#688261 (C++14) No.650 行列木クエリ

提出ソース
結果

問題	No.650 行列木クエリ
ユーザー	ミドリムシ
提出日時	2021-08-12 18:06:31
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,093 ms / 2,000 ms
コード長	11,733 bytes
コンパイル時間	4,335 ms
コンパイル使用メモリ	227,112 KB
実行使用メモリ	112,864 KB
最終ジャッジ日時	2024-10-01 22:35:39
合計ジャッジ時間	10,043 ms
ジャッジサーバーID （参考情報）	judge4 / judge3
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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	3 ms 6,816 KB
testcase_01	AC	699 ms 30,336 KB
testcase_02	AC	1,093 ms 106,616 KB
testcase_03	AC	4 ms 6,816 KB
testcase_04	AC	699 ms 30,336 KB
testcase_05	AC	1,092 ms 106,716 KB
testcase_06	AC	4 ms 6,820 KB
testcase_07	AC	3 ms 6,816 KB
testcase_08	AC	560 ms 31,396 KB
testcase_09	AC	849 ms 112,864 KB
testcase_10	AC	3 ms 6,816 KB
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ソースコード

raw source code
//#include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
constexpr lint mod = 1e9 + 7;
#define all(x) (x).begin(), (x).end()
#define bitcount(n) __builtin_popcountll((lint)(n))
#define fcout cout << fixed << setprecision(15)
#define highest(x) (63 - __builtin_clzll(x))
#define rep(i, n) for(int i = 0; i < int(n); i++)
#define rep2(i, l, r) for(int i = int(l); i < int(r); i++)
#define repr(i, n) for(int i = int(n) - 1; i >= 0; i--)
#define repr2(i, l, r) for(int i = int(r) - 1; i >= int(l); i--)
#define mp(x, y) make_pair(x, y)
constexpr int inf9 = 1e9; constexpr lint inf18 = 1e18;
inline void Yes(bool condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
lint power(lint base, lint exponent, lint module){ if(exponent % 2){ return power(base, exponent - 1, module) * base % module; }else if(exponent){ lint root_ans = power(base, exponent / 2, module); return root_ans * root_ans % module; }else{ return 1; }}
struct position{ int x, y; }; position mv[4] = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}}; double euclidean(position first, position second){ return sqrt((second.x - first.x) * (second.x - first.x) + (second.y - first.y) * (second.y - first.y)); }
template<class itr> void array_output(itr start, itr goal){ for(auto i = start; i != goal; i++) cout << (i == start ? "" : " ") << (*i); cout << endl; }
template<class itr> void cins(itr first, itr last){ for(auto i = first; i != last; i++){ cin >> (*i); } }
template<class T> T gcd(T a, T b){ if(b) return gcd(b, a % b); else return a; }
template<class T> T lcm(T a, T b){ return a / gcd(a, b) * b; }
struct combination{ vector<lint> fact, inv; combination(int sz) : fact(sz + 1), inv(sz + 1){ fact[0] = 1; for(int i = 1; i <= sz; i++){ fact[i] = fact[i - 1] * i % mod; } inv[sz] = power(fact[sz], mod - 2, mod); for(int i = sz - 1; i >= 0; i--){ inv[i] = inv[i + 1] * (i + 1) % mod; } } lint P(int n, int r){ if(r < 0 || n < r) return 0; return (fact[n] * inv[n - r] % mod); } lint C(int p, int q){ if(q < 0 || p < q) return 0; return (fact[p] * inv[q] % mod * inv[p - q] % mod); } };
template<class itr> bool next_sequence(itr first, itr last, int max_bound){ itr now = last; while(now != first){ now--; (*now)++; if((*now) == max_bound){ (*now) = 0; }else{ return true; } } return false; }
template<class itr, class itr2> bool next_sequence2(itr first, itr last, itr2 first2, itr2 last2){ itr now = last; itr2 now2 = last2; while(now != first){ now--, now2--; (*now)++; if((*now) == (*now2)){ (*now) = 0; }else{ return true; } } return false; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b){ if(b < a){ a = b; return 1; } return 0; }
inline int at(lint i, int j){ return (i >> j) & 1; }
random_device rnd;
bool is_in_board(lint y, lint x, lint H, lint W){ return (0 <= y && y < H && 0 <= x && x < W); }
lint inv2 = power(2, mod - 2, mod);

struct io_init {
   io_init() {
     cin.tie(nullptr); cout.tie(nullptr);
     std::ios::sync_with_stdio(false);
   }
} io_init;


template<class T>
struct Matrix{
    int h, w;
    vector<vector<T>> data;
    
    Matrix(){ Matrix(1); }
    Matrix(int n) : h(n), w(n), data(n, vector<T>(n)) {}
    Matrix(int h, int w) : h(h), w(w), data(h, vector<T>(w)) {}
    
