#line 1 "test/yukicoder/1030/main.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1030"
#include <algorithm>
#include <functional>
#include <iostream>
#include <vector>
#line 3 "Mylib/AlgebraicStructure/Monoid/max.cpp"
#include <optional>
namespace haar_lib {
template <typename T>
struct max_monoid {
using value_type = std::optional<T>;
value_type operator()() const { return {}; }
value_type operator()(const value_type &a, const value_type &b) const {
if (not a) return b;
if (not b) return a;
return {std::max(*a, *b)};
}
};
} // namespace haar_lib
#line 3 "Mylib/AlgebraicStructure/Monoid/maybe.cpp"
namespace haar_lib {
template <typename Semigroup>
struct maybe_monoid {
using value_type = std::optional<typename Semigroup::value_type>;
const static Semigroup S;
value_type operator()() const { return std::nullopt; }
value_type operator()(const value_type &a, const value_type &b) const {
if (not a) return b;
if (not b) return a;
return {S(*a, *b)};
}
};
} // namespace haar_lib
#line 3 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include <cassert>
#line 6 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
namespace haar_lib {
template <typename Monoid>
class segment_tree {
public:
using value_type = typename Monoid::value_type;
private:
Monoid M_;
int depth_, size_, hsize_;
std::vector<value_type> data_;
public:
segment_tree() {}
segment_tree(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
size_(1 << depth_),
hsize_(size_ / 2),
data_(size_, M_()) {}
auto operator[](int i) const {
assert(0 <= i and i < hsize_);
return data_[hsize_ + i];
}
auto fold(int l, int r) const {
assert(0 <= l and l <= r and r <= hsize_);
value_type ret_left = M_();
value_type ret_right = M_();
int L = l + hsize_, R = r + hsize_;
while (L < R) {
if (R & 1) ret_right = M_(data_[--R], ret_right);
if (L & 1) ret_left = M_(ret_left, data_[L++]);
L >>= 1, R >>= 1;
}
return M_(ret_left, ret_right);
}
auto fold_all() const {
return data_[1];
}
void set(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = x;
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
void update(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = M_(data_[i], x);
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init_with_vector(const std::vector<T> &val) {
data_.assign(size_, M_());
for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = val[i];
for (int i = hsize_; --i >= 1;) data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init(const T &val) {
init_with_vector(std::vector<value_type>(hsize_, val));
}
private:
template <bool Lower, typename F>
int bound(const int l, const int r, value_type x, F f) const {
std::vector<int> pl, pr;
int L = l + hsize_;
int R = r + hsize_;
while (L < R) {
if (R & 1) pr.push_back(--R);
if (L & 1) pl.push_back(L++);
L >>= 1, R >>= 1;
}
std::reverse(pr.begin(), pr.end());
pl.insert(pl.end(), pr.begin(), pr.end());
value_type a = M_();
for (int i : pl) {
auto b = M_(a, data_[i]);
if ((Lower and not f(b, x)) or (not Lower and f(x, b))) {
while (i < hsize_) {
const auto c = M_(a, data_[i << 1 | 0]);
if ((Lower and not f(c, x)) or (not Lower and f(x, c))) {
i = i << 1 | 0;
} else {
a = c;
i = i << 1 | 1;
}
}
return i - hsize_;
}
a = b;
}
return r;
}
public:
template <typename F = std::less<value_type>>
int lower_bound(int l, int r, value_type x, F f = F()) const {
return bound<true>(l, r, x, f);
}
template <typename F = std::less<value_type>>
int upper_bound(int l, int r, value_type x, F f = F()) const {
return bound<false>(l, r, x, f);
}
};
} // 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 3 "Mylib/Graph/TreeUtils/heavy_light_decomposition.cpp"
#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 14 "test/yukicoder/1030/main.test.cpp"
namespace hl = haar_lib;
struct lca_semigroup {
using value_type = int;
static std::function<int(int, int)> lca;
value_type operator()(value_type a, value_type b) const {
return lca(a, b);
}
};
std::function<int(int, int)> lca_semigroup::lca;
int main() {
int N, K, Q;
std::cin >> N >> K >> Q;
auto C = hl::input_vector<int>(N);
auto A = hl::input_vector<int>(K);
for (auto &x : A) --x;
hl::tree<int> tree(N);
tree.read<1, false, false>(N - 1);
hl::hl_decomposition<int> hld(tree, 0);
lca_semigroup::lca = [&](int a, int b) { return hld.lca(a, b); };
hl::segment_tree<hl::max_monoid<int>> seg1(N);
for (int i = 0; i < N; ++i) {
seg1.set(hld.get_id(i), {C[i]});
}
hl::segment_tree<hl::maybe_monoid<lca_semigroup>> seg2(K);
seg2.init_with_vector(A);
for (auto [T] : hl::input_tuples<int>(Q)) {
if (T == 1) {
int X, Y;
std::cin >> X >> Y;
--X;
--Y;
seg2.set(X, Y);
} else {
int L, R;
std::cin >> L >> R;
int lca = *seg2.fold(L - 1, R);
int ans = 0;
for (auto [l, r, d] : hld.path_query_vertex(0, lca)) {
ans = std::max(ans, seg1.fold(l, r).value());
}
std::cout << ans << "\n";
}
}
return 0;
}
test/yukicoder/1030/main.test.cpp
Max monoid
(Mylib/AlgebraicStructure/Monoid/max.cpp)