#line 1 "verify/graph/tree/zero_one_on_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include <algorithm>
#include <cassert>
#line 1 "utilities/fast_io.hpp"
#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#include <utility>
#include <unistd.h>
#include <vector>
namespace m1une {
namespace utilities {
struct FastOutput;
namespace internal {
// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;
// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};
template <class T>
struct is_range<T, std::void_t<
decltype(std::begin(std::declval<T&>())),
decltype(std::end(std::declval<T&>()))
>> : std::true_type {};
template <class T>
inline constexpr bool is_range_v = is_range<T>::value;
template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));
template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;
template <class T, class = void>
struct range_stored_value {
using type = range_value_t<T>;
};
template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};
template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;
// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};
template <class T, std::size_t N>
struct is_char_array<T[N]>
: std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};
template <class T>
struct is_string_like
: std::bool_constant<
std::is_same_v<std::decay_t<T>, std::string>
|| std::is_same_v<std::decay_t<T>, const char*>
|| std::is_same_v<std::decay_t<T>, char*>
|| is_char_array<std::remove_reference_t<T>>::value
> {};
template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;
// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};
template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
: std::true_type {};
template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;
template <class T, class = void>
struct has_static_mod_raw : std::false_type {};
template <class T>
struct has_static_mod_raw<
T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
: std::true_type {};
template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;
// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
std::is_integral_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>
|| std::is_same_v<std::remove_cv_t<T>, __uint128_t>;
template <class T>
inline constexpr bool is_signed_v =
std::is_signed_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>;
template <class T>
struct make_unsigned {
using type = std::make_unsigned_t<T>;
};
template <>
struct make_unsigned<__int128_t> {
using type = __uint128_t;
};
template <>
struct make_unsigned<__uint128_t> {
using type = __uint128_t;
};
template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;
} // namespace internal
struct FastInput {
static constexpr int buffer_size = 1 << 20;
private:
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _length;
int _file_descriptor;
bool _streaming;
bool refill() {
_position = 0;
if (_streaming) {
ssize_t length;
do {
length = ::read(_file_descriptor, _buffer, buffer_size);
} while (length < 0 && errno == EINTR);
if (length <= 0) {
_length = 0;
return false;
}
_length = int(length);
} else {
_length = int(std::fread(_buffer, 1, buffer_size, _stream));
}
return _length != 0;
}
template <class T>
bool read_integer_from_stream(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-') {
negative = true;
c = read_char_raw();
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
result = negative ? result * 10 - (c - '0')
: result * 10 + (c - '0');
c = read_char_raw();
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + T(c - '0');
c = read_char_raw();
}
value = negative ? T(0) - result : result;
}
return true;
}
bool prepare_number() {
if (_length - _position >= 64) return true;
const int remaining = _length - _position;
if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
_position = 0;
_length = remaining + added;
if (_length < buffer_size) _buffer[_length] = '\0';
return _length != 0;
}
public:
