#397142 (C++17) No.922 東北きりきざむたん

• 問題: No.922 東北きりきざむたん
• ユーザー: kimiyuki
• 提出日時: 2019-11-09 10:50:29
• 言語: C++17 (gcc 13.2.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 215 ms / 2,000 ms
• コード長: 5,445 bytes
• コンパイル時間: 2,686 ms
• コンパイル使用メモリ: 224,676 KB
• 実行使用メモリ: 47,068 KB
• 最終ジャッジ日時: 2023-10-13 07:03:22
• 合計ジャッジ時間: 7,627 ms
• ジャッジサーバーID （参考情報）: judge13 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,348 KB
testcase_01	AC	1 ms; 4,356 KB
testcase_02	AC	2 ms; 4,348 KB
testcase_03	AC	2 ms; 4,348 KB
testcase_04	AC	2 ms; 4,352 KB
testcase_05	AC	1 ms; 4,348 KB
testcase_06	AC	2 ms; 4,348 KB
testcase_07	AC	3 ms; 4,352 KB
testcase_08	AC	2 ms; 4,352 KB
testcase_09	AC	76 ms; 24,888 KB
testcase_10	AC	52 ms; 9,568 KB
testcase_11	AC	68 ms; 20,168 KB
testcase_12	AC	42 ms; 29,080 KB
testcase_13	AC	22 ms; 9,480 KB
testcase_14	AC	116 ms; 39,048 KB
testcase_15	AC	35 ms; 31,108 KB
testcase_16	AC	188 ms; 41,312 KB
testcase_17	AC	193 ms; 40,924 KB
testcase_18	AC	192 ms; 40,932 KB
testcase_19	AC	190 ms; 40,980 KB
testcase_20	AC	190 ms; 40,928 KB
testcase_21	AC	215 ms; 41,260 KB
testcase_22	AC	215 ms; 41,168 KB
testcase_23	AC	201 ms; 41,016 KB
testcase_24	AC	197 ms; 41,076 KB
testcase_25	AC	185 ms; 41,872 KB
testcase_26	AC	185 ms; 41,732 KB
testcase_27	AC	181 ms; 41,868 KB
testcase_28	AC	99 ms; 37,944 KB
testcase_29	AC	190 ms; 47,068 KB

ソースコード

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
using namespace std;
template <class T, class U> inline void chmin(T & a, U const & b) { a = min<T>(a, b); }

/**
 * @brief sparse table on a semilattice
 * @note a semilattice is a commutative idempotent semigroup
 * @note for convenience, it requires the unit
 * @note O(N log N) space
 */
template <class Semilattice>
struct sparse_table {
    typedef typename Semilattice::value_type value_type;
    std::vector<std::vector<value_type> > table;
    Semilattice lat;
    sparse_table() = default;
    /**
     * @note O(N \log N) time
     */
    sparse_table(std::vector<value_type> const & data, Semilattice const & a_lat = Semilattice())
            : lat(a_lat) {
        int n = data.size();
        int log_n = 32 - __builtin_clz(n);
        table.resize(log_n, std::vector<value_type>(n));
        table[0] = data;
        REP (k, log_n - 1) {
            REP (i, n) {
                table[k + 1][i] = i + (1ll << k) < n ?
                    lat.append(table[k][i], table[k][i + (1ll << k)]) :
                    table[k][i];
            }
        }
    }
    /**
     * @note O(1)
     */
    value_type range_concat(int l, int r) const {
        if (l == r) return lat.unit();  // if there is no unit, remove this line
        assert (0 <= l and l < r and r <= table[0].size());
        int k = 31 - __builtin_clz(r - l);  // log2
        return lat.append(table[k][l], table[k][r - (1ll << k)]);
    }
};

struct indexed_min_semilattice {
    typedef std::pair<int, int> value_type;
    value_type unit() const { return { INT_MAX, INT_MAX }; }
    value_type append(value_type a, value_type b) const { return std::min(a, b); }
};

