csoj S0125 离散数学

只想到了二分图的做法

#include <bits/stdc++.h>
/*
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
*/
using namespace std;

const double eps = 1e-10;
const double pi = 3.1415926535897932384626433832795;
const double eln = 2.718281828459045235360287471352;

#define f(i, a, b) for (int i = a; i <= b; i++)
#define scan(x) scanf("%d", &x)
#define mp make_pair
#define pb push_back
#define lowbit(x) (x&(-x))

#define fi first
#define se second
#define SZ(x) int((x).size())
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define summ(a) (accumulate(all(a), 0ll))

typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;

using ll=long long;

int n,m,k,ans,tot=1,hd[(int)2e5+9],cur[(int)2e5+9],s,t,dep[(int)2e5+9];
vector<pii> v;
map<pii,int> exi;
pii dir[4]={{1,0},{0,1},{-1,0},{0,-1}};

map<pii,int> cov;
struct Edge{
    int to,nxt,v;
}e[(int)1e7+9];
void add(int u,int v){
    e[++tot]={v,hd[u],1},hd[u]=tot;
    e[++tot]={u,hd[v],0},hd[v]=tot;
}

bool bfs(int st,int en){
    for(int i=0;i<=t;++i)dep[i]=0;
    queue<int>q;
    memcpy(cur,hd,sizeof(hd));
    q.push(st);
    dep[st]=1;
    while(!q.empty()){
        auto u=q.front();
        q.pop();
        for(int eg=hd[u];eg;eg=e[eg].nxt){
            if(!dep[e[eg].to]&&e[eg].v>0){
                dep[e[eg].to]=dep[u]+1;
                q.push(e[eg].to);
            }
        }
    }
    return !!dep[en];
}

int dfs(int u,int en,int flow){
    if(u==en)return flow;
    int r=flow;
    for(int eg=cur[u];eg&&r;eg=e[eg].nxt){
        cur[u]=eg;
        if(e[eg].v>0&&dep[e[eg].to]==dep[u]+1){
            int c=dfs(e[eg].to,en,min(r,e[eg].v));
            r-=c;
            e[eg].v-=c,e[eg^1].v+=c;
        }
    }
    return flow-r;
}

int dinic(int st,int en){
    int ret=0;
    while(bfs(st,en)){
        ret+=dfs(st,en,0x3f3f3f3f);
    }
    return ret;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>n>>m>>k;
    v.resize(k+1);
    for(int i=1,x,y;i<=k;++i){
        cin>>x>>y;
        cov[{x,y}]=i,v[i]={x,y},exi[{x,y}]=1;
    }
    s=2*k+1,t=2*k+2;
    for(int i=1;i<=k;++i){
        auto it=v[i];
        auto p=cov[it];
        add(s,p),add(p+k,t);
        for(auto [aa,bb]:dir){
            aa+=it.first,bb+=it.second;
            //cerr<<it.first<<"--"<<it.second<<":::"<<aa<<"--"<<bb<<"\n";
            if(exi.count({aa,bb})){
                auto pp=cov[{aa,bb}];
                add(p,pp+k);
            }
        }
    }
    bool ok=(dinic(s,t)==k);
    cout<<(ok?"YES\n":"NO\n");
    return 0;
}