explicit FastInput(std::FILE* stream = stdin)
: _stream(stream),
_position(0),
_length(0),
_file_descriptor(::fileno(stream)),
_streaming([&] {
struct stat status;
return _file_descriptor >= 0
&& ::fstat(_file_descriptor, &status) == 0
&& !S_ISREG(status.st_mode);
}()) {}
FastInput(const FastInput&) = delete;
FastInput& operator=(const FastInput&) = delete;
int read_char_raw() {
if (_position == _length && !refill()) return EOF;
return _buffer[_position++];
}
bool skip_spaces() {
int c = read_char_raw();
while (c != EOF && c <= ' ') c = read_char_raw();
if (c == EOF) return false;
--_position;
return true;
}
bool read(char& value) {
if (!skip_spaces()) return false;
value = char(read_char_raw());
return true;
}
bool read(std::string& value) {
if (!skip_spaces()) return false;
value.clear();
while (true) {
const int begin = _position;
while (_position < _length &&
static_cast<unsigned char>(_buffer[_position]) > ' ') {
++_position;
}
value.append(_buffer + begin, _position - begin);
if (_position < _length) {
++_position;
return true;
}
if (!refill()) return true;
}
}
bool read(bool& value) {
int x;
if (!read(x)) return false;
value = x != 0;
return true;
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>,
bool
>
read(T& value) {
if (_streaming) return read_integer_from_stream(value);
if (!prepare_number()) return false;
int c = static_cast<unsigned char>(_buffer[_position++]);
while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);
bool negative = false;
if (c == '-') {
negative = true;
c = static_cast<unsigned char>(_buffer[_position++]);
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
const int first = c - '0';
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = negative ? result * 100 - (first * 10 + second)
: result * 100 + (first * 10 + second);
++_position;
} else {
result = negative ? result * 10 - first : result * 10 + first;
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
const unsigned first = unsigned(c - '0');
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = result * 100 + T(first * 10 + unsigned(second));
++_position;
} else {
result = result * 10 + T(first);
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = negative ? T(0) - result : result;
}
if (_position > _length) _position = _length;
return true;
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>, bool>
read(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-' || c == '+') {
negative = c == '-';
c = read_char_raw();
}
long double result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + (c - '0');
c = read_char_raw();
}
if (c == '.') {
long double place = 0.1L;
c = read_char_raw();
while ('0' <= c && c <= '9') {
result += (c - '0') * place;
place *= 0.1L;
c = read_char_raw();
}
}
if (c == 'e' || c == 'E') {
c = read_char_raw();
bool exponent_negative = false;
if (c == '-' || c == '+') {
exponent_negative = c == '-';
c = read_char_raw();
}
int exponent = 0;
while ('0' <= c && c <= '9') {
exponent = exponent * 10 + (c - '0');
c = read_char_raw();
}
long double scale = 1;
long double power = 10;
while (exponent > 0) {
if (exponent & 1) scale *= power;
power *= power;
exponent >>= 1;
}
result = exponent_negative ? result / scale : result * scale;
}
value = static_cast<T>(negative ? -result : result);
return true;
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>,
bool
>
read(T& value) {
long long x;
if (!read(x)) return false;
if constexpr (internal::has_static_mod_raw_v<T>) {
if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
value = T::raw(uint32_t(x));
} else {
value = T(x);
}
} else {
value = T(x);
}
return true;
}
template <class First, class Second>
bool read(std::pair<First, Second>& value) {
if (!read(value.first)) return false;
return read(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>,
bool
>
read(Range& range) {
using StoredValue = internal::range_stored_value_t<Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
