cp-library
競技プログラミング用 C++ ライブラリ
test/link_cut_tree_composite.test.cpp
test/link_cut_tree_composite.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite"
#include "../tree/link_cut_tree.hpp"
#include "../math/mint.hpp"
#include <array>
#include "components/fast_io.hpp"
#include <vector>
using namespace std;
using S = array<mint, 2>;
S op(const S &a, const S &b) { return {a[0] * b[0], a[1] * b[0] + b[1]}; }
S e() { return {1, 0}; }
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
vector<S> values(n);
for (auto &v : values) {
unsigned a, b;
input.read(a), input.read(b);
v = {a, b};
}
LinkCutTree<S, op, e> tree(values);
std::vector<std::pair<int, int>> edges(n - 1);
for (auto &[u, v] : edges) input.read(u), input.read(v);
tree.build_forest(edges);
for (int repeat_index = 0; repeat_index < q; ++repeat_index) {
int type, u;
input.read(type), input.read(u);
if (type == 0) {
int v, w, x;
input.read(v), input.read(w), input.read(x);
tree.cut(u, v);
tree.link(w, x);
} else if (type == 1) {
unsigned a, b;
input.read(a), input.read(b);
S f{a, b};
tree.set(u, f);
} else {
int v;
unsigned initial;
input.read(v), input.read(initial);
mint x = initial;
auto f = tree.prod(u, v);
output.println((f[0] * x + f[1]).val());
}
}
}
#line 1 "test/link_cut_tree_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite"
#line 1 "tree/link_cut_tree.hpp"
#include <cassert>
#include <concepts>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <span>
#include <type_traits>
#include <utility>
#include <vector>
template <class S, auto op, auto e, bool commutative = false>
class LinkCutTree {
static constexpr bool scalar = commutative && std::is_arithmetic_v<S>;
struct Empty {};
using Back = std::conditional_t<commutative, Empty, S>;
struct Node {
int ch[2] = {}, parent = 0;
std::uint32_t count : 31 = 1;
std::uint32_t rev : 1 = 0;
S value, prod;
[[no_unique_address]] Back back;
static Back make_back(const S &v) {
if constexpr (commutative) return {};
else return v;
}
explicit Node(const S &v) : value(v), prod(v), back(make_back(v)) {}
};
std::vector<Node> t;
void init(int n) {
assert(0 <= n && n < std::numeric_limits<int>::max());
t.reserve(std::size_t(n) + 1);
t.emplace_back(e());
t[0].count = 0;
}
int node(int v) const {
assert(0 <= v && v < size());
return v + 1;
}
bool is_root(int x) const { return t[x].parent <= 0; }
void pull(int x) {
auto &v = t[x];
int l = v.ch[0], r = v.ch[1];
v.count = t[l].count + t[r].count + 1;
if constexpr (scalar) v.prod = op(op(t[l].prod, v.value), t[r].prod);
else {
v.prod = l ? op(t[l].prod, v.value) : v.value;
if (r) v.prod = op(std::move(v.prod), t[r].prod);
}
if constexpr (!commutative) {
v.back = r ? op(t[r].back, v.value) : v.value;
if (l) v.back = op(std::move(v.back), t[l].back);
}
}
void flip(int x) {
if constexpr (!scalar) if (!x) return;
std::swap(t[x].ch[0], t[x].ch[1]);
if constexpr (!commutative) std::ranges::swap(t[x].prod, t[x].back);
t[x].rev ^= 1;
}
void push(int x) {
if (!t[x].rev) return;
flip(t[x].ch[0]);
flip(t[x].ch[1]);
t[x].rev = 0;
}
void rotate(int x) {
int p = t[x].parent, g = t[p].parent;
int d = t[p].ch[1] == x, c = t[x].ch[d ^ 1];
if (g > 0) t[g].ch[t[g].ch[1] == p] = x;
t[x].parent = g;
t[p].ch[d] = c;
t[c].parent = p;
t[x].ch[d ^ 1] = p;
t[p].parent = x;
pull(p);
}
void splay(int x) {
if (is_root(x)) {
push(x);
return;
}
do {
int p = t[x].parent, g = t[p].parent;
bool top = is_root(p);
if (!top) push(g);
push(p);
push(x);
if (!top) rotate((t[p].ch[0] == x) == (t[g].ch[0] == p) ? p : x);
rotate(x);
} while (!is_root(x));
}
int access(int x) {
splay(x);
if (t[x].ch[1]) t[t[x].ch[1]].parent = -x;
t[x].ch[1] = 0;
int last = x;
while (t[x].parent) {
int p = -t[x].parent;
splay(p);
if (t[p].ch[1]) t[t[p].ch[1]].parent = -p;
t[p].ch[1] = x;
