#line 1 "test/yukicoder/235/main.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/235"
#include <iostream>
#line 2 "Mylib/DataStructure/SegmentTree/lazy_segment_tree_with_coefficients.cpp"
#include <cassert>
#include <vector>
namespace haar_lib {
template <typename T>
class lazy_segment_tree_with_coefficients {
public:
using value_type = T;
private:
int depth_, size_, hsize_;
std::vector<T> data_, lazy_, coeff_;
void propagate(int i) {
if (lazy_[i] == 0) return;
if (i < hsize_) {
lazy_[i << 1 | 0] = lazy_[i] + lazy_[i << 1 | 0];
lazy_[i << 1 | 1] = lazy_[i] + lazy_[i << 1 | 1];
}
data_[i] = data_[i] + lazy_[i] * coeff_[i];
lazy_[i] = 0;
}
T update(int i, int l, int r, int s, int t, const T &x) {
propagate(i);
if (r <= s or t <= l) return data_[i];
if (s <= l and r <= t) {
lazy_[i] += x;
propagate(i);
return data_[i];
}
return data_[i] =
update(i << 1 | 0, l, (l + r) / 2, s, t, x) +
update(i << 1 | 1, (l + r) / 2, r, s, t, x);
}
T get(int i, int l, int r, int x, int y) {
propagate(i);
if (r <= x or y <= l) return 0;
if (x <= l and r <= y) return data_[i];
return get(i << 1 | 0, l, (l + r) / 2, x, y) + get(i << 1 | 1, (l + r) / 2, r, x, y);
}
public:
lazy_segment_tree_with_coefficients() {}
lazy_segment_tree_with_coefficients(int n, std::vector<T> coeff) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
size_(1 << depth_),
hsize_(size_ / 2),
data_(size_, 0),
lazy_(size_, 0),
coeff_(size_, 0) {
for (int i = hsize_; i < size_; ++i) coeff_[i] = coeff[i - hsize_];
for (int i = hsize_; --i >= 1;) coeff_[i] = coeff_[i << 1 | 0] + coeff_[i << 1 | 1];
}
void update(int l, int r, const T &x) {
assert(0 <= l and l <= r and r <= hsize_);
update(1, 0, hsize_, l, r, x);
}
void update(int i, const T &x) { update(i, i + 1, x); }
T fold(int l, int r) {
assert(0 <= l and l <= r and r <= hsize_);
return get(1, 0, hsize_, l, r);
}
T fold_all() { return fold(0, hsize_); }
T operator[](int i) { return fold(i, i + 1); }
void init(const T &val) {
init_with_vector(std::vector<T>(hsize_, val));
}
void init_with_vector(const std::vector<T> &val) {
data_.assign(size_, 0);
lazy_.assign(size_, 0);
for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = val[i];
for (int i = hsize_; --i >= 0;) data_[i] = data_[i << 1 | 0] + data_[i << 1 | 1];
}
};
} // namespace haar_lib
#line 4 "Mylib/Graph/Template/graph.cpp"
namespace haar_lib {
template <typename T>
struct edge {
int from, to;
T cost;
int index = -1;
edge() {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
};
template <typename T>
struct graph {
using weight_type = T;
using edge_type = edge<T>;
std::vector<std::vector<edge<T>>> data;
auto& operator[](size_t i) { return data[i]; }
const auto& operator[](size_t i) const { return data[i]; }
auto begin() const { return data.begin(); }
auto end() const { return data.end(); }
graph() {}
graph(int N) : data(N) {}
bool empty() const { return data.empty(); }
int size() const { return data.size(); }
void add_edge(int i, int j, T w, int index = -1) {
data[i].emplace_back(i, j, w, index);
}
void add_undirected(int i, int j, T w, int index = -1) {
add_edge(i, j, w, index);
add_edge(j, i, w, index);
}
template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
void read(int M) {
for (int i = 0; i < M; ++i) {
int u, v;
std::cin >> u >> v;
u -= I;
v -= I;
T w = 1;
if (WEIGHTED) std::cin >> w;
if (DIRECTED)
add_edge(u, v, w, i);
else
add_undirected(u, v, w, i);
}
}
};
template <typename T>
using tree = graph<T>;
} // namespace haar_lib
#line 2 "Mylib/Graph/TreeUtils/heavy_light_decomposition.cpp"
#include <algorithm>
#include <utility>
#line 6 "Mylib/Graph/TreeUtils/heavy_light_decomposition.cpp"
namespace haar_lib {
template <typename T>
class hl_decomposition {
int n_;
std::vector<int> sub_, // subtree size
par_, // parent id
head_, // chain head id
id_, // id[original id] = hld id
rid_, // rid[hld id] = original id
next_, // next node in a chain
end_; //
int dfs_sub(tree<T> &tr, int cur, int p) {
par_[cur] = p;
int t = 0;
for (auto &e : tr[cur]) {
if (e.to == p) continue;
sub_[cur] += dfs_sub(tr, e.to, cur);
if (sub_[e.to] > t) {