for (auto&& value : range) {
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
bool x;
if (!read(x)) return false;
value = x;
} else {
if (!read(value)) return false;
}
}
return true;
}
template <class First, class Second, class... Rest>
bool read(First& first, Second& second, Rest&... rest) {
if (!read(first)) return false;
return read(second, rest...);
}
template <class T>
FastInput& operator>>(T& value) {
if (!read(value)) std::abort();
return *this;
}
};
struct FastOutput {
static constexpr int buffer_size = 1 << 20;
private:
inline static const auto digit_quads = [] {
std::array<char, 40000> result{};
for (int i = 0; i < 10000; i++) {
int value = i;
for (int j = 3; j >= 0; j--) {
result[4 * i + j] = char('0' + value % 10);
value /= 10;
}
}
return result;
}();
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _precision;
std::chars_format _float_format;
char _range_separator;
std::string* _capture = nullptr;
template <class T>
std::string format_cell(const T& value) {
std::string result;
struct CaptureGuard {
std::string*& target;
std::string* previous;
~CaptureGuard() { target = previous; }
} guard{_capture, _capture};
_capture = &result;
write(value);
return result;
}
template <class Matrix>
void write_aligned_matrix(const Matrix& matrix) {
std::vector<std::vector<std::string>> rows;
std::vector<std::size_t> widths;
for (const auto& row : matrix) {
auto& cells = rows.emplace_back();
std::size_t column = 0;
for (const auto& value : row) {
cells.push_back(format_cell(value));
if (column == widths.size()) widths.push_back(0);
widths[column] = std::max(widths[column], cells.back().size());
++column;
}
}
bool first = true;
for (const auto& row : rows) {
if (!first) write_char('\n');
first = false;
for (std::size_t column = 0; column < row.size(); ++column) {
if (column != 0) write_char(_range_separator);
for (std::size_t padding = row[column].size();
padding < widths[column]; ++padding) {
write_char(' ');
}
write(row[column]);
}
}
}
public:
explicit FastOutput(std::FILE* stream = stdout)
: _stream(stream),
_position(0),
_precision(6),
_float_format(std::chars_format::general),
_range_separator(' ') {
if (_stream == stdout
&& internal::standard_output_instance == nullptr) {
internal::standard_output_instance = this;
}
}
FastOutput(const FastOutput&) = delete;
FastOutput& operator=(const FastOutput&) = delete;
~FastOutput() {
flush();
if (internal::standard_output_instance == this) {
internal::standard_output_instance = nullptr;
}
}
void flush() {
if (_position != 0) {
std::fwrite(_buffer, 1, _position, _stream);
_position = 0;
}
std::fflush(_stream);
}
void write_char(char c) {
if (_capture != nullptr) {
_capture->push_back(c);
return;
}
if (_position == buffer_size) flush();
_buffer[_position++] = c;
}
void write(const char* s) {
while (*s != '\0') write_char(*s++);
}
void write(const std::string& s) {
if (_capture != nullptr) {
_capture->append(s);
return;
}
std::size_t position = 0;
while (position < s.size()) {
if (_position == buffer_size) flush();
const std::size_t copied =
std::min<std::size_t>(buffer_size - _position, s.size() - position);
std::memcpy(_buffer + _position, s.data() + position, copied);
_position += int(copied);
position += copied;
}
}
void write(char c) {
write_char(c);
}
void write(bool value) {
write_char(value ? '1' : '0');
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>>
write(T value) {
char digits[128];
auto [end, error] = std::to_chars(
digits,
digits + sizeof(digits),
value,
_float_format,
_precision
);
if (error != std::errc()) std::abort();
for (const char* pointer = digits; pointer != end; pointer++) {
write_char(*pointer);
}
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>
>
write(T value) {
using Raw = std::remove_cv_t<T>;
using Unsigned = internal::make_unsigned_t<Raw>;
Unsigned magnitude;
if constexpr (internal::is_signed_v<Raw>) {
