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#define PROBLEM "https://yukicoder.me/problems/no/650" #include "../../template/template.hpp" #include "../../graph/tree/heavy-light-decomposition.hpp" #include "../../structure/segment-tree/segment-tree.hpp" #include "../../math/combinatorics/mod-int.hpp" #include "../../math/matrix/square-matrix.hpp" int main() { int N; cin >> N; vector< int > X(N), Y(N); HeavyLightDecomposition<> g(N); for(int i = 1; i < N; i++) { cin >> X[i] >> Y[i]; g.add_edge(X[i], Y[i]); } g.build(); for(int i = 1; i < N; i++) { if(g.in[X[i]] > g.in[Y[i]]) swap(X[i], Y[i]); } using Mat = SquareMatrix< modint, 2 >; auto f = [](const Mat &a, const Mat &b) { return a * b; }; auto seg = get_segment_tree(N, f, Mat::mul_identity()); int Q; cin >> Q; while(Q--) { char x; cin >> x; if(x == 'x') { int v; cin >> v; Mat m; cin >> m[0][0] >> m[0][1] >> m[1][0] >> m[1][1]; seg.set(g.in[Y[v + 1]], m); } else { int y, z; cin >> y >> z; auto mat = g.query(y, z, Mat::mul_identity(), [&](int a, int b) { return seg.prod(a, b); }, f, true); cout << mat[0][0] << " " << mat[0][1] << " " << mat[1][0] << " " << mat[1][1] << "\n"; } } }
#line 1 "test/verify/yukicoder-650.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/650" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { explicit FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 4 "test/verify/yukicoder-650.test.cpp" #line 2 "graph/tree/heavy-light-decomposition.hpp" #line 2 "graph/graph-template.hpp" /** * @brief Graph Template(グラフテンプレート) */ template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector< Edge< T > > &operator[](const int &k) { return g[k]; } inline const vector< Edge< T > > &operator[](const int &k) const { return g[k]; } }; template< typename T = int > using Edges = vector< Edge< T > >; #line 4 "graph/tree/heavy-light-decomposition.hpp" /** * @brief Heavy-Light-Decomposition(HL分解) * @see https://smijake3.hatenablog.com/entry/2019/09/15/200200 */ template< typename T = int > struct HeavyLightDecomposition : Graph< T > { public: using Graph< T >::Graph; using Graph< T >::g; vector< int > sz, in, out, head, rev, par, dep; void build() { sz.assign(g.size(), 0); in.assign(g.size(), 0); out.assign(g.size(), 0); head.assign(g.size(), 0); rev.assign(g.size(), 0); par.assign(g.size(), 0); dep.assign(g.size(), 0); dfs_sz(0, -1, 0); int t = 0; dfs_hld(0, -1, t); } /* k: 0-indexed */ int la(int v, int k) { while(1) { int u = head[v]; if(in[v] - k >= in[u]) return rev[in[v] - k]; k -= in[v] - in[u] + 1; v = par[u]; } } int lca(int u, int v) const { for(;; v = par[head[v]]) { if(in[u] > in[v]) swap(u, v); if(head[u] == head[v]) return u; } } int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; } template< typename E, typename Q, typename F, typename S > E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s, bool edge = false) { E l = ti, r = ti; for(;; v = par[head[v]]) { if(in[u] > in[v]) swap(u, v), swap(l, r); if(head[u] == head[v]) break; l = f(q(in[head[v]], in[v] + 1), l); } return s(f(q(in[u] + edge, in[v] + 1), l), r); } template< typename E, typename Q, typename F > E query(int u, int v, const E &ti, const Q &q, const F &f, bool edge = false) { return query(u, v, ti, q, f, f, edge); } template< typename Q > void add(int u, int