CodeForces-1243D 0 - 1 MST

传送门：CodeForces-1243D

思路分析

显然，答案为补图中连通块的数量-1
用一个set维护补图中剩余未连通的点
遍历所有点，如果在set中，说明连通块数量+1
然后计算包含这个点$u$的补图连通块
如果set中的点$v$与$u$之间没有连边，说明在补图里他们是连通的
在set里面删去这个点，最后再计算包含$v$的连通块

样例输入

6 11
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6

样例输出

2

AC代码

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
#define ls x<<1
#define rs x<<1|1
#define fi first
#define se second
#define ll long long
#define pb push_back
#define mp make_pair
#define fun function
#define sz(x) (x).size()
#define lowbit(x) (x)&(-x)
#define all(x) (x).begin(),(x).end()
#define mem(a,b) memset(a,b,sizeof(a))

namespace FastIO {
#define BUF_SIZE 100000
#define OUT_SIZE 100000
    bool IOerror=0;
    inline char nc() {
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if(p1==pend) {
            p1=buf;
            pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if(pend==p1) {
                IOerror=1;
                return -1;
            }
        }
        return *p1++;
    }
    inline bool blank(char ch) {
        return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';
    }
    template<class T> inline bool read(T &x) {
        bool sign=0;
        char ch=nc();
        x=0;
        for(; blank(ch); ch=nc());
        if(IOerror)return false;
        if(ch=='-')sign=1,ch=nc();
        for(; ch>='0'&&ch<='9'; ch=nc())x=x*10+ch-'0';
        if(sign)x=-x;
        return true;
    }
    template<class T,class... U>bool read(T& h,U&... t) {
        return read(h)&&read(t...);
    }
#undef OUT_SIZE
#undef BUF_SIZE
};
using namespace std;
using namespace FastIO;
using namespace __gnu_pbds;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> rbtree;

const int INF = 0x3f3f3f3f;
const int N= 1e5+10;

set<int>s,e[N];

void dfs(int u){
    vector<int>temp;
    for(auto v:s) if(!e[u].count(v)) temp.push_back(v);
    for(auto v:temp) s.erase(v);
    for(auto v:temp) dfs(v);
}

int main() {

#ifdef xiaofan
    freopen("1.in","r",stdin);
    freopen("1.out","w",stdout);
#endif

    int n,m;
    read(n,m);
    for(int i=1;i<=m;i++){
        int u,v;
        read(u,v);
        e[u].insert(v);
        e[v].insert(u);
    }
    for(int i=1;i<=n;i++) s.insert(i);
    int ans=0;
    for(int i=1;i<=n;i++){
        if(s.count(i)){
            ans++;
            dfs(i);
        }
    }
    cout<<ans-1<<endl;




    return 0;
}