if (value < 0) {
write_char('-');
magnitude = Unsigned(0) - Unsigned(value);
} else {
magnitude = Unsigned(value);
}
} else {
magnitude = value;
}
if (magnitude == 0) {
write_char('0');
return;
}
unsigned chunks[16];
int count = 0;
while (magnitude >= 10000) {
const Unsigned quotient = magnitude / 10000;
chunks[count++] = unsigned(magnitude - quotient * 10000);
magnitude = quotient;
}
if (_capture == nullptr && _position > buffer_size - 64) flush();
char captured[64];
char* const begin = _capture != nullptr ? captured : _buffer + _position;
char* destination = begin;
const unsigned leading = unsigned(magnitude);
const char* first = digit_quads.data() + 4 * leading;
int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
for (; skip < 4; skip++) *destination++ = first[skip];
while (count--) {
const char* digits = digit_quads.data() + 4 * chunks[count];
std::memcpy(destination, digits, 4);
destination += 4;
}
if (_capture != nullptr) {
_capture->append(begin, destination - begin);
} else {
_position += int(destination - begin);
}
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>
>
write(const T& value) {
write(value.val());
}
template <class First, class Second>
void write(const std::pair<First, Second>& value) {
write(value.first);
write_char(' ');
write(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>
>
write(const Range& range) {
using StoredValue = internal::range_stored_value_t<const Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
bool first = true;
for (const auto& value : range) {
if (!first) write_char(nested ? '\n' : _range_separator);
first = false;
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
write(static_cast<bool>(value));
} else {
write(value);
}
}
}
template <class First, class... Rest>
void print(const First& first, const Rest&... rest) {
write(first);
((write_char(' '), write(rest)), ...);
}
void println() {
write_char('\n');
}
void set_precision(int precision) {
_precision = precision;
}
void set_fixed(int precision = 6) {
_float_format = std::chars_format::fixed;
_precision = precision;
}
void set_general(int precision = 6) {
_float_format = std::chars_format::general;
_precision = precision;
}
void set_range_separator(char separator) {
_range_separator = separator;
}
template <class Matrix>
void write_aligned(const Matrix& matrix) {
using Row = internal::range_stored_value_t<const Matrix>;
using Cell = internal::range_stored_value_t<const Row>;
static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
"write_aligned requires a two-dimensional range");
static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
"write_aligned requires scalar cells");
write_aligned_matrix(matrix);
}
template <class Matrix>
void println_aligned(const Matrix& matrix) {
write_aligned(matrix);
write_char('\n');
}
template <class... Args>
void println(const Args&... args) {
print(args...);
write_char('\n');
}
template <class T>
FastOutput& operator<<(const T& value) {
write(value);
return *this;
}
};
} // namespace utilities
} // namespace m1une
#line 6 "verify/graph/tree/zero_one_on_tree.test.cpp"
#include <limits>
#include <random>
#line 9 "verify/graph/tree/zero_one_on_tree.test.cpp"
#line 1 "graph/graph.hpp"
#line 8 "graph/graph.hpp"
namespace m1une {
namespace graph {
template <class T = int>
struct Edge {
using cost_type = T;
int from;
int to;
T cost;
int id;
bool alive;
Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
: from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}
int other(int v) const {
assert(v == from || v == to);
return from ^ to ^ v;
}
};
template <class T = int>
struct Graph {
using edge_type = Edge<T>;
using cost_type = T;
private:
struct EdgePositions {
std::array<std::pair<int, int>, 2> value{};
int size = 0;
void push_back(std::pair<int, int> position) {
assert(size < 2);
value[size++] = position;
}
};
int _n;
int _edge_count;
std::vector<std::vector<edge_type>> _g;
