#913633 (C++17(gcc12)) No.977 アリス仕掛けの摩天楼

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問題	No.977 アリス仕掛けの摩天楼
ユーザー	kuhaku
提出日時	2023-09-17 11:00:52
言語	C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
結果	AC
実行時間	80 ms / 2,000 ms
コード長	11,312 bytes
コンパイル時間	12,590 ms
コンパイル使用メモリ	288,856 KB
最終ジャッジ日時	2025-02-16 23:09:03
ジャッジサーバーID （参考情報）	judge1 / judge3
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ファイルパターン	結果
other	AC * 26
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ソースコード

raw source code
#line 1 "a.cpp"
#define PROBLEM ""
#line 2 "/home/kuhaku/atcoder/github/algo/lib/template/template.hpp"
#pragma GCC target("sse4.2,avx2,bmi2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
template <class T, class U>
bool chmax(T &a, const U &b) {
    return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
bool chmin(T &a, const U &b) {
    return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr int MOD = 1000000007;
constexpr int MOD_N = 998244353;
constexpr double EPS = 1e-7;
constexpr double PI = M_PI;
#line 3 "/home/kuhaku/atcoder/github/algo/lib/graph/graph.hpp"

/**
 * @brief 重み付きグラフ
 *
 * @tparam T 辺の重みの型
 */
template <class T>
struct Graph {
  private:
    struct _edge {
        constexpr _edge() : _from(), _to(), _weight() {}
        constexpr _edge(int from, int to, T weight) : _from(from), _to(to), _weight(weight) {}
        constexpr bool operator<(const _edge &rhs) const { return this->weight() < rhs.weight(); }
        constexpr bool operator>(const _edge &rhs) const { return rhs < *this; }

        constexpr int from() const { return this->_from; }
        constexpr int to() const { return this->_to; }
        constexpr T weight() const { return this->_weight; }

      private:
        int _from, _to;
        T _weight;
    };

  public:
    using edge_type = typename Graph<T>::_edge;

    Graph() : _size(), edges() {}
    Graph(int v) : _size(v), edges(v) {}

    const auto &operator[](int i) const { return this->edges[i]; }
    auto &operator[](int i) { return this->edges[i]; }
    const auto begin() const { return this->edges.begin(); }
    auto begin() { return this->edges.begin(); }
    const auto end() const { return this->edges.end(); }
    auto end() { return this->edges.end(); }
    constexpr int size() const { return this->_size; }

    void add_edge(const edge_type &e) { this->edges[e.from()].emplace_back(e); }
    void add_edge(int from, int to, T weight = T(1)) {
        this->edges[from].emplace_back(from, to, weight);
    }
    void add_edges(int from, int to, T weight = T(1)) {
        this->edges[from].emplace_back(from, to, weight);
        this->edges[to].emplace_back(to, from, weight);
    }

    void input_edge(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            T weight;
            std::cin >> from >> to >> weight;
            this->add_edge(from - base, to - base, weight);
        }
    }
    void input_edges(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            T weight;
            std::cin >> from >> to >> weight;
            this->add_edges(from - base, to - base, weight);
        }
    }

  private:
    int _size;
    std::vector<std::vector<edge_type>> edges;
};

template <>
struct Graph<void> {
  private:
    struct _edge {
        constexpr _edge() : _from(), _to() {}
        constexpr _edge(int from, int to) : _from(from), _to(to) {}

        constexpr int from() const { return this->_from; }
        constexpr int to() const { return this->_to; }
        constexpr int weight() const { return 1; }
        constexpr bool operator<(const _edge &rhs) const { return this->weight() < rhs.weight(); }
        constexpr bool operator>(const _edge &rhs) const { return rhs < *this; }

      private:
        int _from, _to;
    };

  public:
    using edge_type = typename Graph<void>::_edge;

    Graph() : _size(), edges() {}
    Graph(int v) : _size(v), edges(v) {}

    const auto &operator[](int i) const { return this->edges[i]; }
    auto &operator[](int i) { return this->edges[i]; }
    const auto begin() const { return this->edges.begin(); }
    auto begin() { return this->edges.begin(); }
    const auto end() const { return this->edges.end(); }
    auto end() { return this->edges.end(); }
    constexpr int size() const { return this->_size; }

    void add_edge(const edge_type &e) { this->edges[e.from()].emplace_back(e); }
    void add_edge(int from, int to) { this->edges[from].emplace_back(from, to); }
    void add_edges(int from, int to) {
        this->edges[from].emplace_back(from, to);
        this->edges[to].emplace_back(to, from);
    }

    void input_edge(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            std::cin >> from >> to;
            this->add_edge(from - base, to - base);
        }
    }
    void input_edges(int m, int base = 1) {
        for (int i = 0; i < m; ++i) {
            int from, to;
            std::cin >> from >> to;
            this->add_edges(from - base, to - base);
        }
    }

  private:
    int _size;
    std::vector<std::vector<edge_type>> edges;
};
#line 3 "/home/kuhaku/atcoder/github/algo/lib/graph/lowlink.hpp"

