#985541 (C++23) No.399 動的な領主

• 問題: No.399 動的な領主
• ユーザー: MitI_7
• 提出日時: 2024-06-02 11:19:58
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 313 ms / 2,000 ms
• コード長: 15,124 bytes
• コンパイル時間: 5,187 ms
• コンパイル使用メモリ: 188,892 KB
• 実行使用メモリ: 39,992 KB
• 最終ジャッジ日時: 2024-12-23 08:22:28
• 合計ジャッジ時間: 10,392 ms
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
other	AC * 19

ソースコード

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <map>
#include <memory>
#include <numeric>
#include <iomanip>
#include <iostream>
#include <queue>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <random>

#define LEN(x) (long long)(x.size())
#define FOR(i, a, n) for(int i=(a);i<(n); ++i)
#define FOE(i, a) for(auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define BIT_COUNT32(bit) (__builtin_popcount(bit))
#define BIT_COUNT64(bit) (__builtin_popcountll(bit))

template<typename T> using MinPriorityQueue = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<typename T> using MaxPriorityQueue = std::priority_queue<T>;

// @formatter:off
typedef long long LL;
typedef __int128_t LLL;
template<typename T> std::vector<T> make_v(size_t a){return std::vector<T>(a);}
template<typename T,typename... Ts> auto make_v(size_t a, Ts... ts){ return std::vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));}    // C++14
template<typename T,typename V> typename std::enable_if<std::is_class<T>::value==0>::type fill_v(T &t,const V &v){t=v;}
template<typename T,typename V> typename std::enable_if<std::is_class<T>::value!=0>::type fill_v(T &t,const V &v){for(auto &e:t) fill_v(e,v);}
template<class T> inline T ceil(T a, T b) { assert(a >= 0 and b > 0); return (a + b - 1) / b; }
void print() { std::cout << std::endl; }
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) { std::cout << head; if (sizeof...(tail) != 0) {std::cout << " ";} print(std::forward<Tail>(tail)...); }
template <class T> void print(std::vector<T> &v) {for (auto& a : v) { std::cout << a; if (&a != &v.back()) {std::cout << " ";} }std::cout << std::endl;}
template <class T> void print(std::pair<T, T> &p) { std::cout << p.first << " " << p.second << std::endl; }
void debug() { std::cerr << std::endl; }
template <class Head, class... Tail> void debug(Head&& head, Tail&&... tail) { std::cerr << head; if (sizeof...(tail) != 0) {std::cerr << " ";} debug(std::forward<Tail>(tail)...); }
template <class T> void debug(std::vector<T> &v) {for (auto& a : v) { std::cerr << a; if (&a != &v.back()) {std::cerr << " ";} }std::cerr << std::endl;}
template <class T> void debug(std::pair<T, T> &p) { std::cerr << p.first << " " << p.second << std::endl; }
inline bool inside(long long y, long long x, long long H, long long W) {return 0 <= y and y < H and 0 <= x and x < W; }
template<class T> inline double euclidean_distance(T y1, T x1, T y2, T x2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); }
template<class T> inline T euclidean_distance2(T y1, T x1, T y2, T x2) { return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2); }
template<class T> inline T manhattan_distance(T y1, T x1, T y2, T x2) { return abs(x1 - x2) + abs(y1 - y2); }
template<typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }
bool is_bit_on(const unsigned long long bit, const unsigned int i) { return (bit >> i) & 1u; }
unsigned long long get_bit_set(const unsigned long long bit, const unsigned int i, const unsigned int b) { assert(b == 0 or b == 1); if (b == 0) { return bit & ~(1ull << i); } else {return bit | (1ull << i);}}

// 初項s交差d長さnの数列の和
long long sum_of_arithmetic_progression(long long s, long long d, long long n) {
    return n * (2 * s + (n - 1) * d) / 2;
}

// 三角数
long long triangular_number(long long n) {
    return n * (n + 1) / 2;
}

// sqrt(x)の整数解を求める
// 整数解がなければ-1
long long sqrt_integer(const long long x) {
    if (x < 0) {
        return -1;
    }
    auto a = (long long)sqrt(x);
    if (a * a == x) {
        return a;
    }
    if((a - 1) * (a - 1) == x) {
        return a - 1;
    }
    if((a + 1) * (a + 1) == x) {
        return a + 1;
    }

    return -1;
}

// xが2の階乗かどうか判定
bool is_power_of_two(long long x) {
    return !(x & (x - 1));
}

// O(log max(a, b))
long long gcd(long long a, long long b) {
    if (b == 0) { return a; }
    return gcd(b, a % b);
}

long long lcm(long long a, long long b) {
    long long g = gcd(a, b);
    return a / g * b;
}

const int INF = 1u << 29u;  // 536,870,912
const long long LINF = 1ull << 60u;
const double EPS = 1e-9;
const long double PI = acos(-1.0);
// 2次元配列上での移動．右，下，左，上，右上，右下，左下，左上
const std::vector<int> dy8 = {0, 1, 0, -1, -1, 1, 1, -1}, dx8 = {1, 0, -1, 0, 1, 1, -1, -1};
// @formatter:on

template<typename T>
class Edge {
public:
    int from;
    int to;
    T w;
    int no;

