#209029 (C++14) No.235 めぐるはめぐる (5)

提出ソース
結果

問題	No.235 めぐるはめぐる (5)
ユーザー	rpy3cpp
提出日時	2017-10-12 01:27:01
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,799 ms / 10,000 ms
コード長	11,913 bytes
コンパイル時間	2,750 ms
コンパイル使用メモリ	196,876 KB
実行使用メモリ	74,992 KB
最終ジャッジ日時	2024-11-17 09:55:54
合計ジャッジ時間	10,002 ms
ジャッジサーバーID （参考情報）	judge4 / judge5
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	1,799 ms 74,372 KB
testcase_01	AC	1,201 ms 74,992 KB
testcase_02	AC	1,658 ms 74,560 KB
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ソースコード

raw source code
// Heavy Light Decomposition
//
// Supports the following operations on tree with weighted vertexes.
// Assign/add a value to a vertex. O(log(n))
// Assign/add a value to a subtree. O(log(n))
// Assign/add a value to a path. O(log(n)^2)
// Get a value of a vertex. O(log(n))
// Get sum of the values of a subtree. O(log(n))
// Get sum of the values of a path. O(log(n)^2)


#include <bits/stdc++.h>

using namespace std;
using vvi = vector<vector<int>>;
constexpr long long mod = 1e9+7;

template<typename T>
struct LazyData {
    T add;
    T assign;
    bool has_assign;

    LazyData(T v = 0, T w = 0, bool tf = false) : add(v), assign(w), has_assign(tf) {}
};

template<typename T>
class SegTree {
    size_t n;
    int h;
    vector<T> data;           // data[i]: 区間i の重みづけ合計
    vector<T> weight;         // weight[i]: 区間i の重み
    vector<LazyData<T>> lazy; // lazy[i]: 区間i の未伝搬の遅延評価データ
    static T combine(T L, T R) { return ((L + R) % mod + mod) % mod; }

    void apply(size_t i, T v, int command_type) {
        if (command_type == 0) {
            apply_assign(i, v);
        } else {
            apply_add(i, v);
        }
    }

    void apply_assign(size_t i, T v) {  // v: value to assign
        data[i] = (weight[i] * v) % mod;
        if (i < n) {
            lazy[i].add = 0;
            lazy[i].assign = v;
            lazy[i].has_assign = true;
        }
    }

    void apply_add(size_t i, T v) {
        data[i] = (data[i] + (weight[i] * v) % mod) % mod;
        if (i < n) {
            if (lazy[i].has_assign) {
                lazy[i].assign = (lazy[i].assign + v) % mod;
            } else {
                lazy[i].add = (lazy[i].add + v) % mod;
            }
        }
    }

    void build(size_t i) {      // update all the parents of node i.
        while (i >>= 1) if (not lazy[i].has_assign) data[i] = combine(combine(data[i * 2], data[i * 2 + 1]), (lazy[i].add * weight[i]) % mod);
    }

    void push(size_t p) {       // propagates the changes from the root to node p.
        for (int s = h; s > 0; --s) {
            size_t i = p >> s;
            if (lazy[i].has_assign) {
                apply_assign(i * 2, lazy[i].assign);
                apply_assign(i * 2 + 1, lazy[i].assign);
                lazy[i].has_assign = false;
            } else if (lazy[i].add != 0) {
                apply_add(i * 2, lazy[i].add);
                apply_add(i * 2 + 1, lazy[i].add);
                lazy[i].add = 0;
            }
        }
    }

    int calc_h(size_t nn) {
        int hh = 1;
        for (; nn > 1; ++hh, nn >>= 1);
        return hh;
    }

    void process_command(size_t L, size_t R, T v, int command_type) {
        L += n;
        R += n;
        size_t L0 = L;
        size_t R0 = R;
        push(L);
        push(R - 1);
        for (; L < R; L >>= 1, R >>= 1) {
            if (L & 1) apply(L++, v, command_type);
            if (R & 1) apply(--R, v, command_type);
        }
        build(L0);
        build(R0 - 1);
    }

    void fill_weight(const vector<T> &ws) {
        copy(begin(ws), end(ws), begin(weight) + n);
        for (int i = n - 1; i > 0; --i) weight[i] = combine(weight[i * 2], weight[i * 2 + 1]);
    }

public:
    SegTree() : n(0), h(1), data(), weight(), lazy() {}

    explicit SegTree(const vector<T> &_weight) : n(_weight.size()), h(calc_h(n)), data(2 * n, 0), weight(2 * n, 0),
                                                 lazy(n) {
        fill_weight(_weight);
    }

