#line 1 "test/yosupo-judge/vertex_set_path_composite/main.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#include <iostream>
#include <utility>
#include <vector>
#line 3 "Mylib/AlgebraicStructure/Monoid/affine.cpp"
namespace haar_lib {
template <typename T>
struct affine_monoid {
using value_type = std::pair<T, T>;
value_type operator()() const { return std::make_pair(1, 0); }
value_type operator()(const value_type &a, const value_type &b) const {
return std::make_pair(a.first * b.first, a.first * b.second + a.second);
}
};
} // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/Monoid/dual.cpp"
namespace haar_lib {
template <typename Monoid>
struct dual_monoid {
using value_type = typename Monoid::value_type;
const static Monoid M;
value_type operator()() const { return M(); }
value_type operator()(const value_type &a, const value_type &b) const { return M(b, a); }
};
} // namespace haar_lib
#line 2 "Mylib/DataStructure/SegmentTree/segment_tree_both_foldable.cpp"
#include <cassert>
#line 4 "Mylib/DataStructure/SegmentTree/segment_tree_both_foldable.cpp"
namespace haar_lib {
template <typename Monoid>
class segment_tree_both_foldable {
public:
using value_type = typename Monoid::value_type;
private:
Monoid M_;
int depth_, size_, hsize_;
std::vector<value_type> data_left_, data_right_;
public:
segment_tree_both_foldable() {}
segment_tree_both_foldable(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
size_(1 << depth_),
hsize_(size_ / 2),
data_left_(size_, M_()),
data_right_(size_, M_()) {}
auto operator[](int i) const {
assert(0 <= i and i < hsize_);
return data_left_[hsize_ + i];
}
auto fold_left(int l, int r) const {
assert(0 <= l and l <= r and r <= hsize_);
value_type ret_left = M_();
value_type ret_right = M_();
l += hsize_, r += hsize_;
while (l < r) {
if (r & 1) ret_right = M_(data_left_[--r], ret_right);
if (l & 1) ret_left = M_(ret_left, data_left_[l++]);
l >>= 1, r >>= 1;
}
return M_(ret_left, ret_right);
}
auto fold_right(int l, int r) const {
assert(0 <= l and l <= r and r <= hsize_);
value_type ret_left = M_();
value_type ret_right = M_();
l += hsize_, r += hsize_;
while (l < r) {
if (r & 1) ret_right = M_(ret_right, data_right_[--r]);
if (l & 1) ret_left = M_(data_right_[l++], ret_left);
l >>= 1, r >>= 1;
}
return M_(ret_right, ret_left);
}
void set(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_left_[i] = data_right_[i] = x;
while (i > 1) {
i >>= 1;
data_left_[i] = M_(data_left_[i << 1 | 0], data_left_[i << 1 | 1]);
data_right_[i] = M_(data_right_[i << 1 | 1], data_right_[i << 1 | 0]);
}
}
template <typename T>
void init_with_vector(const std::vector<T> &val) {
data_left_.assign(size_, M_());
data_right_.assign(size_, M_());
for (int i = 0; i < (int) val.size(); ++i) {
data_left_[hsize_ + i] = val[i];
data_right_[hsize_ + i] = val[i];
}
for (int i = hsize_; --i >= 1;) {
data_left_[i] = M_(data_left_[i << 1 | 0], data_left_[i << 1 | 1]);
data_right_[i] = M_(data_right_[i << 1 | 1], data_right_[i << 1 | 0]);
}
}
template <typename T>
void init(const T &val) {
init_with_vector(std::vector<value_type>(hsize_, val));
}
};
} // 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>
#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 14 "test/yosupo-judge/vertex_set_path_composite/main.test.cpp"
namespace hl = haar_lib;
using mint = hl::modint<998244353>;
using Monoid = hl::dual_monoid<hl::affine_monoid<mint>>;
const Monoid M;
int main() {
std::cin.tie(0);
std::ios::sync_with_stdio(false);
int N, Q;
std::cin >> N >> Q;
auto f = hl::input_vector<std::pair<mint, mint>>(N);
hl::tree<int> tree(N);
tree.read<0, false, false>(N - 1);
hl::hl_decomposition<int> hld(tree, 0);
hl::segment_tree_both_foldable<Monoid> seg(N);
for (int i = 0; i < N; ++i) {
seg.set(hld.get_id(i), f[i]);
}
for (auto [type] : hl::input_tuples<int>(Q)) {
if (type == 0) {
int64_t p, c, d;
std::cin >> p >> c >> d;
seg.set(hld.get_id(p), std::make_pair(c, d));
} else {
int64_t u, v, x;
std::cin >> u >> v >> x;
auto res = M();
for (auto [l, r, d] : hld.path_query_vertex(u, v)) {
if (d)
res = M(res, seg.fold_left(l, r));
else
res = M(res, seg.fold_right(l, r));
}
mint ans = res.first * x + res.second;
std::cout << ans << "\n";
}
}
return 0;
}
test/yosupo-judge/vertex_set_path_composite/main.test.cpp
Basic graph
(Mylib/Graph/Template/graph.cpp)