std::vector<EdgePositions> _edge_positions;
public:
Graph() : _n(0), _edge_count(0) {}
explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
assert(0 <= n);
}
int size() const {
return _n;
}
bool empty() const {
return _n == 0;
}
int edge_count() const {
return _edge_count;
}
int add_vertex() {
_g.emplace_back();
return _n++;
}
int add_directed_edge(int from, int to, T cost = T(1)) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
int id = _edge_count++;
int idx = int(_g[from].size());
_g[from].push_back(edge_type(from, to, cost, id));
_edge_positions.emplace_back();
_edge_positions.back().push_back({from, idx});
return id;
}
int add_edge(int u, int v, T cost = T(1)) {
assert(0 <= u && u < _n);
assert(0 <= v && v < _n);
int id = _edge_count++;
int u_idx = int(_g[u].size());
_g[u].push_back(edge_type(u, v, cost, id));
int v_idx = int(_g[v].size());
_g[v].push_back(edge_type(v, u, cost, id));
_edge_positions.emplace_back();
_edge_positions.back().push_back({u, u_idx});
_edge_positions.back().push_back({v, v_idx});
return id;
}
void set_edge_alive(int id, bool alive) {
assert(0 <= id && id < _edge_count);
for (int i = 0; i < _edge_positions[id].size; ++i) {
auto [v, idx] = _edge_positions[id].value[i];
_g[v][idx].alive = alive;
}
}
void erase_edge(int id) {
set_edge_alive(id, false);
}
void revive_edge(int id) {
set_edge_alive(id, true);
}
bool is_edge_alive(int id) const {
assert(0 <= id && id < _edge_count);
assert(_edge_positions[id].size != 0);
auto [v, idx] = _edge_positions[id].value[0];
return _g[v][idx].alive;
}
const std::vector<edge_type>& operator[](int v) const {
assert(0 <= v && v < _n);
return _g[v];
}
std::vector<edge_type>& operator[](int v) {
assert(0 <= v && v < _n);
return _g[v];
}
const std::vector<std::vector<edge_type>>& adjacency() const {
return _g;
}
std::vector<std::vector<edge_type>>& adjacency() {
return _g;
}
std::vector<edge_type> edges(bool include_inactive = false) const {
std::vector<edge_type> result;
result.reserve(_edge_count);
std::vector<char> used(_edge_count, false);
for (int v = 0; v < _n; v++) {
for (const auto& e : _g[v]) {
if (!include_inactive && !e.alive) continue;
if (0 <= e.id && e.id < _edge_count) {
if (used[e.id]) continue;
used[e.id] = true;
}
result.push_back(e);
}
}
return result;
}
Graph reversed() const {
Graph result(_n);
result._edge_count = _edge_count;
result._edge_positions.assign(_edge_count, {});
for (int v = 0; v < _n; v++) {
for (const auto& e : _g[v]) {
int idx = int(result._g[e.to].size());
result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
}
}
return result;
}
};
} // namespace graph
} // namespace m1une
#line 1 "graph/tree/zero_one_on_tree.hpp"
#line 5 "graph/tree/zero_one_on_tree.hpp"
#include <set>
#line 7 "graph/tree/zero_one_on_tree.hpp"
#line 1 "graph/tree/rooted_tree.hpp"
#line 7 "graph/tree/rooted_tree.hpp"
#line 9 "graph/tree/rooted_tree.hpp"
namespace m1une {
namespace tree {
template <class T = int>
struct RootedTree {
using cost_type = T;
using edge_type = m1une::graph::Edge<T>;
int root;
std::vector<int> parent;
std::vector<int> parent_edge;
std::vector<int> depth;
std::vector<T> dist;
std::vector<int> subtree_size;
std::vector<int> tin;
std::vector<int> tout;
std::vector<int> order;
std::vector<std::vector<int>> up;
private:
int _n;
int _log;
void check_vertex(int v) const {
assert(0 <= v && v < _n);
assert(tin[v] != -1);
}
public:
RootedTree() : root(-1), _n(0), _log(0) {}
explicit RootedTree(const m1une::graph::Graph<T>& g, int root_ = 0) {
build(g, root_);
}
void build(const m1une::graph::Graph<T>& g, int root_ = 0) {
_n = g.size();
root = _n == 0 ? -1 : root_;
_log = 1;
while ((1U << _log) <= (unsigned int)(std::max(1, _n))) _log++;
parent.assign(_n, -1);
parent_edge.assign(_n, -1);
depth.assign(_n, 0);
dist.assign(_n, T(0));
subtree_size.assign(_n, 0);
tin.assign(_n, -1);
tout.assign(_n, -1);
order.clear();