/**
 * @brief lowest common ancestor with \pm 1 RMQ and sparse table
 * @see https://www.slideshare.net/yumainoue965/lca-and-rmq
 * @note verified http://www.utpc.jp/2011/problems/travel.html
 */
struct lowest_common_ancestor_for_forest {
    sparse_table<indexed_min_semilattice> table;
    std::vector<int> index;
    lowest_common_ancestor_for_forest() = default;
    /**
     * @note O(N)
     * @param g is an adjacent list of a tree
     */
    lowest_common_ancestor_for_forest(std::vector<std::vector<int> > const & g) {
        std::vector<std::pair<int, int> > tour;
        index.assign(g.size(), -1);
        REP (root, g.size()) if (index[root] == -1) {
            dfs(root, -1, 0, g, tour);
            tour.emplace_back(-1, -1);
        }
        table = sparse_table<indexed_min_semilattice>(tour);
    }
private:
    /**
     * @note to avoid stack overflow
     */
    void dfs(int x, int parent, int depth, std::vector<std::vector<int> > const & g, std::vector<std::pair<int, int> > & tour) {
        index[x] = tour.size();
        tour.emplace_back(depth, x);
        for (int y : g[x]) if (y != parent) {
            dfs(y, x, depth + 1, g, tour);
            tour.emplace_back(depth, x);
        }
    }
public:
    /**
     * @note O(1)
     */
    int operator () (int x, int y) const {
        assert (0 <= x and x < index.size());
        assert (0 <= y and y < index.size());
        x = index[x];
        y = index[y];
        if (x > y) std::swap(x, y);
        return table.range_concat(x, y + 1).second;
    }
    int get_depth(int x) const {
        assert (0 <= x and x < index.size());
        return table.range_concat(index[x], index[x] + 1).first;
    }
    bool is_in_same_tree(int x, int y) const {
        return (*this)(x, y) != -1;
    }
    int get_dist(int x, int y) const {
        assert (0 <= x and x < index.size());
        assert (0 <= y and y < index.size());
        int z = (*this)(x, y);
        return get_depth(x) + get_depth(y) - 2 * get_depth(z);
    }
};

int64_t solve(int n, int m, int q, const vector<vector<int> > & g, const vector<int> & a, const vector<int> & b) {
    lowest_common_ancestor_for_forest lca(g);
    int64_t answer = 0;
    vector<int> cnt(n);
    REP (i, q) {
        if (lca.is_in_same_tree(a[i], b[i])) {
            answer += lca.get_dist(a[i], b[i]);
        } else {
            ++ cnt[a[i]];
            ++ cnt[b[i]];
        }
    }
    vector<int64_t> imos(n);
    REP (root, n) if (lca.get_depth(root) == 0) {
        int sum_cnt = 0;
        function<int (int, int, int)> go1 = [&](int x, int parent, int depth) {
            sum_cnt += cnt[x];
            imos[root] += depth * cnt[x];
            int k = cnt[x];
            for (int y : g[x]) if (y != parent) {
                k += go1(y, x, depth + 1);
            }
            if (x != root) {
                imos[x] += - 2 * k;
            }
            return k;
        };
        go1(root, -1, 0);
        int64_t min_cost = INT64_MAX;
        function<void (int, int)> go2 = [&](int x, int parent) {
            chmin(min_cost, imos[x]);
            for (int y : g[x]) if (y != parent) {
                imos[y] += imos[x] + sum_cnt;
                go2(y, x);
            }
        };
        go2(root, -1);
        answer += min_cost;
    }
    return answer;
}

int main() {
    int n, m, q; cin >> n >> m >> q;
    vector<vector<int> > g(n);
    REP (i, m) {
        int u, v; cin >> u >> v;
        -- u;
        -- v;
        g[u].push_back(v);
        g[v].push_back(u);
    }
    vector<int> a(q), b(q);
    REP (i, q) {
        cin >> a[i] >> b[i];
        -- a[i];
        -- b[i];
    }
    cout << solve(n, m, q, g, a, b) << endl;
    return 0;
}