Codeforces 1140F Extending Set of Points (线段树分治+并查集)

这题有以下几个步骤

1.离线处理出每个点的作用范围

2.根据线段树得出作用范围

3.根据分治把每个范围内的点记录和处理

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 3e5 + 50;
typedef pair<int, int> pii;
#define bug cout << "bug" << endl;
vector<pii> rt[maxn << 2];
void update(int o,int l,int r,int ql,int qr,pii pi){
    //cout << "o=" << o <<" l="<<l<<" r="<<r<<" ql="<<ql<<" qr="<<qr<<endl;
    if(ql<=l&&qr>=r){
        rt[o].push_back(pi);
        return;
    }
    int mid = (l + r)/2;
    if(ql<=mid)
        update(o << 1, l, mid, ql, qr, pi);
    if(qr>mid)
        update(o << 1 | 1, mid + 1, r, ql, qr, pi);
}

int fa[maxn << 1];
ll sz[maxn << 1], szx[maxn << 1], szy[maxn << 1];

int find(int x){
    if(fa[x]==x)
        return x;
    return find(fa[x]);
}
ll value;
ll ans[maxn];

void ins(int x,int y,stack<pii> &st){
    int xx = find(x);
    int yy = find(y);
    if(xx==yy)
        return;
    if(sz[xx]<sz[yy])
        swap(xx, yy);
    st.push({xx, yy});
    value -= 1LL*szx[yy] * szy[yy];
    value -= 1LL*szx[xx] * szy[xx];
    sz[xx] += 1LL*sz[yy];
    szx[xx] += 1LL*szx[yy];
    szy[xx] += 1LL*szy[yy];
    value += 1LL*szx[xx] * szy[xx];
    fa[yy] = fa[xx];
}
void del(stack<pii> &st){
    while(!st.empty()){
        int x = st.top().first;
        int y = st.top().second;
        st.pop();
        value -= 1LL*szx[x] * szy[x];
        sz[x] -= 1LL*sz[y];
        szx[x] -= 1LL*szx[y];
        szy[x] -= 1LL*szy[y];
        fa[y] = y;
        value += 1LL*szx[x] * szy[x];
        value += 1LL*szx[y] * szy[y];
    }
}
void dfs(int o,int l,int r){
    //cout << "o=" << o << " l=" << l << " r=" << r << endl;
    stack<pii> st;
    for(auto i:rt[o]){
        int x = i.first;
        int y = i.second;
        ins(x, y, st);
    }
    if(l==r)
        ans[l] = value;
    else{
        int mid = (l + r) / 2;
        dfs(o << 1, l, mid);
        dfs(o << 1 | 1, mid + 1, r);
    }
    del(st);
}

map<pii, int> mp;

int main(){
    int q;
    //freopen("in.txt", "r", stdin);
    //freopen("out.txt", "w", stdout);
    cin >> q;
    for (int i = 1; i <= q;i++){
        int x, y;
        cin >> x >> y;
        y += 3e5;
        pii pi = make_pair(x, y);
        if(mp.find(pi)==mp.end()){
            mp[pi] = i;
        }
        else{
            update(1, 1, q, mp[pi], i - 1, pi);
            mp.erase(pi);
        }
    }
    for(auto i:mp){
        update(1, 1, q, i.second, q, i.first);
    }
    for (int i = 1; i <= 3e5;i++){
        fa[i] = i;
        sz[i] = 1;
        szx[i] = 1;
    }
    for (int i = 3e5 + 1; i <= 6e5;i++){
        fa[i] = i;
        szy[i] = 1;
        sz[i] = 1;
    }
    dfs(1, 1, q);
    for (int i = 1; i <= q;i++){
        cout << ans[i] << " ";
    }
        return 0;
}