order.reserve(_n);
up.assign(_log, std::vector<int>(_n, -1));
if (_n == 0) return;
assert(0 <= root && root < _n);
struct Frame {
int v;
int state;
};
std::vector<char> visited(_n, false);
std::vector<Frame> stack;
stack.push_back({root, 0});
visited[root] = true;
int timer = 0;
while (!stack.empty()) {
Frame frame = stack.back();
stack.pop_back();
int v = frame.v;
if (frame.state == 0) {
tin[v] = timer++;
order.push_back(v);
up[0][v] = parent[v];
for (int k = 1; k < _log; k++) {
int p = up[k - 1][v];
up[k][v] = p == -1 ? -1 : up[k - 1][p];
}
stack.push_back({v, 1});
const auto& adj = g[v];
for (int i = int(adj.size()) - 1; i >= 0; i--) {
const auto& e = adj[i];
if (!e.alive) continue;
if (visited[e.to]) continue;
visited[e.to] = true;
parent[e.to] = v;
parent_edge[e.to] = e.id;
depth[e.to] = depth[v] + 1;
dist[e.to] = dist[v] + e.cost;
stack.push_back({e.to, 0});
}
} else {
subtree_size[v]++;
if (parent[v] != -1) subtree_size[parent[v]] += subtree_size[v];
tout[v] = timer;
}
}
}
int size() const {
return _n;
}
bool empty() const {
return _n == 0;
}
int log() const {
return _log;
}
bool is_ancestor(int u, int v) const {
check_vertex(u);
check_vertex(v);
return tin[u] <= tin[v] && tout[v] <= tout[u];
}
bool in_subtree(int v, int u) const {
return is_ancestor(u, v);
}
int kth_ancestor(int v, int k) const {
check_vertex(v);
assert(0 <= k);
int bit = 0;
while (k > 0 && v != -1) {
if (k & 1) {
if (_log <= bit) return -1;
v = up[bit][v];
}
k >>= 1;
bit++;
}
return v;
}
int lca(int u, int v) const {
check_vertex(u);
check_vertex(v);
if (depth[u] < depth[v]) std::swap(u, v);
u = kth_ancestor(u, depth[u] - depth[v]);
if (u == v) return u;
for (int k = _log - 1; k >= 0; k--) {
if (up[k][u] != up[k][v]) {
u = up[k][u];
v = up[k][v];
}
}
return parent[u];
}
int dist_edges(int u, int v) const {
int w = lca(u, v);
return depth[u] + depth[v] - 2 * depth[w];
}
T dist_cost(int u, int v) const {
int w = lca(u, v);
return dist[u] + dist[v] - dist[w] - dist[w];
}
int jump(int from, int to, int k) const {
check_vertex(from);
check_vertex(to);
assert(0 <= k);
int w = lca(from, to);
int up_len = depth[from] - depth[w];
int down_len = depth[to] - depth[w];
if (up_len + down_len < k) return -1;
if (k <= up_len) return kth_ancestor(from, k);
return kth_ancestor(to, down_len - (k - up_len));
}
std::vector<int> path(int u, int v) const {
check_vertex(u);
check_vertex(v);
int w = lca(u, v);
std::vector<int> a, b;
for (int x = u; x != w; x = parent[x]) a.push_back(x);
a.push_back(w);
for (int x = v; x != w; x = parent[x]) b.push_back(x);
std::reverse(b.begin(), b.end());
a.insert(a.end(), b.begin(), b.end());
return a;
}
std::vector<int> path_edges(int u, int v) const {
check_vertex(u);
check_vertex(v);
int w = lca(u, v);
std::vector<int> a, b;
for (int x = u; x != w; x = parent[x]) a.push_back(parent_edge[x]);
for (int x = v; x != w; x = parent[x]) b.push_back(parent_edge[x]);
std::reverse(b.begin(), b.end());
a.insert(a.end(), b.begin(), b.end());
return a;
}
std::pair<int, int> subtree_range(int v) const {
check_vertex(v);
return {tin[v], tout[v]};
}
std::vector<int> subtree_vertices(int v) const {
check_vertex(v);
return std::vector<int>(order.begin() + tin[v], order.begin() + tout[v]);
}
};
} // namespace tree
} // namespace m1une
#line 9 "graph/tree/zero_one_on_tree.hpp"
namespace m1une {
namespace tree {
inline long long zero_one_on_tree(const std::vector<int>& parent,
const std::vector<int>& value) {
const int n = int(parent.size());
assert(int(value.size()) == n);
if (n == 0) return 0;
int root = -1;
std::vector<std::vector<int>> children(n);
for (int v = 0; v < n; v++) {
assert(value[v] == 0 || value[v] == 1);
if (parent[v] == -1) {
assert(root == -1);
root = v;
} else {
assert(0 <= parent[v] && parent[v] < n && parent[v] != v);
children[parent[v]].push_back(v);
}
}
assert(root != -1);
std::vector<int> stack(1, root);
