#include "Graph.h"
#include <queue>
#include <algorithm>
#include <functional>

int Graph::checkBipart(std::vector<char>& marks) const {
    marks.assign(n + 1, 0);
    auto nb = toSimpleAdj();

    std::queue<int> q;
    for (int s = 1; s <= n; ++s) {
        if (marks[s]) continue;
        marks[s] = 'A';
        q.push(s);
        while (!q.empty()) {
            int u = q.front();
            q.pop();
            char opposite = (marks[u] == 'A') ? 'B' : 'A';
            for (int v : nb[u]) {
                if (marks[v] == 0) {
                    marks[v] = opposite;
                    q.push(v);
                } else if (marks[v] == marks[u]) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

std::vector<std::pair<int, int>> Graph::getMaximumMatchingBipart() const {
    std::vector<std::pair<int, int>> matching;
    std::vector<char> marks;
    if (!checkBipart(marks)) return matching;

    auto nb = toSimpleAdj();
    std::vector<int> match(n + 1, 0); // right vertex -> matched left vertex
    std::vector<char> used(n + 1, 0);

    std::function<bool(int)> augment = [&](int u) -> bool {
        used[u] = 1;
        for (int v : nb[u]) {
            if (marks[v] != 'B') continue;
            if (match[v] == 0 || (!used[match[v]] && augment(match[v]))) {
                match[v] = u;
                return true;
            }
        }
        return false;
    };

    for (int u = 1; u <= n; ++u) {
        if (marks[u] != 'A') continue;
        std::fill(used.begin(), used.end(), (char)0);
        augment(u);
    }
    for (int v = 1; v <= n; ++v)
        if (match[v] != 0) matching.push_back({match[v], v});
    return matching;
}