t[x].parent = p;
rotate(x);
last = p;
}
return last;
}
void reroot(int x) {
access(x);
flip(x);
}
int expose(int u, int v) {
u = node(u), v = node(v);
reroot(u);
access(v);
assert(u == v || t[u].parent != 0);
return v;
}
public:
explicit LinkCutTree(int n = 0) {
init(n);
for (int repeat_index = 0; repeat_index < n; ++repeat_index) t.emplace_back(t[0].value);
}
explicit LinkCutTree(const std::vector<S> &values) {
assert(values.size() < std::size_t(std::numeric_limits<int>::max()));
init(static_cast<int>(values.size()));
for (const S &v : values) t.emplace_back(v);
}
int size() const { return t.empty() ? 0 : static_cast<int>(t.size()) - 1; }
void build_forest(std::span<const std::pair<int, int>> edges) {
assert(edges.size() < std::size_t(size()) || (edges.empty() && size() == 0));
std::vector<int> degree(size()), neighbors(size()), parent(size(), -1), order;
order.reserve(size());
for (auto [u, v] : edges) {
assert(0 <= u && u < size() && 0 <= v && v < size() && u != v);
++degree[u], ++degree[v];
neighbors[u] ^= v, neighbors[v] ^= u;
}
for (int v = 0; v < size(); ++v) if (degree[v] <= 1) order.push_back(v);
for (std::size_t i = 0; i < order.size(); ++i) {
int v = order[i];
if (!degree[v]) continue;
int p = neighbors[v];
parent[v] = p;
degree[v] = 0;
neighbors[p] ^= v;
if (--degree[p] == 1) order.push_back(p);
}
assert(order.size() == std::size_t(size()));
for (int v = 0; v < size(); ++v) {
auto &x = t[v + 1];
x.ch[0] = x.ch[1] = 0;
x.parent = -parent[v] - 1;
x.count = 1, x.rev = 0;
x.prod = x.value;
if constexpr (!commutative) x.back = x.value;
}
}
S get(int v) const { return t[node(v)].value; }
void set(int v, S value) {
int x = node(v);
splay(x);
t[x].value = std::move(value);
}
void make_root(int v) { reroot(node(v)); }
int root(int v) {
int x = node(v);
access(x);
push(x);
while (t[x].ch[0]) push(x = t[x].ch[0]);
splay(x);
return x - 1;
}
bool same(int u, int v) {
u = node(u), v = node(v);
if (u == v) return true;
access(u);
access(v);
return t[u].parent != 0;
}
bool link(int u, int v) {
u = node(u), v = node(v);
if (u == v) return false;
reroot(u);
access(v);
if (t[u].parent) return false;
t[u].parent = -v;
return true;
}
bool cut(int u, int v) {
u = node(u), v = node(v);
if (u == v) return false;
reroot(u);
access(v);
if (t[v].ch[0] != u || t[u].ch[1]) return false;
t[v].ch[0] = t[u].parent = 0;
return true;
}
S prod(int u, int v) {
int x = expose(u, v), l = t[x].ch[0];
return l ? op(t[l].prod, t[x].value) : t[x].value;
}
int path_size(int u, int v) {
int x = expose(u, v);
return t[t[x].ch[0]].count + 1;
}
int distance(int u, int v) { return path_size(u, v) - 1; }
int jump(int u, int v, int k) {
int x = expose(u, v);
if (k < 0 || k > int(t[t[x].ch[0]].count)) return -1;
for (;;) {
push(x);
int l = t[x].ch[0], count = t[l].count;
if (k == count) break;
if (k < count) x = l;
else k -= count + 1, x = t[x].ch[1];
}
splay(x);
return x - 1;
}
int lca(int r, int u, int v) {
r = node(r), u = node(u), v = node(v);
reroot(r);
access(u);
assert(r == u || t[r].parent != 0);
int w = access(v);
assert(u == v || t[u].parent != 0);
return w - 1;
}
};
#line 1 "math/mint.hpp"
#line 4 "math/mint.hpp"
#include <istream>
#include <ostream>
#line 7 "math/mint.hpp"
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
namespace mint_detail {
template <class I>
constexpr bool mint_integral = std::is_integral_v<I>
#if defined(__SIZEOF_INT128__)
|| std::is_same_v<I, __int128> || std::is_same_v<I, unsigned __int128>
#endif
;
struct [[gnu::warn_unused]] Mint {
using mint = Mint;
unsigned v = 0;
[[nodiscard]] static constexpr unsigned mod() { return 998244353; }
[[nodiscard, gnu::always_inline]] static unsigned reduce(unsigned long long x) {
return (x + (unsigned long long)(unsigned(x) * 998244351u) * mod()) >> 32;