    SegTree(const vector<T> &src, const vector<T> &_weight) : n(src.size()), h(calc_h(n)), data(2 * n, 0),
                                                              weight(2 * n, 0), lazy(n) {
        fill_weight(_weight);
        for (int i = 0; i < n; ++i) data[n + i] = (src[i] * weight[n + i]) % mod;
        for (int i = n - 1; i > 0; --i) data[i] = combine(data[i * 2], data[i * 2 + 1]);
    }

    void init(const vector<T> &_src, const vector<T> &_weight) {
        n = _weight.size();
        h = calc_h(n);
        data.assign(2 * n, 0);
        for (int i = 0; i < n; ++i) data[n + i] = _src[i]; // _src[i] * _weight[i] としていない点に注意。
        for (int i = n - 1; i > 0; --i) data[i] = combine(data[i * 2], data[i * 2 + 1]);
        weight.assign(2 * n, 0);
        lazy.resize(n);
        fill_weight(_weight);
    }

    void modify(size_t L, size_t R, T w) { process_command(L, R, w, 0); } // assign w to range [L, R)
    void add(size_t L, size_t R, T v) { process_command(L, R, v, 1); } // add v to range [L, R)
    T query(size_t L, size_t R) {
        L += n;
        R += n;
        push(L);
        push(R - 1);
        T ret = 0;
        for (; L < R; L >>= 1, R >>= 1) {
            if (L & 1) ret = combine(ret, data[L++]);
            if (R & 1) ret = combine(data[--R], ret);
        }
        return ret;
    }
};

class RMQidx {
private:
    int n;  // size of val
    vvi idx; // doubling range min index. idx[k][p]: index of min(val[p:p+2^k]) including p and not including p+2^k.
    vector<int> val;

    void init(const vector<int> &src) {
        n = src.size();
        val = src;
        idx.emplace_back(vector<int>(n, 0));
        for (int i = 0; i != n; ++i) idx[0][i] = i;
        for (int k = 0, r = 1; r < n; ++k, r <<= 1) {
            idx.emplace_back(idx[k]);
            for (int p = 0; p + r < n; ++p) {
                auto idxL = idx[k][p];
                auto idxR = idx[k][p + r];
                idx[k + 1][p] = (val[idxL] > val[idxR]) ? idxR : idxL;
            }
        }
    }

public:
    RMQidx() : n(0), idx(vvi()), val(vector<int>()) {}

    RMQidx(const vector<int> &src) { init(src); }

    int query(int L, int R) { // index of min(data[0][L..R] including both ends. [L, R]
        assert(L <= R);
        if (L == R) return L;
        int k = 31 - __builtin_clz(R - L);
        auto idxL = idx[k][L];
        auto idxR = idx[k][R + 1 - (1 << k)];
        return (val[idxL] > val[idxR]) ? idxR : idxL;
    }
};

class LCA {
private:
    int n;          // number of vertexes
    int root;
    vector<int> height;     // height[v] = height of vertex v.
    vector<int> i2v;        // i2v[i] = v. Euler tour order of vertexes.
    vector<int> v2i;        // v2i[v] = i. Last position of vertex v in the Euler tour.
    RMQidx rmq;             // Range Minimum Query object which returns the position (idx) of the minimum value in the euler tour.
    void dfs(int v, int h, const vvi &Es) {
        height[v] = h;
        i2v.push_back(v);
        for (auto u : Es[v]) {
            if (height[u] == -1) {
                dfs(u, h + 1, Es);
                i2v.push_back(v);
            }
        }
    }

public:
    LCA(const vvi &Es, int _root = 0) : n(Es.size()), root(_root), height(n, -1), i2v(), v2i(n, -1) {
        dfs(root, 0, Es);
        assert(i2v.size() == 2 * n - 1);
        vector<int> val(2 * n - 1);
        for (int i = 0; i != 2 * n - 1; ++i) {
            val[i] = height[i2v[i]];
            v2i[i2v[i]] = i;
        }
        rmq = RMQidx(val);
    }

    int query(int u, int v) {
        // returns lowest common ancestor of vertex u and vertex v.
        int i = v2i[u];
        int j = v2i[v];
        if (i > j) swap(i, j);
        return i2v[rmq.query(i, j)];
    }
};

class HLDecompose {
    int n;                      // number of vertexes
    vector<int> subtree_size;   // sizes of subtrees
    void dfs0(int v, const vvi &Es) {
        subtree_size[v] = 1;
        for (auto u : Es[v]) {
            if (u == parent[v]) continue;
            parent[u] = v;
            dfs0(u, Es);
            subtree_size[v] += subtree_size[u];
        }
    }

    int find_heavy_edge(int v, const vvi &Es) {
        int heavy = v;
        for (auto u : Es[v]) if (u != parent[v] and (subtree_size[u] > subtree_size[heavy] or heavy == v)) heavy = u;
        return heavy;
    }

    int dfs1(int v, int c, int r, const vvi &Es) {
        first[v] = c;
        head[v] = r;
        int heavy = find_heavy_edge(v, Es);
        if (heavy != v) c = dfs1(heavy, c + 1, r, Es);
        for (auto u : Es[v]) if (u != parent[v] and u != heavy) c = dfs1(u, c + 1, u, Es);
        last[v] = c;
        return c;
    }

public:
    vector<int> parent, first, last, head;