t = sub_[e.to];
next_[cur] = e.to;
std::swap(e, tr[cur][0]);
}
}
return sub_[cur];
}
void dfs_build(const tree<T> &tr, int cur, int &i) {
id_[cur] = i;
rid_[i] = cur;
++i;
for (auto &e : tr[cur]) {
if (e.to == par_[cur]) continue;
head_[e.to] = (e.to == tr[cur][0].to ? head_[cur] : e.to);
dfs_build(tr, e.to, i);
}
end_[cur] = i;
}
public:
hl_decomposition() {}
hl_decomposition(tree<T> tr, int root) : n_(tr.size()), sub_(n_, 1), par_(n_, -1), head_(n_), id_(n_), rid_(n_), next_(n_, -1), end_(n_, -1) {
dfs_sub(tr, root, -1);
int i = 0;
dfs_build(tr, root, i);
}
std::vector<std::tuple<int, int, bool>> path_query_vertex(int x, int y) const {
std::vector<std::tuple<int, int, bool>> ret;
const int w = lca(x, y);
{
int y = w;
bool d = true;
while (1) {
if (id_[x] > id_[y]) std::swap(x, y), d = not d;
int l = std::max(id_[head_[y]], id_[x]), r = id_[y] + 1;
if (l != r) ret.emplace_back(l, r, d);
if (head_[x] == head_[y]) break;
y = par_[head_[y]];
}
}
x = y;
y = w;
{
std::vector<std::tuple<int, int, bool>> temp;
bool d = false;
while (1) {
if (id_[x] > id_[y]) std::swap(x, y), d = not d;
int l = std::max({id_[head_[y]], id_[x], id_[w] + 1}), r = id_[y] + 1;
if (l != r) temp.emplace_back(l, r, d);
if (head_[x] == head_[y]) break;
y = par_[head_[y]];
}
std::reverse(temp.begin(), temp.end());
ret.insert(ret.end(), temp.begin(), temp.end());
}
return ret;
}
std::vector<std::pair<int, int>> path_query_edge(int x, int y) const {
std::vector<std::pair<int, int>> ret;
while (1) {
if (id_[x] > id_[y]) std::swap(x, y);
if (head_[x] == head_[y]) {
if (x != y) ret.emplace_back(id_[x] + 1, id_[y] + 1);
break;
}
ret.emplace_back(id_[head_[y]], id_[y] + 1);
y = par_[head_[y]];
}
return ret;
}
std::pair<int, int> subtree_query_edge(int x) const {
return {id_[x] + 1, end_[x]};
}
std::pair<int, int> subtree_query_vertex(int x) const {
return {id_[x], end_[x]};
}
int get_edge_id(int u, int v) const { // 辺に対応するid
if (par_[u] == v) return id_[u];
if (par_[v] == u) return id_[v];
return -1;
}
int parent(int x) const { return par_[x]; };
int lca(int u, int v) const {
while (1) {
if (id_[u] > id_[v]) std::swap(u, v);
if (head_[u] == head_[v]) return u;
v = par_[head_[v]];
}
}
int get_id(int x) const {
return id_[x];
}
};
} // namespace haar_lib
#line 2 "Mylib/IO/input_tuples.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuples.cpp"
#include <tuple>
#line 6 "Mylib/IO/input_tuple.cpp"
namespace haar_lib {
template <typename T, size_t... I>
static void input_tuple_helper(std::istream &s, T &val, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(s >> std::get<I>(val)), 0)...};
}
template <typename T, typename U>
std::istream &operator>>(std::istream &s, std::pair<T, U> &value) {
s >> value.first >> value.second;
return s;
}
template <typename... Args>
std::istream &operator>>(std::istream &s, std::tuple<Args...> &value) {
input_tuple_helper(s, value, std::make_index_sequence<sizeof...(Args)>());
return s;
}
} // namespace haar_lib
#line 8 "Mylib/IO/input_tuples.cpp"
namespace haar_lib {
template <typename... Args>
class InputTuples {
struct iter {
using value_type = std::tuple<Args...>;
value_type value;
bool fetched = false;
int N, c = 0;
value_type operator*() {
if (not fetched) {
std::cin >> value;
}
return value;
}
void operator++() {
++c;
fetched = false;
}
bool operator!=(iter &) const {
return c < N;
}
iter(int N) : N(N) {}
};
int N;
public:
InputTuples(int N) : N(N) {}
iter begin() const { return iter(N); }
iter end() const { return iter(N); }
};
template <typename... Args>
auto input_tuples(int N) {
return InputTuples<Args...>(N);
}
} // namespace haar_lib
#line 4 "Mylib/IO/input_vector.cpp"
namespace haar_lib {
template <typename T>
std::vector<T> input_vector(int N) {
std::vector<T> ret(N);
for (int i = 0; i < N; ++i) std::cin >> ret[i];
return ret;
}
template <typename T>
std::vector<std::vector<T>> input_vector(int N, int M) {
std::vector<std::vector<T>> ret(N);
for (int i = 0; i < N; ++i) ret[i] = input_vector<T>(M);
return ret;
}
} // namespace haar_lib
#line 4 "Mylib/Number/Mint/mint.cpp"
namespace haar_lib {