std::vector<char> visited(n, false);
visited[root] = true;
int visited_count = 0;
while (!stack.empty()) {
const int v = stack.back();
stack.pop_back();
visited_count++;
for (int child : children[v]) {
assert(!visited[child]);
visited[child] = true;
stack.push_back(child);
}
}
assert(visited_count == n);
struct Component {
long long zeros;
long long ones;
int vertex;
};
struct Compare {
bool operator()(const Component& lhs, const Component& rhs) const {
const long long lhs_product = lhs.zeros * rhs.ones;
const long long rhs_product = rhs.zeros * lhs.ones;
if (lhs_product != rhs_product) return lhs_product < rhs_product;
return lhs.vertex < rhs.vertex;
}
};
std::vector<long long> zeros(n), ones(n);
std::vector<int> dsu(n);
std::set<Component, Compare> components;
for (int v = 0; v < n; v++) {
zeros[v] = value[v] == 0;
ones[v] = value[v] == 1;
dsu[v] = v;
if (v != root) components.insert(Component{zeros[v], ones[v], v});
}
auto leader = [&](int v) {
int result = v;
while (dsu[result] != result) result = dsu[result];
while (dsu[v] != v) {
const int next = dsu[v];
dsu[v] = result;
v = next;
}
return result;
};
long long answer = 0;
while (!components.empty()) {
auto it = components.end();
--it;
const Component child = *it;
components.erase(it);
const int p = leader(parent[child.vertex]);
if (p != root) {
const int erased = int(components.erase(Component{zeros[p], ones[p], p}));
assert(erased == 1);
}
answer += ones[p] * zeros[child.vertex];
zeros[p] += zeros[child.vertex];
ones[p] += ones[child.vertex];
dsu[child.vertex] = p;
if (p != root) components.insert(Component{zeros[p], ones[p], p});
}
return answer;
}
template <class T>
long long zero_one_on_tree(const m1une::graph::Graph<T>& graph,
const std::vector<int>& value, int root = 0) {
const int n = graph.size();
assert(int(value.size()) == n);
if (n == 0) return 0;
assert(0 <= root && root < n);
assert(int(graph.edges().size()) == n - 1);
RootedTree<T> rooted_tree(graph, root);
assert(int(rooted_tree.order.size()) == n);
return zero_one_on_tree(rooted_tree.parent, value);
}
} // namespace tree
} // namespace m1une
#line 12 "verify/graph/tree/zero_one_on_tree.test.cpp"
long long brute_force(const std::vector<int>& parent, const std::vector<int>& value) {
const int n = int(parent.size());
const int size = 1 << n;
const long long infinity = std::numeric_limits<long long>::max() / 4;
std::vector<long long> dp(size, infinity);
dp[0] = 0;
for (int mask = 0; mask < size; mask++) {
if (dp[mask] == infinity) continue;
int previous_ones = 0;
for (int v = 0; v < n; v++) {
if (mask >> v & 1) previous_ones += value[v];
}
for (int v = 0; v < n; v++) {
if (mask >> v & 1) continue;
if (parent[v] != -1 && !(mask >> parent[v] & 1)) continue;
const int next = mask | (1 << v);
dp[next] = std::min(dp[next], dp[mask] + (value[v] == 0 ? previous_ones : 0));
}
}
return dp.back();
}
void randomized_test() {
std::mt19937 random(712367);
for (int iteration = 0; iteration < 500; iteration++) {
const int n = 1 + int(random() % 9);
std::vector<int> permutation(n);
for (int v = 0; v < n; v++) permutation[v] = v;
std::shuffle(permutation.begin(), permutation.end(), random);
std::vector<int> parent(n, -2);
const int root = permutation[0];
parent[root] = -1;
m1une::graph::Graph<int> graph(n);
for (int i = 1; i < n; i++) {
const int v = permutation[i];
const int p = permutation[random() % i];
parent[v] = p;
graph.add_edge(p, v);
}
std::vector<int> value(n);
for (int& x : value) x = int(random() & 1);
const long long expected = brute_force(parent, value);
assert(m1une::tree::zero_one_on_tree(parent, value) == expected);
assert(m1une::tree::zero_one_on_tree(graph, value, root) == expected);
}
}
int main() {
m1une::utilities::FastInput fast_input;
m1une::utilities::FastOutput fast_output;
randomized_test();
long long a, b;
fast_input >> a >> b;
fast_output << a + b << '\n';
}
verify/graph/tree/zero_one_on_tree.test.cpp