    Matrix operator +(Matrix a){ return Matrix(*this) += a; }
    Matrix operator -(Matrix a){ return Matrix(*this) -= a; }
    Matrix operator *(Matrix a){ return Matrix(*this) *= a; }
    
    Matrix& operator +=(Matrix a){
        rep(i, h) rep(j, w){
            data[i][j] += a[i][j];
        }
        return *this;
    }
    
    Matrix& operator -=(Matrix a){
        rep(i, h) rep(j, w){
            data[i][j] -= a[i][j];
        }
        return *this;
    }
    
    Matrix& operator *=(Matrix a){
        assert(w == a.h);
        Matrix ans(h, a.w);
        rep(i, h) rep(j, a.w){
            ans[i][j] = 0;
            rep(k, w){
                ans[i][j] += data[i][k] * a[k][j];
            }
        }
        (*this) = ans;
        return *this;
    }
    
    vector<T>& operator [](int k){
        return data[k];
    }
    
    Matrix pow(lint exp){
        Matrix ans(1), powed = (*this);
        while(exp){
            if(exp % 2) ans *= powed;
            powed *= powed;
            exp /= 2;
        }
        return ans;
    }
};

struct Modint{
    lint x;
    
    Modint(): x(0) {}
    Modint(lint x): x(x >= 0 || x % mod == 0 ? x % mod : mod - (-x) % mod) {}
    
    Modint operator +(Modint a){ return Modint(*this) += a; }
    Modint operator -(Modint a){ return Modint(*this) -= a; }
    Modint operator *(Modint a){ return Modint(*this) *= a; }
    Modint operator /(Modint a){ return Modint(*this) /= a; }
    
    Modint operator -(){ return Modint(0) - Modint(*this); }
    
    Modint& operator +=(Modint a){
        x += a.x;
        if(x >= mod) x -= mod;
        return *this;
    }
    
    Modint& operator -=(Modint a){
        if(x < a.x) x += mod;
        x -= a.x;
        return *this;
    }
    
    Modint& operator *=(Modint a){
        x = x * a.x % mod;
        return *this;
    }
    
    Modint operator /=(Modint a){
        (*this) *= a.inv();
        return *this;
    }
    
    Modint inv(){
        return pow(mod - 2);
    }
    
    Modint pow(lint exp){
        Modint ans(1), powed = (*this);
        while(exp){
            if(exp % 2) ans *= powed;
            powed *= powed;
            exp /= 2;
        }
        return ans;
    }
    
    bool operator ==(Modint a){ return x == a.x; }
    bool operator !=(Modint a){ return x != a.x; }
};

ostream& operator <<(ostream& os, Modint a){
    os << a.x;
    return os;
}

istream &operator >>(istream &is, Modint& a){
    lint x;
    is >> x;
    a = Modint(x);
    return is;
}




template<class T>
struct SegmentTree{
    using F = function<T(T, T)>;
    
    int sz;
    vector<T> data;
    
    F f;
    T id;
    
    SegmentTree() {}
    
    SegmentTree(int n, F f, T id): f(f), id(id) {
        sz = 1;
        while(sz < n) sz *= 2;
        data.assign(sz * 2, id);
    }
    
    void update(int k, T x){
        k += sz;
        data[k] = x;
        while(k > 1){
            k /= 2;
            data[k] = f(data[k * 2], data[k * 2 + 1]);
        }
    }
    
    T query(int a, int b, int l, int r, int at){
        if(a <= l && r <= b){
            return data[at];
        }else if(r <= a || b <= l){
            return id;
        }
        return f(query(a, b, l, (l + r) / 2, at * 2), query(a, b, (l + r) / 2, r, at * 2 + 1));
    }
    
    T query(int a, int b){
        return query(a, b, 0, sz, 1);
    }
    
    T operator [](int k){
        return data[k + sz];
    }
};

template<class T>
struct HLD{
    using F = function<T(T, T)>;
    
    F f;
    T id;
    
    int sz;
    SegmentTree<T> seg, seg_rev;
    
    vector<vector<int>> graph;
    vector<vector<int>> child;
    vector<int> size, depth, par;
    vector<int> in, head;
    
    vector<int> tour, tour_id;
    SegmentTree<int> rmq;
    
    HLD(int n, F f, T id): sz(n), f(f), id(id), graph(n), child(n), size(n), depth(n), par(n), in(n), head(n), tour_id(n) {
        seg = SegmentTree<T>(n, f, id);
        seg_rev = SegmentTree<T>(n, f, id);
    }
    
