魔术球问题

https://www.luogu.org/problemnew/show/P2765

题解：网络流+最大流

/*
*@Author:   STZG
*@Language: C++
*/
#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
#define endl "\n"
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=10000+10;
const int M=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int s,t,n,m,k,p,l,r,u,v;
int ans,cnt,flag,temp,sum,maxflow;
int dis[N];
int pre[N],head[N];
bool vis[N];
struct node{
    int u,v;
    ll c;
    node(){};
    node(int u,int v,ll cap):u(u),v(v),c(cap){}
};
vector<node>edge;
vector<int>G[N];
int find(int x){return pre[x]==x?x:pre[x]=find(pre[x]);}
void Addedge(int u,int v,ll cap){
    edge.push_back({u,v,cap});
    edge.push_back({v,u,0});
    int sz=edge.size();
    G[u].push_back(sz-2);
    G[v].push_back(sz-1);
}
bool bfs(int u){
    memset(dis,-1,sizeof(dis));
    dis[u]=0;
    queue<int>q;
    q.push(u);
    while(!q.empty()){
        int u=q.front();
        q.pop();
        for(int i=0,j=G[u].size();i<j;i++){
            node e=edge[G[u][i]];
            if(dis[e.v]<0&&e.c>0){
                dis[e.v]=dis[u]+1;
                q.push(e.v);
            }
        }
    }
    return dis[t]>0;
}
ll dfs(int u,ll flow){
    if(u==t){
        return flow;
    }
    ll now;
    for(int i=0,j=G[u].size();i<j;i++){
        node e=edge[G[u][i]];
        if(e.c>0&&dis[e.v]==dis[u]+1&&(now=dfs(e.v,min(flow,e.c)))){
            edge[G[u][i]].c-=now;
            edge[G[u][i]^1].c+=now;
            pre[u >> 1] = e.v >> 1;
            return now;
        }
    }
    return 0;
}
ll dinic(){
    ll res;
    ll maxflow=0;
    while(bfs(s)){
        while((res=dfs(s,INF))){
            maxflow+=res;
        }
    }
    return maxflow;
}
void init(){
    s=0;
    t=10000;
    edge.clear();
    for(int i=s;i<=t;i++)G[i].clear();
    ans=0;
    maxflow=0;
    memset(vis,0,sizeof(vis));
    memset(pre,0,sizeof(pre));
}
int main()
{
#ifdef DEBUG
	freopen("input.in", "r", stdin);
	//freopen("output.out", "w", stdout);
#endif
    //ios::sync_with_stdio(false);
    //cin.tie(0);
    //cout.tie(0);
    //scanf("%d",&t);
    //while(t--){
    while(~scanf("%d",&n)){
        init();
        int all=0;
        int num=0;
        while(all<=n){
            num++;
            Addedge(s,num<<1,1);Addedge((num<<1)|1,t,1);
            for(int i=sqrt(num)+1;i*i<2*num;++i)
            Addedge((i*i-num)<<1,(num<<1)|1,1);
            if(!dinic()) head[++all]=num;
        }
        printf("%d\n",--num);
        for(int i = 1; i <= n; i++) {
            if(!vis[head[i]]) {
                for(int u = head[i]; u != 0 && u != (t >> 1); u = pre[u]) {
                    vis[u] = true;
                    printf("%d%c",u," \n"[pre[u]==0||pre[u] == (t >> 1)]);
                }
            }
        }
    }

    //}

#ifdef DEBUG
	printf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC);
#endif
    //cout << "Hello world!" << endl;
    return 0;
}