}
[[gnu::always_inline]] Mint() = default;
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
Mint(I x) {
long long r = x % (long long)mod();
if (r < 0) r += mod();
v = reduce((unsigned long long)r * 932051910);
}
[[nodiscard, gnu::always_inline]] static Mint raw(unsigned x) {
Mint a;
a.v = reduce((unsigned long long)x * 932051910);
return a;
}
[[nodiscard, gnu::always_inline]] static Mint word(unsigned x) {
Mint a;
a.v = x;
return a;
}
[[nodiscard, gnu::always_inline]] unsigned val() const {
unsigned r = reduce(v);
return r < mod() ? r : r - mod();
}
friend std::istream &operator>>(std::istream &is, Mint &x) {
long long value;
if (is >> value) x = Mint(value);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const Mint &x) {
return os << x.val();
}
[[gnu::always_inline]] Mint &operator+=(Mint b) {
v += b.v;
if (v >= 2 * mod()) v -= 2 * mod();
return *this;
}
[[gnu::always_inline]] Mint &operator-=(Mint b) {
v -= b.v;
if (v >> 31) v += 2 * mod();
return *this;
}
[[gnu::always_inline]] Mint &operator*=(Mint b) {
v = reduce((unsigned long long)v * b.v);
return *this;
}
Mint &operator/=(Mint b) { return *this *= b.inv(); }
Mint &operator++() { return *this += Mint(1); }
Mint &operator--() { return *this -= Mint(1); }
Mint operator++(int) {
Mint a = *this;
++*this;
return a;
}
Mint operator--(int) {
Mint a = *this;
--*this;
return a;
}
[[nodiscard, gnu::always_inline]] Mint operator+() const { return *this; }
[[nodiscard, gnu::always_inline]] Mint operator-() const { return word(v ? 2 * mod() - v : 0); }
[[nodiscard, gnu::always_inline]] Mint operator+(Mint b) const { return Mint(*this) += b; }
[[nodiscard, gnu::always_inline]] Mint operator-(Mint b) const { return Mint(*this) -= b; }
[[nodiscard, gnu::always_inline]] Mint operator*(Mint b) const { return Mint(*this) *= b; }
[[nodiscard]] Mint operator/(Mint b) const { return Mint(*this) /= b; }
[[nodiscard, gnu::always_inline]] bool operator==(Mint b) const { return (v < mod() ? v : v - mod()) == (b.v < mod() ? b.v : b.v - mod()); }
[[nodiscard, gnu::always_inline]] bool operator!=(Mint b) const { return !(*this == b); }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator+(I a, Mint b) { return Mint(a) + b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator-(I a, Mint b) { return Mint(a) - b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator*(I a, Mint b) { return Mint(a) * b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator/(I a, Mint b) { return Mint(a) / b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend bool operator==(I a, Mint b) { return Mint(a) == b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend bool operator!=(I a, Mint b) { return Mint(a) != b; }
[[nodiscard]] Mint pow(long long n) const {
assert(n >= 0);
if (!n) return Mint(1);
Mint r(1), a = *this;
for (; n > 1; n >>= 1, a *= a)
if (n & 1) r *= a;
return r * a;
}
[[nodiscard, gnu::noinline]] Mint inv() const {
assert(*this != Mint(0));
Mint a2 = *this * *this, a3 = a2 * *this;
Mint a7 = a3 * a3 * *this;
Mint a31 = a7;
for (int i = 0; i < 2; ++i) a31 *= a31;
a31 *= a3;
Mint r = a7;
for (int i = 0; i < 3; ++i) r *= r;
r *= a3;
r *= r;
for (int j = 0; j < 4; ++j) {
for (int i = 0; i < 5; ++i) r *= r;
r *= a31;
}
for (int i = 0; i < 3; ++i) r *= r;
return r * a7;
}
};
} // namespace mint_detail
using mint = mint_detail::Mint;
using fps_mint = mint;
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif
#line 4 "test/link_cut_tree_composite.test.cpp"
#include <array>
#line 1 "components/fast_io.hpp"
#include <algorithm>
#line 6 "components/fast_io.hpp"
#include <bit>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#line 18 "components/fast_io.hpp"
#if defined(__unix__) || defined(__APPLE__)
#include <sys/mman.h>