    T seg_rev_query(int a, int b){ return seg_rev.query(sz - b, sz - a); }
    
    void add_edge(int a, int b){
        graph[a].push_back(b);
        graph[b].push_back(a);
    }
    
    void dfs_sz(int at, int back){
        size[at] = 1;
        par[at] = back;
        for(int to: graph[at]){
            if(to == back) continue;
            
            depth[to] = depth[at] + 1;
            dfs_sz(to, at);
            child[at].push_back(to);
            size[at] += size[to];
        }
    }
    
    void dfs_hl(int at, int par, int &num){
        in[at] = num;
        num++;
        if(child[at].empty()) return;
        
        for(int &c: child[at]){
            if(size[c] > size[child[at][0]]){
                swap(c, child[at][0]);
            }
        }
        int heavy = child[at][0];
        for(int c: child[at]){
            if(c == heavy){
                head[c] = head[at];
            }else{
                head[c] = c;
            }
            dfs_hl(c, at, num);
        }
    }
    
    void dfs_lca(int at, int back){
        tour_id[at] = int(tour.size());
        tour.push_back(at);
    
        for(int to: graph[at]){
            if(to == back) continue;
            
            dfs_lca(to, at);
            tour.push_back(at);
        }
    }
    
    void build(){
        depth.resize(sz);
        depth[0] = 0;
        dfs_sz(0, -1);
        
        head[0] = 0;
        int tmp = 0;
        dfs_hl(0, -1, tmp);
        
        tour.clear();
        dfs_lca(0, -1);
        
        depth.push_back(INT_MAX);
        auto f = [&](int a, int b){ if(depth[a] < depth[b]) return a; else return b; };
        rmq = SegmentTree<int>(int(tour.size()), f, sz);
        rep(i, tour.size()){
            rmq.update(i, tour[i]);
        }
    }
    
    // s -> t, [s, t)
    T query_up(int s, int t){
        if(s == t) return id;
        T ans = id;
        while(depth[head[s]] > depth[t]){
            int top = head[s];
            ans = f(ans, seg_rev_query(in[top], in[s] + 1));
            s = par[top];
        }
        ans = f(ans, seg_rev_query(in[t] + 1, in[s] + 1));
        return ans;
    }
    
    // s -> t, (s, t]
    T query_down(int s, int t){
        if(s == t) return id;
        swap(s, t);
        vector<T> items;
        while(depth[head[s]] > depth[t]){
            int top = head[s];
            items.push_back(seg.query(in[top], in[s] + 1));
            s = par[top];
        }
        items.push_back(seg.query(in[t] + 1, in[s] + 1));
        
        T ans = id;
        repr(i, items.size()){
            ans = f(ans, items[i]);
        }
        return ans;
    }
    
    int lca(int a, int b){
        if(tour_id[a] > tour_id[b]) swap(a, b);
        return rmq.query(tour_id[a], tour_id[b] + 1);
    }
    
    // s -> t, [s, t]
    T query(int s, int t, bool is_edge = false){
        int l = lca(s, t);
        
        T ans = query_up(s, l);
        if(!is_edge) ans = f(ans, seg.query(in[l], in[l] + 1));
        ans = f(ans, query_down(l, t));
        return ans;
    }

    void update(int k, T x){
        seg.update(in[k], x);
        seg_rev.update(sz - in[k], x);
    }
};

struct edge{
    int to, num;
};

vector<edge> graph[101010];
int edge_child[101010];

void dfs(int at, int back){
    for(edge e: graph[at]){
        if(e.to == back) continue;
        
        edge_child[e.num] = e.to;
        dfs(e.to, at);
    }
}

int main(){
    int n;
    cin >> n;
    Matrix<Modint> E(2);
    E[0][0] = E[1][1] = 1;
    
    auto f = [](Matrix<Modint> a, Matrix<Modint> b){ return a * b; };
    HLD<Matrix<Modint>> g(n, f, E);
    rep(i, n - 1){
        int u, v;
        cin >> u >> v;
        graph[u].push_back({v, i});
        graph[v].push_back({u, i});
        g.add_edge(u, v);
    }
    dfs(0, -1);
    
    g.build();
    
    int q;
    cin >> q;
    rep(_, q){
        char t;
        cin >> t;
        if(t == 'x'){
            int i, a, b, c, d;
            cin >> i >> a >> b >> c >> d;
            Matrix<Modint> x(2);
            x[0][0] = a;
            x[0][1] = b;
            x[1][0] = c;
            x[1][1] = d;
            g.update(edge_child[i], x);
        }else{
            int i, j;
            cin >> i >> j;
            auto ans = g.query(i, j, true);
            cout << ans[0][0] << " ";
            cout << ans[0][1] << " ";
            cout << ans[1][0] << " ";
            cout << ans[1][1] << endl;
        }
    }
}
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結果

テストケース

ソースコード
