Codeforces-solutions/ITMO Academy: pilot course - Disjoint Sets Union - Step 3/B. Number of Connected Components on Segments.cpp

/* Problem URL: https://codeforces.com/edu/course/2/lesson/7/3/practice/contest/289392/problem/B */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m;
    cin >> n >> m;

    vi dsu(n);
    vi size(n);
    rep(i, n) {
        dsu[i] = i;
        size[i] = 1;
    }

    stack<pair<int, int>> ops;

    int c = n;

    function<int(int)> find_p = [&](int i) {
        if (dsu[i] == i) {
            return i;
        }
        return find_p(dsu[i]);
    };

    auto join = [&](int a, int b) {
        a = find_p(a);
        b = find_p(b);

        if (a == b) {
            return;
        }

        if (size[a] < size[b]) {
            swap(a, b);
        }

        dsu[b] = a;

        if (size[a] == size[b]) {
            size[a]++;
        }

        ops.emplace(a, b);
        c--;
    };

    auto save = [&]() {
        ops.emplace(-1, -1);
    };

    auto rollback = [&]() {
        while (ops.top().first != -1) {
            auto [a, b] = ops.top();
            ops.pop();

            if (size[b] == size[a] - 1) {
                size[a]--;
            }

            dsu[b] = b;
            c++;
        }
        ops.pop();
    };

    V<pair<int, int>> edges(m);
    repv(i, edges) {
        cin >> i.first >> i.second;
        i.first--, i.second--;
    }

    int q;
    cin >> q;

    static int len = sqrt(m) + 1;

    struct query {
        int l;
        int r;
        int i;

        bool operator<(query &b) {
            if (l / len != b.l / len) {
                return l / len < b.l / len;
            }
            return r < b.r;
        }
    };

    V<query> queries(q);
    rep(i, q) {
        cin >> queries[i].l >> queries[i].r;
        queries[i].l--, queries[i].r--;

        queries[i].i = i;
    }
    sortv(queries);
    vi ans(q);

    int now = 0;
    int calc = 1;
    repv(i, queries) {
        int cur = i.l / len;
        if (cur > now) {
            now = cur;
            calc = cur + 1;
            while (!ops.empty()) {
                ops.pop();
            }
            rep(i, n) {
                dsu[i] = i;
                size[i] = 1;
            }
            c = n;
        }

        int stop = i.r / len;
        if (cur == stop) {
            save();
            nrep(j, i.l, i.r + 1) {
                join(edges[j].first, edges[j].second);
            }
            ans[i.i] = c;
            rollback();
            continue;
        }

        while (calc < stop) {
            nrep(i, calc * len, (calc + 1) * len) {
                join(edges[i].first, edges[i].second);
            }
            calc++;
        }

        save();
        nrep(j, calc * len, i.r + 1) {
            join(edges[j].first, edges[j].second);
        }

        nrep(j, i.l, min((now + 1) * len, m)) {
            join(edges[j].first, edges[j].second);
        }

        ans[i.i] = c;
        rollback();
    }

    repv(i, ans) {
        cout << i << '\n';
    }
}