v, const Q &q, bool edge = false) { for(;; v = par[head[v]]) { if(in[u] > in[v]) swap(u, v); if(head[u] == head[v]) break; q(in[head[v]], in[v] + 1); } q(in[u] + edge, in[v] + 1); } /* {parent, child} */ vector< pair< int, int > > compress(vector< int > &remark) { auto cmp = [&](int a, int b) { return in[a] < in[b]; }; sort(begin(remark), end(remark), cmp); remark.erase(unique(begin(remark), end(remark)), end(remark)); int K = (int) remark.size(); for(int k = 1; k < K; k++) remark.emplace_back(lca(remark[k - 1], remark[k])); sort(begin(remark), end(remark), cmp); remark.erase(unique(begin(remark), end(remark)), end(remark)); vector< pair< int, int > > es; stack< int > st; for(auto &k : remark) { while(!st.empty() && out[st.top()] <= in[k]) st.pop(); if(!st.empty()) es.emplace_back(st.top(), k); st.emplace(k); } return es; } explicit HeavyLightDecomposition(const Graph< T > &g) : Graph< T >(g) {} private: void dfs_sz(int idx, int p, int d) { dep[idx] = d; par[idx] = p; sz[idx] = 1; if(g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back()); for(auto &to : g[idx]) { if(to == p) continue; dfs_sz(to, idx, d + 1); sz[idx] += sz[to]; if(sz[g[idx][0]] < sz[to]) swap(g[idx][0], to); } } void dfs_hld(int idx, int p, int ×) { in[idx] = times++; rev[in[idx]] = idx; for(auto &to : g[idx]) { if(to == p) continue; head[to] = (g[idx][0] == to ? head[idx] : to); dfs_hld(to, idx, times); } out[idx] = times; } }; #line 6 "test/verify/yukicoder-650.test.cpp" #line 1 "structure/segment-tree/segment-tree.hpp" /** * @brief Segment Tree(セグメント木) * @docs docs/segment-tree.md */ template< typename T, typename F > struct SegmentTree { int n, sz; vector< T > seg; const F f; const T ti; SegmentTree() = default; explicit SegmentTree(int n, const F f, const T &ti) : n(n), f(f), ti(ti) { sz = 1; while(sz < n) sz <<= 1; seg.assign(2 * sz, ti); } explicit SegmentTree(const vector< T > &v, const F f, const T &ti) : SegmentTree((int) v.size(), f, ti) { build(v); } void build(const vector< T > &v) { assert(n == (int) v.size()); for(int k = 0; k < n; k++) seg[k + sz] = v[k]; for(int k = sz - 1; k > 0; k--) { seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]); } } void set(int k, const T &x) { k += sz; seg[k] = x; while(k >>= 1) { seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]); } } T get(int k) const { return seg[k + sz]; } T operator[](const int &k) const { return get(k); } void apply(int k, const T &x) { k += sz; seg[k] = f(seg[k], x); while(k >>= 1) { seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]); } } T prod(int l, int r) const { T L = ti, R = ti; for(l += sz, r += sz; l < r; l >>= 1, r >>= 1) { if(l & 1) L = f(L, seg[l++]); if(r & 1) R = f(seg[--r], R); } return f(L, R); } T all_prod() const { return seg[1]; } template< typename C > int find_first(int l, const C &check) const { if(l >= n) return n; l += sz; T sum = ti; do { while((l & 1) == 0) l >>= 1; if(check(f(sum, seg[l]))) { while(l < sz) { l <<= 1; auto nxt = f(sum, seg[l]); if(not check(nxt)) { sum = nxt; l++; } } return l + 1 - sz; } sum = f(sum, seg[l++]); } while((l & -l) != l); return n; } template< typename C > int find_last(int r, const C &check) const { if(r <= 0) return -1; r += sz; T sum = ti; do { r--; while(r > 1 and (r & 1)) r >>= 1; if(check(f(seg[r], sum))) { while(r < sz) { r = (r << 1) + 1; auto nxt = f(seg[r], sum); if(not check(nxt)) { sum = nxt; r--; } } return r - sz; } sum = f(seg[r], sum); } while((r & -r) != r); return -1; } }; template< typename T, typename F > SegmentTree< T, F > get_segment_tree(int N, const F &f, const T &ti) { return SegmentTree{N, f, ti}; } template< typename T, typename F > SegmentTree< T, F > get_segment_tree(const vector< T > &v, const F &f, const T &ti) { return SegmentTree{v, f, ti}; } #line 8 "test/verify/yukicoder-650.test.cpp" #line 1 "math/combinatorics/mod-int.hpp" template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; #line 1 "math/matrix/square-matrix.hpp" /** * @brief Square-Matrix(正方行列) */ template< class T, size_t N > struct SquareMatrix { array< array< T, N >, N > A; SquareMatrix() : A{{}} {} size_t size() const { return N; } inline const array< T, N > &operator[](int k) const { return (A.at(k)); } inline array< T, N > &operator[](int k) { return (A.at(k)); } static SquareMatrix add_identity() { return SquareMatrix(); } static SquareMatrix mul_identity() { SquareMatrix mat; for(size_t i = 0; i < N; i++) mat[i][i] = 1; return mat; } SquareMatrix &operator+=(const SquareMatrix &B) { for(size_t i = 0; i < N; i++) { for(size_t j = 0; j < N; j++) { (*this)[i][j] += B[i][j]; } } return *this; } SquareMatrix &operator-=(const SquareMatrix &B) { for(size_t i = 0; i < N; i++) { for(size_t j = 0; j < N; j++) { (*this)[i][j] -= B[i][j]; } } return *this; } SquareMatrix &operator*=(const SquareMatrix &B) { array< array< T, N >, N > C; for(size_t i = 0; i < N; i++) { for(size_t j = 0; j < N; j++) { for(size_t k = 0; k < N; k++) { C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); } } } A.swap(C); return (*this); } SquareMatrix &operator^=(uint64_t k) { SquareMatrix B = SquareMatrix::mul_identity(); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return *this; } SquareMatrix operator+(const SquareMatrix &B) const { return SquareMatrix(*this) += B; } SquareMatrix operator-(const SquareMatrix &B) const { return SquareMatrix(*this) -= B; } SquareMatrix operator*(const SquareMatrix &B) const { return SquareMatrix(*this) *= B; } SquareMatrix operator^(uint64_t k) const { return SquareMatrix(*this) ^= k; } friend ostream &operator<<(ostream &os, SquareMatrix &p) { for(int i = 0; i < N; i++) { os << "["; for(int j = 0; j < N; j++) { os << p[i][j] << (j + 1 == N ? "]\n" : ","); } } return os; } }; #line 11 "test/verify/yukicoder-650.test.cpp" int main() { int N; cin >> N; vector< int > X(N), Y(N); HeavyLightDecomposition<> g(N); for(int i = 1; i < N; i++) { cin >> X[i] >> Y[i]; g.add_edge(X[i], Y[i]); } g.build(); for(int i = 1; i < N; i++) { if(g.in[X[i]] > g.in[Y[i]]) swap(X[i], Y[i]); } using Mat = SquareMatrix< modint, 2 >; auto f = [](const Mat &a, const Mat &b) { return a * b; }; auto seg = get_segment_tree(N, f, Mat::mul_identity()); int Q; cin >> Q; while(Q--) { char x; cin >> x; if(x == 'x') { int v; cin >> v; Mat m; cin >> m[0][0] >> m[0][1] >> m[1][0] >> m[1][1]; seg.set(g.in[Y[v + 1]], m); } else { int y, z; cin >> y >> z; auto mat = g.query(y, z, Mat::mul_identity(), [&](int a, int b) { return seg.prod(a, b); }, f, true); cout << mat[0][0] << " " << mat[0][1] << " " << mat[1][0] << " " << mat[1][1] << "\n"; } } }