template <int32_t M>
class modint {
uint32_t val_;
public:
constexpr static auto mod() { return M; }
constexpr modint() : val_(0) {}
constexpr modint(int64_t n) {
if (n >= M)
val_ = n % M;
else if (n < 0)
val_ = n % M + M;
else
val_ = n;
}
constexpr auto &operator=(const modint &a) {
val_ = a.val_;
return *this;
}
constexpr auto &operator+=(const modint &a) {
if (val_ + a.val_ >= M)
val_ = (uint64_t) val_ + a.val_ - M;
else
val_ += a.val_;
return *this;
}
constexpr auto &operator-=(const modint &a) {
if (val_ < a.val_) val_ += M;
val_ -= a.val_;
return *this;
}
constexpr auto &operator*=(const modint &a) {
val_ = (uint64_t) val_ * a.val_ % M;
return *this;
}
constexpr auto &operator/=(const modint &a) {
val_ = (uint64_t) val_ * a.inv().val_ % M;
return *this;
}
constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }
constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }
constexpr auto &operator++() {
*this += 1;
return *this;
}
constexpr auto &operator--() {
*this -= 1;
return *this;
}
constexpr auto operator++(int) {
auto t = *this;
*this += 1;
return t;
}
constexpr auto operator--(int) {
auto t = *this;
*this -= 1;
return t;
}
constexpr static modint pow(int64_t n, int64_t p) {
if (p < 0) return pow(n, -p).inv();
int64_t ret = 1, e = n % M;
for (; p; (e *= e) %= M, p >>= 1)
if (p & 1) (ret *= e) %= M;
return ret;
}
constexpr static modint inv(int64_t a) {
int64_t b = M, u = 1, v = 0;
while (b) {
int64_t t = a / b;
a -= t * b;
std::swap(a, b);
u -= t * v;
std::swap(u, v);
}
u %= M;
if (u < 0) u += M;
return u;
}
constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }
constexpr auto pow(int64_t p) const { return pow(val_, p); }
constexpr auto inv() const { return inv(val_); }
friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }
friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }
friend std::istream &operator>>(std::istream &s, modint &a) {
s >> a.val_;
return s;
}
friend std::ostream &operator<<(std::ostream &s, const modint &a) {
s << a.val_;
return s;
}
template <int N>
static auto div() {
static auto value = inv(N);
return value;
}
explicit operator int32_t() const noexcept { return val_; }
explicit operator int64_t() const noexcept { return val_; }
};
} // namespace haar_lib
#line 5 "Mylib/Utils/sort_simultaneously.cpp"
#include <numeric>
#line 8 "Mylib/Utils/sort_simultaneously.cpp"
namespace haar_lib {
namespace sort_simultaneously_impl {
template <typename T>
void helper(int N, const std::vector<int> &ord, std::vector<T> &a) {
std::vector<T> temp(N);
for (int i = 0; i < N; ++i) temp[i] = a[ord[i]];
std::swap(temp, a);
}
} // namespace sort_simultaneously_impl
template <typename Compare, typename... Args>
void sort_simultaneously(const Compare &compare, std::vector<Args> &... args) {
const int N = std::max({args.size()...});
assert((int) std::min({args.size()...}) == N);
std::vector<int> ord(N);
std::iota(ord.begin(), ord.end(), 0);
std::sort(ord.begin(), ord.end(), compare);
(void) std::initializer_list<int>{
(void(sort_simultaneously_impl::helper(N, ord, args)), 0)...};
}
} // namespace haar_lib
#line 11 "test/yukicoder/235/main.test.cpp"
namespace hl = haar_lib;
using mint = hl::modint<1000000007>;
int main() {
std::cin.tie(0);
std::ios::sync_with_stdio(false);
int N;
std::cin >> N;
auto S = hl::input_vector<mint>(N);
auto C = hl::input_vector<mint>(N);
hl::tree<int> tr(N);
tr.read<1, false, false>(N - 1);
auto hld = hl::hl_decomposition(tr, 0);
hl::sort_simultaneously(
[&](int i, int j) { return hld.get_id(i) < hld.get_id(j); },
S, C);
auto seg = hl::lazy_segment_tree_with_coefficients<mint>(N, C);
seg.init_with_vector(S);
int Q;
std::cin >> Q;
for (auto [type] : hl::input_tuples<int>(Q)) {
if (type == 0) {
int X, Y, Z;
std::cin >> X >> Y >> Z;
--X, --Y;
for (auto [l, r, d] : hld.path_query_vertex(X, Y)) {
seg.update(l, r, Z);
}
} else {
int X, Y;
std::cin >> X >> Y;
--X, --Y;
mint ans = 0;
for (auto [l, r, d] : hld.path_query_vertex(X, Y)) {
ans += seg.fold(l, r);
}
std::cout << ans << "\n";
}
}
}
test/yukicoder/235/main.test.cpp
Basic graph
(Mylib/Graph/Template/graph.cpp)