/**
 * @brief LowLink
 *
 * @tparam T
 */
template <class T>
struct LowLink {
    LowLink(const Graph<T> &_graph)
        : g(_graph), ord(_graph.size()), low(_graph.size()), used(_graph.size()) {
        this->build();
    }

    /**
     * @brief Get the articulation points object
     *
     * @return std::vector<int>
     */
    auto get_articulation_points() { return this->articulation_points; }
    /**
     * @brief Get the bridges object
     *
     * @return std::vector<typename Graph<T>::edge_type>
     */
    auto get_bridges() { return this->bridges; }

  private:
    const Graph<T> &g;
    std::vector<int> ord, low;
    std::vector<bool> used;
    std::vector<int> articulation_points;               // 関節点
    std::vector<typename Graph<T>::edge_type> bridges;  // 橋

    void build() {
        int number = 0;
        for (int i = 0; i < this->g.size(); i++) {
            if (!this->used[i]) number = this->dfs(i, number, -1);
        }
    }

    int dfs(int index, int number, int parent) {
        this->used[index] = true;
        this->ord[index] = number++;
        this->low[index] = this->ord[index];
        bool is_articulation_point = false;
        int count = 0;
        for (auto &e : this->g[index]) {
            if (!this->used[e.to()]) {
                ++count;
                number = this->dfs(e.to(), number, index);
                chmin(low[index], low[e.to()]);
                is_articulation_point |= ~parent && this->low[e.to()] >= this->ord[index];
                if (this->ord[index] < this->low[e.to()]) this->bridges.emplace_back(e);
            } else if (e.to() != parent) {
                chmin(this->low[index], this->ord[e.to()]);
            }
        }
        is_articulation_point |= parent == -1 && count > 1;
        if (is_articulation_point) this->articulation_points.emplace_back(index);
        return number;
    }
};
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/macro.hpp"
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/sonic.hpp"
struct Sonic {
    Sonic() {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
    }

    constexpr void operator()() const {}
} sonic;
#line 5 "/home/kuhaku/atcoder/github/algo/lib/template/atcoder.hpp"
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
    return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &i : v) is >> i;
    return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
    return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (auto it = v.begin(); it != v.end(); ++it) {
        os << (it == v.begin() ? "" : " ") << *it;
    }
    return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
    else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
    else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
template <typename T, typename... Args>
auto make_vector(T x, int arg, Args... args) {
    if constexpr (sizeof...(args) == 0) return std::vector<T>(arg, x);
    else return std::vector(arg, make_vector<T>(x, args...));
}
void setp(int n) {
    std::cout << std::fixed << std::setprecision(n);
}
void Yes(bool is_correct = true) {
    std::cout << (is_correct ? "Yes" : "No") << '\n';
}
void No(bool is_not_correct = true) {
    Yes(!is_not_correct);
}
void YES(bool is_correct = true) {
    std::cout << (is_correct ? "YES" : "NO") << '\n';
}
void NO(bool is_not_correct = true) {
    YES(!is_not_correct);
}
void Takahashi(bool is_correct = true) {
    std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n';
}
void Aoki(bool is_not_correct = true) {
    Takahashi(!is_not_correct);
}
#line 2 "/home/kuhaku/atcoder/github/algo/lib/tree/union_find.hpp"

/**
 * @brief 素集合データ構造
 * @details Implement (union by size) + (path compression)
 * @see https://github.com/atcoder/ac-library/blob/master/atcoder/dsu.hpp
 */
struct union_find {
    union_find() : data() {}
    union_find(int _n) : data(_n, -1) {}

    int root(int x) { return this->data[x] < 0 ? x : this->data[x] = this->root(this->data[x]); }
    int get_root(int x) { return this->root(x); }

    bool is_root(int x) const { return this->data[x] < 0; }

    bool same(int x, int y) { return this->root(x) == this->root(y); }
    bool is_same(int x, int y) { return this->same(x, y); }

    int size(int x) { return -(this->data[this->root(x)]); }
    int get_size(int x) { return this->size(x); }

    bool unite(int x, int y) {
        x = this->root(x), y = this->root(y);
        if (x == y) return false;
        if (this->data[x] > this->data[y]) std::swap(x, y);
        this->data[x] += this->data[y];
        this->data[y] = x;
        return true;
    }

    template <class F>
    bool unite(int x, int y, F f) {
        x = this->root(x), y = this->root(y);
        if (x != y) {
            if (this->data[x] > this->data[y]) std::swap(x, y);
            this->data[x] += this->data[y];
            this->data[y] = x;
        }
        f(x, y);
        return x != y;
    }

  private:
    std::vector<int> data;
};
#line 6 "a.cpp"

int main(void) {
    int n;
    cin >> n;
    Graph<void> g(n);
    g.input_edges(n - 1, 0);
    union_find uf(n);
    for (auto &es : g) {
        for (auto &e : es) uf.unite(e.from(), e.to());
    }
    if (uf.size(0) == n) {
        co("Bob");
        return 0;
    }

    LowLink llink(g);
    if ((uf.size(0) == n - 1 || uf.size(1) == n - 1) && llink.get_bridges().size() == 0)
        co("Bob");
    else
        co("Alice");

    return 0;
}
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