#include <sys/stat.h>
#include <unistd.h>
#endif
namespace fast_io_detail { struct BulkInput; struct BulkOutput; }
class FastInput {
friend struct fast_io_detail::BulkInput;
static constexpr std::size_t capacity = 1 << 16;
FILE *file = nullptr;
std::unique_ptr<char[]> buffer;
const char *current = "", *end = current;
std::string scratch;
void *mapping = nullptr;
std::size_t mapped_size = 0;
bool refill() {
if (!file) return false;
std::size_t n = std::fread(buffer.get(), 1, capacity, file);
current = buffer.get();
end = current + n;
return n;
}
static const char *scan(const char *p, const char *end) {
while (end - p >= 8) {
std::uint64_t x;
std::memcpy(&x, p, 8);
if ((x - 0x2121212121212121ULL) & ~x & 0x8080808080808080ULL) break;
p += 8;
}
while (p != end && static_cast<unsigned char>(*p) > ' ') ++p;
return p;
}
public:
explicit FastInput(FILE *input = stdin) {
#if defined(__unix__) || defined(__APPLE__)
struct stat status;
int fd = fileno(input);
auto offset = ftello(input);
if (fd >= 0 && offset >= 0 && !fstat(fd, &status) && S_ISREG(status.st_mode) && status.st_size > offset) {
mapped_size = status.st_size;
mapping = mmap(nullptr, mapped_size, PROT_READ, MAP_PRIVATE, fd, 0);
if (mapping != MAP_FAILED) {
current = static_cast<const char *>(mapping) + offset;
end = static_cast<const char *>(mapping) + mapped_size;
return;
}
mapping = nullptr;
}
#endif
file = input;
buffer = std::make_unique_for_overwrite<char[]>(capacity);
}
explicit FastInput(std::string_view input) : current(input.empty() ? "" : input.data()), end(current + input.size()) {}
FastInput(const FastInput &) = delete;
FastInput &operator=(const FastInput &) = delete;
~FastInput() {
#if defined(__unix__) || defined(__APPLE__)
if (mapping) munmap(mapping, mapped_size);
#endif
}
std::string_view token() {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return {};
}
const char *begin = current;
current = scan(current, end);
if (current != end || !file) return {begin, std::size_t(current - begin)};
scratch.assign(begin, end);
while (refill()) {
current = scan(current, end);
scratch.append(buffer.get(), std::size_t(current - buffer.get()));
if (current != end) break;
}
return scratch;
}
template <class T>
bool read(T &value) {
if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool>) {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return false;
}
if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4 && std::endian::native == std::endian::little) {
if (end - current >= 11) {
std::uint64_t x;
std::memcpy(&x, current, 8);
if (!(((x + 0x4646464646464646ULL) | (x - 0x3030303030303030ULL)) & 0x8080808080808080ULL)) {
x &= 0x0f0f0f0f0f0f0f0fULL;
x = (x * 10 + (x >> 8)) & 0x00ff00ff00ff00ffULL;
x = (x * 100 + (x >> 16)) & 0x0000ffff0000ffffULL;
std::uint64_t v = std::uint32_t(x * 10000 + (x >> 32));
int n = 8;
for (; n < 10 && static_cast<unsigned char>(current[n]) - unsigned('0') < 10; ++n)
v = v * 10 + (current[n] - '0');
if (static_cast<unsigned char>(current[n]) <= ' ' && v <= 0xffffffffULL) {
current += n;
value = T(v);
return true;
}
}
}
}
T parsed{};
auto result = std::from_chars(current, end, parsed);
if (result.ec == std::errc{} && (result.ptr != end ? static_cast<unsigned char>(*result.ptr) <= ' ' : !file)) {
current = result.ptr;
value = parsed;
return true;
}
}
auto s = token();
if (s.empty()) return false;
if constexpr (std::is_same_v<T, bool>) {
assert(s == "0" || s == "1");
value = s[0] == '1';
} else if constexpr (std::is_integral_v<T>) {
auto result = std::from_chars(s.data(), s.data() + s.size(), value);
assert(result.ec == std::errc{} && result.ptr == s.data() + s.size());
(void)result;
} else value = T(s);
return true;
}
};
class FastOutput {
friend struct fast_io_detail::BulkOutput;