    HLDecompose(const vvi &Es) : n(Es.size()), subtree_size(n, 0), parent(n, n), first(n, -1), last(n, -1), head(n, -1) {
        dfs0(0, Es);
        dfs1(0, 0, 0, Es);
    }
};

class HLDSeg {
    int n;
    LCA lca;
    vector<int> parent, first, last, head;
    SegTree<long long> seg;

    void init_seg(const vector<long long> &src, const vector<long long> &ws) {
        assert(ws.size() == n);
        vector<long long> vals(n + 1, 0);
        for (int i = 0; i < src.size(); ++i) vals[first[i]] = src[i];
        vector<long long> weights(n + 1, 0); // n + 1 個目の要素は、root の親を表すダミー頂点
        for (int i = 0; i < ws.size(); ++i) weights[first[i]] = ws[i];
        seg.init(vals, weights);
    }

    void modify_core(int u, int v, long long x) { // root -> u -> v -> leaf の順序とする。
        for (; head[u] != head[v]; v = parent[head[v]]) seg.modify(first[head[v]], first[v] + 1, x);
        seg.modify(first[u], first[v] + 1, x);
    }

    void add_core(int u, int v, long long x) { // root -> u -> v -> leaf の順序とする。
        for (; head[u] != head[v]; v = parent[head[v]]) seg.add(first[head[v]], first[v] + 1, x);
        seg.add(first[u], first[v] + 1, x);
    }

    long long query_core(int u, int v) { // root -> u -> v -> leaf の順序とする。
        long long ret = 0;
        for (; head[u] != head[v]; v = parent[head[v]]) ret = (ret + seg.query(first[head[v]], first[v] + 1)) % mod;
        return (ret + seg.query(first[u], first[v] + 1)) % mod;
    }

public:
    HLDSeg(const vvi &Es, const vector<long long> & src, const vector<long long> &ws) : n(Es.size()), lca(Es), seg() {
        HLDecompose hld(Es);
        parent = hld.parent;
        first = hld.first;
        last = hld.last;
        head = hld.head;
        init_seg(src, ws);
    }

    void modify_vertex(int v, long long x) { seg.modify(first[v], first[v] + 1, x); }

    void add_vertex(int v, long long x) { seg.add(first[v], first[v] + 1, x); }

    void modify_subtree(int v, long long x) { seg.modify(first[v], last[v] + 1, x); }

    void add_subtree(int v, long long x) { seg.add(first[v], last[v] + 1, x); }

    void modify_path(int u, int v, long long x) {
        int w = lca.query(u, v);
        modify_core(w, u, x);
        modify_core(w, v, x);
    }

    void add_path(int u, int v, long long x) {
        int w = lca.query(u, v);
        add_core(w, u, x);
        add_core(w, v, x);
        add_vertex(w, -x);
    }

    long long query_vertex(int v) { return seg.query(first[v], first[v] + 1); }

    long long query_subtree(int v) { return seg.query(first[v], last[v] + 1); }

    long long query_path(int u, int v) {
        int w = lca.query(u, v);
        return ((query_core(w, u) + query_core(w, v)) % mod + mod - query_vertex(w)) % mod;
    }
};


int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int N;
    cin >> N;
    vector<long long> S(N, 0);
    for (auto & s : S) cin >> s;
    vector<long long> C(N, 0);
    for (auto & c : C) cin >> c;
    vvi Es(N, vector<int>());
    for (int i = 1; i < N; ++i){
        int a, b;
        cin >> a >> b;
        --a;
        --b;
        Es[a].push_back(b);
        Es[b].push_back(a);
    }
    HLDSeg hldseg(Es, S, C);
    int Q;
    cin >> Q;
    while (Q--){
        int p;
        cin >> p;
        if (p == 0){
            int x, y;
            long long z;
            cin >> x >> y >> z;
            hldseg.add_path(x - 1, y - 1, z);
        }else{
            int x, y;
            cin >> x >> y;
            cout << hldseg.query_path(x - 1, y - 1) << '\n';
        }
    }
    return 0;
}
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結果

テストケース

ソースコード
