Editorial for Hai Bộ Bài


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#include <bits/stdc++.h>

#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>


#include <vector>

namespace atcoder {

namespace internal {

template <class T> struct simple_queue {
    std::vector<T> payload;
    int pos = 0;
    void reserve(int n) { payload.reserve(n); }
    int size() const { return int(payload.size()) - pos; }
    bool empty() const { return pos == int(payload.size()); }
    void push(const T& t) { payload.push_back(t); }
    T& front() { return payload[pos]; }
    void clear() {
        payload.clear();
        pos = 0;
    }
    void pop() { pos++; }
};

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

template <class Cap> struct mf_graph {
  public:
    mf_graph() : _n(0) {}
    explicit mf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap});
        g[to].push_back(_edge{from, from_id, 0});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
    };

    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result;
        for (int i = 0; i < m; i++) {
            result.push_back(get_edge(i));
        }
        return result;
    }
    void change_edge(int i, Cap new_cap, Cap new_flow) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        assert(0 <= new_flow && new_flow <= new_cap);
        auto& _e = g[pos[i].first][pos[i].second];
        auto& _re = g[_e.to][_e.rev];
        _e.cap = new_cap - new_flow;
        _re.cap = new_flow;
    }

    Cap flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    Cap flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        std::vector<int> level(_n), iter(_n);
        internal::simple_queue<int> que;

        auto bfs = [&]() {
            std::fill(level.begin(), level.end(), -1);
            level[s] = 0;
            que.clear();
            que.push(s);
            while (!que.empty()) {
                int v = que.front();
                que.pop();
                for (auto e : g[v]) {
                    if (e.cap == 0 || level[e.to] >= 0) continue;
                    level[e.to] = level[v] + 1;
                    if (e.to == t) return;
                    que.push(e.to);
                }
            }
        };
        auto dfs = [&](auto self, int v, Cap up) {
            if (v == s) return up;
            Cap res = 0;
            int level_v = level[v];
            for (int& i = iter[v]; i < int(g[v].size()); i++) {
                _edge& e = g[v][i];
                if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
                Cap d =
                    self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));
                if (d <= 0) continue;
                g[v][i].cap += d;
                g[e.to][e.rev].cap -= d;
                res += d;
                if (res == up) return res;
            }
            level[v] = _n;
            return res;
        };

        Cap flow = 0;
        while (flow < flow_limit) {
            bfs();
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = dfs(dfs, t, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    std::vector<bool> min_cut(int s) {
        std::vector<bool> visited(_n);
        internal::simple_queue<int> que;
        que.push(s);
        while (!que.empty()) {
            int p = que.front();
            que.pop();
            visited[p] = true;
            for (auto e : g[p]) {
                if (e.cap && !visited[e.to]) {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }

  private:
    int _n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

}  // namespace atcoder

using namespace std;
using namespace atcoder;

struct dsu {
    vector<int> par, fre;

    dsu(int n) : par(n, -1), fre(n, 1) {}

    int trace(int u) { return par[u] < 0 ? u : par[u] = trace(par[u]); }

    int connect(int u, int v) {
        if ((u = trace(u)) == (v = trace(v))) {
            return u;
        }
        if (par[u] > par[v]) {
            swap(par[u], par[v]);
        }
        par[u] += par[v]; par[v] = u;
        fre[u] += fre[v];
        return u;
    }

    int& operator[](int u) { return fre[u]; }
};

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int t; cin >> t;
    while (t--) {
        int n, m; cin >> n >> m;
        vector<pair<int, int>> a(n), b(m);
        for (int i = 0; i < n; i++) {
            cin >> a[i].first >> a[i].second;
            a[i].first--; a[i].second--;
        }
        for (int i = 0; i < m; i++) {
            cin >> b[i].first >> b[i].second;
            b[i].first--; b[i].second--;
        }
        int value_set = 2 * (n + m);
        auto gen_con_components = [&](vector<pair<int, int>>& a, vector<int>& com) {
            dsu dsu(value_set);
            for (auto [u, v] : a) {
                int p = dsu.connect(u, v);
                dsu[p]--;
            }
            for (int i = 0; i < value_set; i++) {
                int p = dsu.trace(i);
                if (dsu[p] < 0) {
                    return false;
                } else if (dsu[p] > 0) {
                    com[i] = p;
                }
            }
            return true;
        };
        vector<int> com_a(value_set, -1), com_b(value_set, -1);
        if (!gen_con_components(a, com_a) || !gen_con_components(b, com_b)) {
            cout << "-1\n";
            continue;
        }
        mf_graph<int> remove_values(2 * value_set + 2);
        vector<int> rep_edg(value_set, -1);
        auto left_side = [&](int u) { return u + 2; };
        auto right_side = [&](int u) { return u + value_set + 2; };
        int src = 0, snk = 1;
        for (int i = 0; i < value_set; i++) {
            remove_values.add_edge(src, left_side(i), 1);
            remove_values.add_edge(right_side(i), snk, 1);
            if (com_a[i] != -1 && com_b[i] != -1) {
                rep_edg[i] = remove_values.add_edge(left_side(com_a[i]), right_side(com_b[i]), 1);
            }
        }
        cout << value_set - remove_values.flow(src, snk) << '\n';

        vector<bool> ok(value_set, true);
        for (int v = 0; v < value_set; v++) {
            if (rep_edg[v] != -1 && remove_values.get_edge(rep_edg[v]).flow == 1) {
                ok[v] = false;
            }
        }
        auto construct = [&](vector<pair<int, int>>& a) {
            int n = a.size();
            vector<pair<int, int>> choice(n);
            mf_graph<int> mf(n + value_set + 2);
            int src = 0, snk = 1;
            auto card = [&](int i) { return 2 + i; };
            auto value = [&](int v) { return 2 + n + v; };
            for (int i = 0; i < n; i++) {
                auto [l, r] = a[i];
                mf.add_edge(src, card(i), 1);
                int el = mf.add_edge(card(i), value(l), 1);
                int er = mf.add_edge(card(i), value(r), 1);
                choice[i] = {el, er};
            }
            for (int v = 0; v < value_set; v++) {
                if (ok[v]) {
                    mf.add_edge(value(v), snk, 1);
                }
            }
            assert(mf.flow(src, snk) == n);
            for (int i = 0; i < n; i++) {
                auto [l, r] = a[i];
                auto [el, er] = choice[i];
                int val = mf.get_edge(el).flow == 1 ? l : r;
                cout << val + 1 << " \n"[i + 1 == n];
            }
        };
        construct(a); construct(b);
    }
}

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