    Edge() : from(-1), to(-1), w(-1), no(-1) {}

    Edge(int from, int to, T w = 1, int no = -1) : from(from), to(to), w(w), no(no) {

    }
};

template<typename T=int>
class Tree {
private:
    bool build_done = false;

public:
    const int num_nodes;
    std::vector<std::vector<Edge<T>>> graph;
    std::vector<int> parent;
    std::vector<std::vector<Edge<T>>> children;

    explicit Tree(const int num_nodes) : num_nodes(num_nodes), graph(num_nodes) {
    }

    void add_directed_edge(const int u, const int v, const T w = 1, const int no = -1) {
        this->graph[u].emplace_back(Edge(u, v, w, no));
    }

    void add_undirected_edge(const int u, const int v, const T w = 1, const int no = -1) {
        this->graph[u].emplace_back(Edge(u, v, w, no));
        this->graph[v].emplace_back(Edge(v, u, w, no));
    }

    std::vector<Edge<T>> &operator[](const int u) {
        return this->graph[u];
    }

    // 各ノードについて，親と子供を求める
    void build(const int root) {
        if (not this->build_done) {
            this->parent.resize(this->num_nodes, -1);
            this->children.resize(this->num_nodes);
            this->dfs(root, -1);
        }
        this->build_done = true;
    }

private:
    void dfs(const int u, const int p) {
        this->parent[u] = p;
        for (auto e: this->graph[u]) {
            if (e.to != p) {
                this->children[u].emplace_back(e);
                this->dfs(e.to, u);
            }
        }
    }
};

template<typename T>
class HeavyLightDecomposition {
public:
    Tree<T> tree;
    std::vector<int> num_children;
    std::vector<int> depth;

    std::vector<int> hld;
    std::vector<int> hld_index;// ノードが対応する hld のインデックス
    std::vector<int> top;      // 連結成分のうち最も浅い頂点
    std::vector<int> in, out;

    HeavyLightDecomposition(const Tree<T> &tree) : tree(tree),
                                                   num_children(tree.num_nodes), depth(tree.num_nodes),
                                                   hld_index(tree.num_nodes), top(tree.num_nodes),
                                                   in(tree.num_nodes), out(tree.num_nodes) {
    }

    void build(const int root) {
        this->tree.build(root);
        this->dfs(root, 0);
        this->heavy_light_decomposition(root, root);
    }

    // hld の index が対応する木の頂点番号
    int idx_node(const int i) const {
        return this->hld[i];
    }

    // u が対応する hld の index
    int node_idx(int u) const {
        return this->hld_index[u];
    }

    // 頂点 u を根とする部分木が対応する hld の区間(半開区間)
    std::pair<int, int> subtree_query(const int u) const {
        return {this->in[u], this->out[u]};
    }

    // u から v までが対応する hld の区間の集合(半開区間)
    // クエリの個数は　O(log N)
    // 辺の情報を扱うときは，u の親への辺の情報をノード u にいれるが，
    // path_queries では，lca(u, v)の親への辺の情報も含まれてしまうのでこの分を引く必要があることに注意
    std::vector<std::pair<int, int>> path_queries(int u, int v) const {
        std::vector<std::pair<int, int>> ret;
        while (this->top[u] != this->top[v]) {
            if (this->depth[this->top[u]] <= this->depth[this->top[v]]) {
                ret.emplace_back(this->hld_index[this->top[v]], this->hld_index[v] + 1);
                v = this->tree.parent[this->top[v]];
            } else {
                ret.emplace_back(this->hld_index[this->top[u]], this->hld_index[u] + 1);
                u = this->tree.parent[this->top[u]];
            }
        }
        ret.emplace_back(std::min(this->hld_index[u], this->hld_index[v]), std::max(this->hld_index[u], this->hld_index[v]) + 1);
        return ret;
    }

    // u と v の最小共通祖先
    // O(log N)
    int lca(int u, int v) const {
        while (u != v) {

            if (this->top[u] == this->top[v]) {
                break;
            }

            if (this->depth[this->top[u]] > this->depth[this->top[v]]) {
                u = this->tree.parent[this->top[u]];
            } else {
                v = this->tree.parent[this->top[v]];
            }
        }

        if (this->depth[u] < this->depth[v]) {
            return u;
        }
        return v;
    }

private:
    int time = 0;

    // 各頂点について，深さ，その頂点を根とする部分木のサイズを求める
    int dfs(const int u, const int d) {
        this->num_children[u] = 1;
        this->depth[u] = d;
        for (const auto &edge: this->tree.children[u]) {
            this->num_children[u] += this->dfs(edge.to, d + 1);
        }
        return this->num_children[u];
    }

    void heavy_light_decomposition(const int u, const int now_top) {
        this->hld_index[u] = this->hld.size();
        this->hld.emplace_back(u);
        this->top[u] = now_top;
        this->in[u] = time++;

        if (this->tree.children[u].size() == 0) {
            this->out[u] = time;
            return;
        }

