#686791 (C++17) No.1639 最小通信路

• 問題: No.1639 最小通信路
• ユーザー: atree
• 提出日時: 2021-08-06 22:32:53
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 25 ms / 2,000 ms
• コード長: 3,440 bytes
• コンパイル時間: 5,739 ms
• コンパイル使用メモリ: 397,812 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-09-17 02:37:13
• 合計ジャッジ時間: 7,263 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,816 KB
testcase_01	AC	1 ms; 6,944 KB
testcase_02	AC	8 ms; 6,944 KB
testcase_03	AC	25 ms; 6,940 KB
testcase_04	AC	25 ms; 6,940 KB
testcase_05	AC	3 ms; 6,940 KB
testcase_06	AC	4 ms; 6,944 KB
testcase_07	AC	2 ms; 6,944 KB
testcase_08	AC	6 ms; 6,944 KB
testcase_09	AC	2 ms; 6,940 KB
testcase_10	AC	3 ms; 6,944 KB
testcase_11	AC	5 ms; 6,940 KB
testcase_12	AC	3 ms; 6,944 KB
testcase_13	AC	8 ms; 6,944 KB
testcase_14	AC	2 ms; 6,944 KB
testcase_15	AC	2 ms; 6,940 KB
testcase_16	AC	5 ms; 6,940 KB
testcase_17	AC	7 ms; 6,940 KB
testcase_18	AC	2 ms; 6,944 KB
testcase_19	AC	3 ms; 6,940 KB
testcase_20	AC	6 ms; 6,940 KB
testcase_21	AC	1 ms; 6,944 KB
testcase_22	AC	3 ms; 6,940 KB
testcase_23	AC	4 ms; 6,940 KB
testcase_24	AC	3 ms; 6,944 KB
testcase_25	AC	3 ms; 6,944 KB
testcase_26	AC	2 ms; 6,944 KB
testcase_27	AC	2 ms; 6,940 KB
testcase_28	AC	2 ms; 6,944 KB
testcase_29	AC	7 ms; 6,944 KB
testcase_30	AC	12 ms; 6,944 KB
testcase_31	AC	3 ms; 6,940 KB
testcase_32	AC	9 ms; 6,940 KB
testcase_33	AC	2 ms; 6,940 KB
testcase_34	AC	7 ms; 6,944 KB
testcase_35	AC	18 ms; 6,944 KB
testcase_36	AC	7 ms; 6,944 KB
testcase_37	AC	9 ms; 6,944 KB
testcase_38	AC	2 ms; 6,940 KB
testcase_39	AC	4 ms; 6,944 KB
testcase_40	AC	2 ms; 6,944 KB
testcase_41	AC	3 ms; 6,944 KB
testcase_42	AC	11 ms; 6,940 KB
testcase_43	AC	3 ms; 6,940 KB
testcase_44	AC	2 ms; 6,944 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define overload3(_1, _2, _3, name, ...) name
#define rep1(n) for (decltype(n) _tmp = 0; _tmp < (n); _tmp++)
#define rep2(i, n) for (decltype(n) i = 0; i < (n); i++)
#define rep3(i, a, b) for (decltype(b) i = a; i < (b); i++)
#define rep(...) overload3(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#if __has_include(<debug.hpp>)
    #include <debug.hpp>
#else
    #define dbg(...) (void(0))
#endif
struct IOSetup {
    IOSetup() noexcept {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout << fixed << setprecision(10);
        cerr << fixed << setprecision(10);
    }
} iosetup;
template<class T> void drop(const T &x) {
    cout << x << "\n";
    exit(0);
}
template<class T> bool chmax(T &a, const T &b) { return a < b and (a = b, true); }
template<class T> bool chmin(T &a, const T &b) { return a > b and (a = b, true); }
using i64 = long long;
using f64 = long double;

#include <boost/multiprecision/cpp_int.hpp>
using Bint = boost::multiprecision::cpp_int;

/**
 * @brief Union Find
 * @note a.k.a DSU; Disjoint Set Union
 */
struct UnionFind {
    vector<int> parents_or_size;
    UnionFind(int size_):
        parents_or_size(size_, -1) {}
    bool unite(int u, int v) {
        u = root(u), v = root(v);
        if (u == v) return false;
        if (parents_or_size[u] > parents_or_size[v]) swap(u, v);
        parents_or_size[u] += parents_or_size[v];
        parents_or_size[v] = u;
        return true;
    }
    int root(int k) { return parents_or_size[k] < 0 ? k : parents_or_size[k] = root(parents_or_size[k]); }
    int size(int k) { return -parents_or_size[root(k)]; }
    bool same(int u, int v) { return root(u) == root(v); }
    vector<vector<int>> groups() {
        size_t n = parents_or_size.size();
        vector<vector<int>> ret(n);
        rep(i, n) ret[root(i)].emplace_back(i);
        ret.erase(remove_if(begin(ret), end(ret), [&](const vector<int> &v) { return v.empty(); }));
        return ret;
    }
};

/**
 * @brief Kruskal's Algorithm
 * @note Solve MST; Minimum Spanning Tree in $O(|E|log|E)$.
 * @note The sum of the weights of the edges can be obtained from
 * ```accumulate(begin(ret), end(ret), 0, [](T acc, auto e) { return acc + get<2>(e); })```.
 * @return Set of edges by vector<tuple<u, v, weight>>
*/

template<typename T> vector<tuple<size_t, size_t, T>> kruskal(vector<vector<pair<size_t, T>>> const &graph) {
    using Edge = tuple<size_t, size_t, T>;
    vector<Edge> edges{};
    size_t n = size(graph);
    if (n == 1) return {};
    rep(i, n) for (const auto &[j, cost]: graph[i]) edges.emplace_back(Edge{i, j, cost});
    sort(begin(edges), end(edges), [](Edge a, Edge b) { return get<2>(a) < get<2>(b); });
    UnionFind uf(n);
    vector<Edge> ret{};
    for (const auto &[u, v, cost]: edges) {
        if (not uf.same(u, v)) {
            ret.emplace_back(Edge{u, v, cost});
            uf.unite(u, v);
        }
        if (size(ret) == n - 1) break;
    }
    return ret;
}

int main() {
    size_t n;
    cin >> n;
    vector graph(n, vector<pair<size_t, Bint>>{});
    rep(n * (n - 1) / 2) {
        size_t a, b;
        Bint c;
        cin >> a >> b >> c;
        graph[--a].emplace_back(pair{--b, c});
        graph[b].emplace_back(pair{a, c});
    }
    auto edges = kruskal(graph);
    Bint ans = get<2>(edges.front());
    for (const auto &[a, b, c]: edges) chmax(ans, c);
    cout << ans << "\n";
}