inline static constexpr auto quads = [] {
std::array<std::array<char, 4>, 10000> table{};
for (int i = 0; i < 10000; ++i)
table[i] = {char('0' + i / 1000), char('0' + i / 100 % 10), char('0' + i / 10 % 10), char('0' + i % 10)};
return table;
}();
FILE *file;
std::unique_ptr<char[]> buffer = std::make_unique_for_overwrite<char[]>(1 << 16);
std::size_t capacity = 1 << 16, length = 0;
char *reserve(std::size_t n) {
if (n > capacity - length) {
if (!flush()) throw std::runtime_error("output failed");
if (n > capacity) {
std::size_t next = std::max(n, 2 * capacity);
buffer = std::make_unique_for_overwrite<char[]>(next);
capacity = next;
}
}
return buffer.get() + length;
}
public:
explicit FastOutput(FILE *output = stdout) : file(output) {}
FastOutput(const FastOutput &) = delete;
FastOutput &operator=(const FastOutput &) = delete;
~FastOutput() { flush(); }
bool flush() {
std::size_t offset = 0;
while (offset < length) {
auto n = std::fwrite(buffer.get() + offset, 1, length - offset, file);
if (!n) {
std::memmove(buffer.get(), buffer.get() + offset, length - offset);
length -= offset;
return false;
}
offset += n;
}
length = 0;
return std::fflush(file) == 0;
}
void write(char c) { *reserve(1) = c; ++length; }
void write(__uint128_t value) {
char digits[40];
char *end = digits + sizeof(digits), *begin = end;
do { *--begin = char('0' + value % 10); value /= 10; } while (value);
write(std::string_view(begin, end - begin));
}
void write(__int128_t value) {
__uint128_t magnitude = __uint128_t(value);
if (value < 0) write('-'), magnitude = 0 - magnitude;
write(magnitude);
}
void write(std::string_view s) {
char *out = reserve(s.size());
if (!s.empty()) std::memcpy(out, s.data(), s.size());
length += s.size();
}
template <class T> requires std::is_integral_v<T>
void write(T value) {
char *out = reserve(32);
if constexpr (std::is_same_v<T, bool>) *out = '0' + value, ++length;
else if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4) {
char *p = out;
if (value >= 100000000) {
auto high = value / 100000000, low = value % 100000000;
p = std::to_chars(p, p + 2, high).ptr;
std::memcpy(p, quads[low / 10000].data(), 4);
std::memcpy(p + 4, quads[low % 10000].data(), 4);
p += 8;
} else if (value >= 10000) {
p = std::to_chars(p, p + 4, value / 10000).ptr;
std::memcpy(p, quads[value % 10000].data(), 4);
p += 4;
} else p = std::to_chars(p, p + 4, value).ptr;
length += p - out;
} else length += std::to_chars(out, out + 32, value).ptr - out;
}
template <class T> requires requires(const T &value, char *out) { value.decimal_capacity(); value.to_chars(out); }
void write(const T &value) {
char *out = reserve(value.decimal_capacity());
length += value.to_chars(out) - out;
}
template <class T>
void println(const T &value) { write(value); write('\n'); }
};
#line 7 "test/link_cut_tree_composite.test.cpp"
using namespace std;
using S = array<mint, 2>;
S op(const S &a, const S &b) { return {a[0] * b[0], a[1] * b[0] + b[1]}; }
S e() { return {1, 0}; }
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
vector<S> values(n);
for (auto &v : values) {
unsigned a, b;
input.read(a), input.read(b);
v = {a, b};
}
LinkCutTree<S, op, e> tree(values);
std::vector<std::pair<int, int>> edges(n - 1);
for (auto &[u, v] : edges) input.read(u), input.read(v);
tree.build_forest(edges);
for (int repeat_index = 0; repeat_index < q; ++repeat_index) {
int type, u;
input.read(type), input.read(u);
if (type == 0) {
int v, w, x;
input.read(v), input.read(w), input.read(x);
tree.cut(u, v);
tree.link(w, x);
} else if (type == 1) {
unsigned a, b;
input.read(a), input.read(b);
S f{a, b};
tree.set(u, f);
} else {
int v;
unsigned initial;
input.read(v), input.read(initial);
mint x = initial;
auto f = tree.prod(u, v);
output.println((f[0] * x + f[1]).val());
}
}
}