i++){
        scanf("%d %d", &orz[i].too, &orz[i].nxt);
        orz[i].nxt += nu;
        deg[orz[i].too]++;
        deg[orz[i].nxt]++;
    }
    for(int i=1; i<=n; i++)
        minDeg = min(minDeg, deg[i]);
    for(int i=1; i<=nu; i++)
        addEdge(ss, i, deg[i]-minDeg-1);
    for(int i=1; i<=nv; i++)
        addEdge(nu+i, tt, deg[nu+i]-minDeg-1);
    int tmp=cnt;
    for(int i=1; i<=m; i++)
        addEdge(orz[i].too, orz[i].nxt, 1);
    for(int i=minDeg; i>=0; i--){
        for(int j=0; j<tmp; j+=2)
            edge[j].val++;
        dinic();
        for(int j=tmp; j<cnt; j+=2)
            if(edge[j].val)
                vec[i].push_back((j-tmp)/2+1);
    }
    for(int i=0; i<=minDeg; i++){
        printf("%d ", vec[i].size());
        for(int j=0; j<vec[i].size(); j++)
            printf("%d ", vec[i][j]);
        printf("\n");
    }
    return 0;
}