cp-library
競技プログラミング用 C++ ライブラリ
test/rerooting.test.cpp
test/rerooting.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"
#include "tree/rerooting.hpp"
#include "components/fast_io.hpp"
#include "math/mint.hpp"
int main() {
FastInput input;
FastOutput output;
int n = 0;
input.read(n);
Rerooting<std::pair<mint, mint>> tree(n);
std::vector<mint> a(n), b(n - 1), c(n - 1);
for (auto &x : a) { unsigned value = 0; input.read(value); x = value; }
for (int id = 0; id < n - 1; ++id) {
int u = 0, v = 0;
unsigned x = 0, y = 0;
input.read(u), input.read(v), input.read(x), input.read(y);
b[id] = x, c[id] = y;
tree.add_edge(u, v);
}
using Data = std::pair<mint, mint>;
tree.build(Data{0, 0}, [](Data x, Data y) { return Data{x.first + y.first, x.second + y.second}; },
[&](Data x, int v) { return Data{x.first + a[v], x.second + 1}; },
[&](Data x, int, int, int id) { return Data{x.first * b[id] + x.second * c[id], x.second}; });
for (auto x : tree.values()) output.write(x.first.val()), output.write(' ');
output.write('\n');
}
#line 1 "test/rerooting.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"
#line 1 "tree/rerooting.hpp"
#line 1 "components/undirected_csr.hpp"
#include <cassert>
#include <cstddef>
#include <limits>
#include <memory>
#include <span>
#include <type_traits>
#include <utility>
#include <vector>
namespace undirected_csr_detail {
template <class Arc>
void build(int n, std::span<const std::pair<int, int>> edges, std::vector<int>& start, std::unique_ptr<Arc[]>& adj) {
assert(0 <= n && n < std::numeric_limits<int>::max());
assert(edges.size() <= std::size_t(std::numeric_limits<int>::max() / 2));
start.assign(std::size_t(n) + 1, 0);
for (auto [u, v] : edges) {
assert(0 <= u && u < n && 0 <= v && v < n);
++start[u + 1], ++start[v + 1];
}
for (int v = 0; v < n; ++v) start[v + 1] += start[v];
adj.reset(new Arc[2 * edges.size()]);
std::vector<int> cursor(start.begin(), start.end() - 1);
for (int i = 0; i < static_cast<int>(edges.size()); ++i) {
auto [u, v] = edges[i];
if constexpr (std::is_same_v<Arc, int>) adj[cursor[u]++] = v, adj[cursor[v]++] = u;
else adj[cursor[u]++] = {v, i}, adj[cursor[v]++] = {u, i};
}
}
}
struct UndirectedCSR {
struct Arc { int to, id; };
int n;
std::vector<int> start;
std::unique_ptr<Arc[]> adj;
UndirectedCSR(int n, std::span<const std::pair<int, int>> edges) : n(n) {
undirected_csr_detail::build(n, edges, start, adj);
}
std::span<const Arc> operator[](int v) const {
assert(0 <= v && v < n);
return {adj.get() + start[v], std::size_t(start[v + 1] - start[v])};
}
};
struct UndirectedVertexCSR {
int n;
std::vector<int> start;
std::unique_ptr<int[]> adj;
UndirectedVertexCSR(int n, std::span<const std::pair<int, int>> edges) : n(n) {
undirected_csr_detail::build(n, edges, start, adj);
}
std::span<const int> operator[](int v) const {
assert(0 <= v && v < n);
return {adj.get() + start[v], std::size_t(start[v + 1] - start[v])};
}
};
#line 5 "tree/rerooting.hpp"
#include <algorithm>
#line 11 "tree/rerooting.hpp"
template<class T, class E = T>
class Rerooting {
int n_;
bool built_ = false;
std::vector<std::pair<int, int>> edges_;
std::vector<T> values_;
std::vector<E> messages_;
public:
using Vertex = T;
using Edge = E;
explicit Rerooting(int n = 0) : n_(n) {
assert(0 <= n && n < std::numeric_limits<int>::max());
edges_.reserve(std::max(0, n - 1));
}
int size() const { return n_; }
bool empty() const { return n_ == 0; }
int edge_count() const { return static_cast<int>(edges_.size()); }
int add_edge(int u, int v) {
assert(0 <= u && u < n_ && 0 <= v && v < n_ && u != v);
assert(edges_.size() < std::size_t(std::numeric_limits<int>::max() / 2));
built_ = false;
edges_.emplace_back(u, v);
return edge_count() - 1;
}
const std::pair<int, int>& edge(int id) const {
assert(0 <= id && id < edge_count());
return edges_[id];
}
const T& operator[](int v) const {
assert(built_ && 0 <= v && v < n_);
return values_[v];
}
const std::vector<T>& values() const {
