ZOJ4100 Vertices in the Pocket（并查集+权值线段树+二分）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=1e6+14;
ll father[maxn];
ll num[maxn];
ll N,Q;
ll block;
ll ans;//表示在当前的图下，不增加连通块数量所能增加的边数 

//线段树部分
struct node {
    ll l,r;
    ll cnt;//大小为这样的连通块的数量
    ll sum;//连通块的总的点数
    ll pfh;//各连通块之间点数的平方和 
}segTree[maxn*4]; 
void pushup (ll i) {
    segTree[i].cnt=segTree[i<<1].cnt+segTree[i<<1|1].cnt;
    segTree[i].sum=segTree[i<<1].sum+segTree[i<<1|1].sum;
    segTree[i].pfh=segTree[i<<1].pfh+segTree[i<<1|1].pfh; 
}
void build (ll i,ll l,ll r) {
    segTree[i].l=l;
    segTree[i].r=r;
    if (l==r) {
        segTree[i].pfh=l==1?N:0;
        segTree[i].sum=l==1?N:0;
        segTree[i].cnt=l==1?N:0;
        return;
    }
    ll mid=(l+r)>>1;
    build(i<<1,l,mid);
    build(i<<1|1,mid+1,r);
    pushup(i); 
}
void update (ll i,ll t,ll b) {
    if (segTree[i].l==segTree[i].r) {
        segTree[i].cnt+=b;
        segTree[i].sum+=b*t;
        segTree[i].pfh+=b*t*t;
        return;
    }
    ll mid=(segTree[i].l+segTree[i].r)>>1;
    if (t<=mid) update(i<<1,t,b);
    else update(i<<1|1,t,b);
    pushup(i);
}
ll ask (ll i,ll k,ll sum) {
    if (segTree[i].l==segTree[i].r) {
        ll l=1;
        ll r=segTree[i].cnt;
        ll mid=(l+r)>>1;
        while (l<r) {
            mid=(l+r)>>1;
            ll tmp=mid*(mid-1)/2*segTree[i].l*segTree[i].l+mid*segTree[i].l*sum;
            if (tmp>=k) r=mid;
            else l=mid+1;
        }
        return l;
    }
    ll mid=(segTree[i].l+segTree[i].r)>>1;
    ll tmp=(segTree[i<<1|1].sum*segTree[i<<1|1].sum-segTree[i<<1|1].pfh)/2+segTree[i<<1|1].sum*sum;
    if (tmp<k)
        return segTree[i<<1|1].cnt+ask(i<<1,k-tmp,sum+segTree[i<<1|1].sum);
    else return ask(i<<1|1,k,sum);
}
void init () {
    for (int i=1;i<=N;i++) {
        num[i]=1;
        father[i]=i;
    }
    block=N;
    build(1,1,N);
    ans=0;
}

ll findfather (ll x) {
    ll a=x;
    while (x!=father[x]) x=father[x];
    while (a!=father[a]) {
        ll z=a;
        a=father[a];
        father[z]=x;
    }
    return x;
}

void Union (int a,int b) {
    ll faA=findfather(a);
    ll faB=findfather(b);
    if (faA==faB) {
        ans--;
        return;
    }
    if (faA>faB) swap(faA,faB);
    update(1,num[faA],-1);
    update(1,num[faB],-1);
    
    father[faA]=faB;
    block--;
    ans+=num[faB]*num[faA]-1;
    num[faB]+=num[faA];
    num[faA]=0;
    update(1,num[faB],1);
}

ll getMin (ll k) {
    return max(1LL,block-k); 
}

ll getMax (ll k) {
    if (k<=ans) return block;
    k-=ans;
    ll ck=ask(1,k,0);
    return block-ck+1;
}

int main () {
    int T;
    scanf("%d",&T);
    while (T--) {
        scanf("%lld %lld",&N,&Q);
        init(); 
        ll a,b;
        ll query;
        while (Q--) {
            scanf("%lld",&query);
            if (query==1) {
                scanf("%lld %lld",&a,&b);
                Union(a,b);
            }
            else {
               scanf("%lld",&a);
               printf("%lld %lld
",getMin(a),getMax(a));
            }
        }
    }
    return 0;
}