graph/test/enumerate_cliques.aoj2306.test.cpp

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• Last update: 2023-03-10 15:00:17+09:00
• Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2306

Depends on

• Enumerate cliques （グラフのクリーク全列挙） (graph/enumerate_cliques.hpp)

Code

#include "../enumerate_cliques.hpp"
#include <iostream>
#include <vector>
using namespace std;

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2306"

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

    int N, M;
    cin >> N >> M;
    vector F(N, vector<int>(N));
    enumerate_cliques ec(N);
    while (M--) {
        int u, v, f;
        cin >> u >> v >> f;

        --u, --v;
        ec.add_bi_edge(u, v);

        F[u][v] = max(F[u][v], f);
        F[v][u] = max(F[v][u], f);
    }
    int ret = 0;

    auto op = [&](const std::vector<int> &clique) -> void {
        if (clique.size() <= 1) return;
        int tmp = 0;
        for (int s : clique) {
            int a = 1 << 30;
            for (int t : clique) {
                if (s != t) a = min(a, F[s][t]);
            }
            tmp += a;
        }
        ret = max(ret, tmp);
    };
    ec.run(op);

    cout << ret << endl;
}

#line 2 "graph/enumerate_cliques.hpp"

/**
 * @file enumerate_cliques.hpp
 * @brief Enumerate all cliques of given undirected graph
 * @author hitonanode
 * @date 2023/03/10
 */

#include <algorithm>
#include <cassert>
#include <numeric>
#include <queue>
#include <utility>
#include <vector>

// Complexity: O(2^sqrt(2m) * n)
// Verify: https://judge.yosupo.jp/problem/enumerate_cliques (~1ms for n <= 100, m <= 100)
// p.15, https://www.slideshare.net/wata_orz/ss-12131479
struct enumerate_cliques {
    std::vector<std::vector<int>> to;
    std::vector<std::pair<int, int>> edges;

    int n() const { return to.size(); }
    int m() const { return edges.size(); }

    enumerate_cliques(int n_) : to(n_) {}

    void add_bi_edge(int u, int v) {
        assert(0 <= u and u < n());
        assert(0 <= v and v < n());
        if (u != v) edges.emplace_back(std::minmax(u, v));
    }

    // Build `to`
    void precalc() {
        std::sort(edges.begin(), edges.end());
        edges.erase(std::unique(edges.begin(), edges.end()), edges.end());

        for (auto &vec : to) vec.clear();
        for (auto [u, v] : edges) to.at(u).push_back(v), to.at(v).push_back(u);
        for (auto &vec : to) std::sort(vec.begin(), vec.end());
    }

    template <class F>
    void bruteforce(const std::vector<int> &cand_vs, int prefix_use, F op) const {
        const int k = cand_vs.size();
        const int mask_all = (1 << k) - 1;
        std::vector<int> ok_masks(k, mask_all);

        for (int i = 0; i < k; ++i) {
            for (int j = 0; j < i; ++j) {
                int u = cand_vs.at(i), v = cand_vs.at(j);
                if (!std::binary_search(to.at(u).cbegin(), to.at(u).cend(), v)) {
                    ok_masks.at(i) &= ~(1 << j), ok_masks.at(j) &= ~(1 << i);
                }
            }
        }

        std::vector<int> seq;
        if (prefix_use >= 0) seq.push_back(prefix_use);
        seq.reserve(seq.size() + k);

        auto rec = [&](auto &&self, int now, const int last_mask) -> void {
            op(seq);
            seq.push_back(-1);
            for (int i = now; i < k; ++i) {
                if ((last_mask >> i) & 1) {
                    seq.back() = cand_vs.at(i);
                    self(self, i + 1, last_mask & ok_masks.at(i));
                }
            }
            seq.pop_back();
        };
        rec(rec, 0, mask_all);
        return;
    }

    template <class F> void run(F op) {
        precalc();

        std::vector<int> deg(n()), is_alive(n(), 1);
        using P = std::pair<int, int>;
        std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
        for (int i = 0; i < n(); ++i) deg.at(i) = to.at(i).size(), pq.emplace(deg.at(i), i);

        int rem_n = n(), rem_m = m();

        std::vector<int> cand_vs;
        while (!pq.empty()) {
            auto [di, i] = pq.top();
            pq.pop();
            if (deg.at(i) != di) continue;

            cand_vs.clear();

            if (di * di > rem_m * 2) { // Avoid "deg[i] = 0" case
                for (int i = 0; i < n(); ++i) {
                    if (is_alive.at(i)) cand_vs.push_back(i);
                }
                bruteforce(cand_vs, -1, op);
                break;
            }

            for (int j : to.at(i)) {
                if (is_alive.at(j)) cand_vs.push_back(j);
            }
            bruteforce(cand_vs, i, op);

            --rem_n, deg.at(i) = 0, is_alive.at(i) = 0;
            for (int j : cand_vs) --rem_m, --deg.at(j), pq.emplace(deg.at(j), j);
        }
    }
};
#line 2 "graph/test/enumerate_cliques.aoj2306.test.cpp"
#include <iostream>
#line 4 "graph/test/enumerate_cliques.aoj2306.test.cpp"
using namespace std;

#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2306"

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

    int N, M;
    cin >> N >> M;
    vector F(N, vector<int>(N));
    enumerate_cliques ec(N);
    while (M--) {
        int u, v, f;
        cin >> u >> v >> f;

        --u, --v;
        ec.add_bi_edge(u, v);

        F[u][v] = max(F[u][v], f);
        F[v][u] = max(F[v][u], f);
    }
    int ret = 0;

    auto op = [&](const std::vector<int> &clique) -> void {
        if (clique.size() <= 1) return;
        int tmp = 0;
        for (int s : clique) {
            int a = 1 << 30;
            for (int t : clique) {
                if (s != t) a = min(a, F[s][t]);
            }
            tmp += a;
        }
        ret = max(ret, tmp);
    };
    ec.run(op);

    cout << ret << endl;
}

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