assert(built_);
return values_;
}
const E& edge_dp(int id, bool reverse = false) const {
assert(built_ && 0 <= id && id < edge_count());
return messages_[2 * id + reverse];
}
template<class Merge, class AddVertex, class AddEdge>
const std::vector<T>& build(E unit, Merge&& merge, AddVertex&& add_vertex, AddEdge&& add_edge, int root = 0) {
assert(n_ == 0 || (0 <= root && root < n_));
built_ = false;
if constexpr (std::is_default_constructible_v<E>) messages_.resize(2 * edges_.size());
else messages_.assign(2 * edges_.size(), unit);
if (n_ == 0) {
values_.clear();
built_ = true;
return values_;
}
UndirectedCSR graph(n_, edges_);
for (int v = 0; v < n_; ++v)
for (int i = graph.start[v]; i < graph.start[v + 1]; ++i) {
int id = graph.adj[i].id;
graph.adj[i].id = 2 * id + (edges_[id].second == v);
}
std::vector<int> parent(n_, -2), parent_edge(n_, -1), order;
order.reserve(n_);
auto visit = [&](int s) {
if (parent[s] != -2) return;
parent[s] = -1;
order.push_back(s);
for (std::size_t i = order.size() - 1; i < order.size(); ++i) {
int v = order[i];
for (auto [to, id] : graph[v]) {
if (id == parent_edge[v]) continue;
assert(parent[to] == -2);
if (parent[to] != -2) continue;
parent[to] = v, parent_edge[to] = id ^ 1;
order.push_back(to);
}
}
};
visit(root);
for (int v = 0; v < n_; ++v) visit(v);
for (auto it = order.rbegin(); it != order.rend(); ++it) {
int v = *it, id = parent_edge[v];
if (id == -1) continue;
E value = unit;
for (auto arc : graph[v])
if (arc.id != id) value = merge(value, messages_[arc.id ^ 1]);
messages_[id] = add_edge(add_vertex(value, v), v, parent[v], id >> 1);
}
if constexpr (std::is_default_constructible_v<T>) values_.resize(n_);
else values_.assign(n_, unit);
int maximum = 0;
for (int v = 0; v < n_; ++v) maximum = std::max(maximum, graph.start[v + 1] - graph.start[v]);
std::vector<E> prefix(maximum, unit);
for (int v : order) {
auto arcs = graph[v];
int degree = static_cast<int>(arcs.size());
if (degree == 0) {
values_[v] = add_vertex(unit, v);
continue;
}
auto incoming = [&](int i) -> const E& { return messages_[arcs[i].id ^ 1]; };
if (degree > 1) prefix[1] = incoming(0);
for (int i = 1; i + 1 < degree; ++i) prefix[i + 1] = merge(prefix[i], incoming(i));
values_[v] = add_vertex(degree == 1 ? incoming(0) : merge(prefix[degree - 1], incoming(degree - 1)), v);
E suffix = unit;
for (int i = degree - 1; i >= 0; --i) {
auto [to, id] = arcs[i];
if (id != parent_edge[v]) {
E value = i == degree - 1 ? prefix[i] : i == 0 ? suffix : merge(prefix[i], suffix);
messages_[id] = add_edge(add_vertex(value, v), v, to, id >> 1);
}
if (i > 0) suffix = i == degree - 1 ? incoming(i) : merge(incoming(i), suffix);
}
}
built_ = true;
return values_;
}
};
#line 1 "components/fast_io.hpp"
#line 5 "components/fast_io.hpp"
#include <array>
#include <bit>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 10 "components/fast_io.hpp"
#include <cstdint>
#include <cstdio>
#include <cstring>
#line 14 "components/fast_io.hpp"
#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 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 5 "test/rerooting.test.cpp"
int main() {
FastInput input;
FastOutput output;
int n = 0;
input.read(n);
Rerooting<std::pair<mint, mint>> tree(n);
std::vector<mint> a(n), b(n - 1), c(n - 1);
for (auto &x : a) { unsigned value = 0; input.read(value); x = value; }
for (int id = 0; id < n - 1; ++id) {
int u = 0, v = 0;
unsigned x = 0, y = 0;
input.read(u), input.read(v), input.read(x), input.read(y);
b[id] = x, c[id] = y;
tree.add_edge(u, v);
}
using Data = std::pair<mint, mint>;
tree.build(Data{0, 0}, [](Data x, Data y) { return Data{x.first + y.first, x.second + y.second}; },
[&](Data x, int v) { return Data{x.first + a[v], x.second + 1}; },
[&](Data x, int, int, int id) { return Data{x.first * b[id] + x.second * c[id], x.second}; });
for (auto x : tree.values()) output.write(x.first.val()), output.write(' ');
output.write('\n');
}