        // heavy な辺を探す
        int idx = -1;
        {
            int maxi_num_children = 0;
            int i = 0;
            for (const auto &e: this->tree.children[u]) {
                if (this->num_children[e.to] > maxi_num_children) {
                    maxi_num_children = this->num_children[e.to];
                    idx = i;
                }
                ++i;
            }
        }

        // heavy な辺に進む（light より先にもぐる必要がある）
        this->heavy_light_decomposition(this->tree.children[u][idx].to, now_top);

        // light な辺に進む
        int i = 0;
        for (const auto &e: this->tree.children[u]) {
            if (i != idx) {
                this->heavy_light_decomposition(e.to, e.to);
            }
            ++i;
        }

        this->out[u] = time;
    }
};

//#include <cassert>
//#include <vector>

// すべて 0-origin
template<class T>
class FenwickTree {
public:
    const int n;
    std::vector<T> v;

    // n: 要素数
    explicit FenwickTree(const int n) : n(n) {
        this->v.assign(n + 1, 0);
    }

    // v[i]
    // O(log n)
    T access(const int i) const {
        return this->sum(i, i + 1);
    }

    // v[i] += x
    // O(log n)
    void add(int i, T x) {
        assert(i < this->n);

        while (i < this->n) {
            this->v[i] += x;
            i |= i + 1;
        }
    }

    // v[i] = x
    // O(log n)
    void update(int i, T x) {
        assert(i < this->n);

        const T now = this->access(i);
        this->add(i, x - now);
    }

    // sum(v[0, i))
    // O(log n)
    T sum(int i) const {
        assert(0 <= i and i <= this->n);

        T s = 0;
        i -= 1;
        while (i >= 0) {
            s += this->v[i];
            i = (i & (i + 1)) - 1;
        }
        return s;
    }

    // sum(v[left, right))
    // O(log n)
    T sum(const int left, const int right) const {
        if (left >= right) {
            return 0;
        }
        return this->sum(right) - this->sum(left);
    }
};

// 区間加算，区間和取得
// すべて 0-origin
template<typename T>
class FenwickTreeRange {
    const int n;
    FenwickTree<T> ft0, ft1;

public:
    explicit FenwickTreeRange(const int n) : n(n), ft0(n + 1), ft1(n + 1) {}

    // v[i]
    // O(log n)
    T access(const int i) const {
        assert(0 <= i and i < this->n);
        return this->sum(i, i + 1);
    }

    // v[i] += x
    // O(log n)
    void add(const int i, const T x) {
        assert(0 <= i and i < this->n);
        this->add(i, i + 1, x);
    }

    // v[left, right) += x
    // O(log n)
    void add(const int left, const int right, const T x) {
        if (left == right) {
            return;
        }
        assert(0 <= left and left < right and right <= this->n);
        this->ft0.add(left, x);
        this->ft0.add(right, -x);
        this->ft1.add(left, -x * left);
        this->ft1.add(right, x * right);
    }

    // v[left, right) += x
    // 加算位置が n 以上の場合は 0 に戻って加算される
    // O(log n)
    void add_circle(long long left, long long right, const T x) {
        assert(left < right);

        const long long num_loop = (right - left) / this->n;
        this->add(0, this->n, x * num_loop);

        // ループで終わり
        if ((right - left) % this->n == 0) {
            return;
        }

        left %= this->n;
        right %= this->n;

        if (left < right) {
            this->add(left, right, x);
        } else {
            this->add(left, this->n, x);
            this->add(0, right, x);
        }
    }

    // sum(v[0, i))
    // O(log n)
    T sum(const int i) const {
        assert(0 <= i and i <= this->n);
        return ft0.sum(i) * i + ft1.sum(i);
    }

    // sum(v[left, right))
    // O(log n)
    T sum(const int left, const int right) const {
        assert(0 <= left and left < right and right <= this->n);
        return this->sum(right) - this->sum(left);
    }

    // sum(v[left, right))
    // O(log n)
    T sum_circle(const int left, const int right) const {
        // TODO
        return 0;
    }

    void dump() {
        for (int i = 0; i < this->n; ++i) {
            if (i != 0) {
                std::cout << " ";
            }
            std::cout << this->access(i);
        }
        std::cout << std::endl;
    }
};

using namespace std;

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

    int N;
    cin >> N;

    Tree<int> tree(N);
    for (int i = 0; i < N - 1; ++i) {
        int U, V;
        cin >> U >> V;
        U--;
        V--;
        tree.add_undirected_edge(U, V);
    }

    HeavyLightDecomposition hld(tree);
    hld.build(0);

    FenwickTreeRange<long long> ftr(N);
    ftr.add(0, N, 1);

    long long ans = 0;
    int Q;
    cin >> Q;
    for (int i = 0; i < Q; ++i) {
        int A, B;
        cin >> A >> B;
        A--;
        B--;

        for (const auto &[l, r]: hld.path_queries(A, B)) {
            ans += ftr.sum(l, r);
        }

        for (const auto &[l, r]: hld.path_queries(A, B)) {
            ftr.add(l, r, 1);
        }
    }

    cout << ans << endl;

    return 0;
}