cp-library
競技プログラミング用 C++ ライブラリ
test/general_matching.test.cpp
test/general_matching.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/general_matching"
#include "../graph/general_matching.hpp"
#include "../components/fast_io.hpp"
int main() {
FastInput in;
FastOutput out;
int n = 0, m = 0;
in.read(n);
in.read(m);
GeneralMatching g(n);
g.reserve(m);
for (int i = 0, u = 0, v = 0; i < m; ++i) {
in.read(u);
in.read(v);
g.add_edge(u, v);
}
out.write(g.build());
out.write('\n');
for (auto [u, v] : g.edges()) {
out.write(u);
out.write(' ');
out.write(v);
out.write('\n');
}
}
#line 1 "test/general_matching.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/general_matching"
#line 1 "graph/general_matching.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <numeric>
#include <utility>
#include <vector>
class GeneralMatching {
int n, cardinality = 0, tail = 0;
std::uint32_t stamp = 0, search_stamp = 0;
std::vector<std::pair<int, int>> input;
std::vector<int> start, adj, base, parent, queue;
std::vector<std::uint32_t> seen, state;
int find(int v) {
while (base[v] != v) v = base[v] = base[base[v]];
return v;
}
int lca(int u, int v) {
if (!++stamp) std::fill(seen.begin(), seen.end(), 0), ++stamp;
for (;; std::swap(u, v)) if (u != -1) {
u = find(u);
if (seen[u] == stamp) return u;
seen[u] = stamp;
u = mate[u] == -1 ? -1 : parent[mate[u]];
}
}
void contract(int u, int v, int b) {
while (find(u) != b) {
parent[u] = v;
v = mate[u];
if (state[v] == (search_stamp | 1)) state[v] = search_stamp, queue[tail++] = v;
if (base[u] == u) base[u] = b;
if (base[v] == v) base[v] = b;
u = parent[v];
}
}
void flip(int v) {
while (v != -1) {
int u = parent[v], next = mate[u];
mate[u] = v;
mate[v] = u;
v = next;
}
}
bool augment(int root) {
search_stamp += 2;
if (!search_stamp) std::fill(state.begin(), state.end(), 0), search_stamp = 2;
tail = 1;
queue[0] = root;
state[root] = search_stamp;
base[root] = root;
for (int head = 0; head < tail; ++head) {
int u = queue[head];
for (int e = start[u]; e < start[u + 1]; ++e) {
int v = adj[e];
if ((state[v] & ~std::uint32_t(1)) != search_stamp) {
parent[v] = u;
state[v] = search_stamp | 1;
base[v] = v;
if (mate[v] == -1) { flip(v); return true; }
state[mate[v]] = search_stamp;
base[mate[v]] = mate[v];
queue[tail++] = mate[v];
} else if (state[v] == search_stamp && find(u) != find(v)) {
int b = lca(u, v);
contract(u, v, b);
contract(v, u, b);
}
}
}
return false;
}
void short_paths() {
std::vector<int> first(n, -1), second(n, -1);
auto save = [&](int u, int v) {
if (first[u] == -1) first[u] = v;
else if (first[u] != v) second[u] = v;
};
for (auto [u, v] : input) {
if (mate[u] == -1) save(v, u);
if (mate[v] == -1) save(u, v);
}
for (int u = 0; u < n; ++u) if (u < mate[u]) {
int v = mate[u];
for (int a : {first[u], second[u]}) if (a != -1 && mate[a] == -1) {
int b = first[v];
if (b == -1 || b == a || mate[b] != -1) b = second[v];
if (b == -1 || b == a || mate[b] != -1) continue;
mate[u] = a;
mate[a] = u;
mate[v] = b;
mate[b] = v;
++cardinality;
break;
}
}
}
int component_bound(std::vector<int> &roots) {
std::fill(parent.begin(), parent.end(), -1);
int bound = 0;
for (int root = 0; root < n; ++root) if (parent[root] == -1) {
int end = 1, count[2] = {1, 0};
bool bipartite = true;
queue[0] = root;
parent[root] = 0;
for (int head = 0; head < end; ++head) {
int u = queue[head];
for (int e = start[u]; e < start[u + 1]; ++e) {
int v = adj[e];
if (parent[v] == -1) {
parent[v] = parent[u] ^ 1;
++count[parent[v]];
queue[end++] = v;
} else if (parent[v] == parent[u]) bipartite = false;
}
}
bound += bipartite ? std::min(count[0], count[1]) : end / 2;
int side = count[0] > count[1];
for (int i = 0; i < end; ++i) {
int u = queue[i];
if (mate[u] == -1 && (!bipartite || parent[u] == side)) roots.push_back(u);
}
}
return bound;
}
public:
std::vector<int> mate;
explicit GeneralMatching(int n) : n(n), mate(n, -1) { assert(n >= 0); }
void reserve(std::size_t m) { input.reserve(m); }
void add_edge(int u, int v) {
assert(0 <= u && u < n && 0 <= v && v < n);
if (u == v || cardinality == n / 2) return;
input.emplace_back(u, v);
if (mate[u] == -1 && mate[v] == -1) {
mate[u] = v;
mate[v] = u;
++cardinality;
}
}
int build() {
if (input.empty() || cardinality == n / 2) return cardinality;
short_paths();
if (cardinality == n / 2) return cardinality;
start.assign(n + 1, 0);
for (auto [u, v] : input) ++start[u + 1], ++start[v + 1];
std::partial_sum(start.begin(), start.end(), start.begin());
adj.resize(input.size() * 2);
parent = start;
for (auto [u, v] : input) adj[parent[u]++] = v, adj[parent[v]++] = u;
parent.resize(n);
queue.resize(n);
std::vector<int> roots;
int limit = component_bound(roots);
if (cardinality == limit) return cardinality;
base.resize(n);
seen.resize(n);
state.resize(n);
for (int u : roots) if (mate[u] == -1 && augment(u)) {
if (++cardinality == limit) break;
}
return cardinality;
}
std::vector<std::pair<int, int>> edges() const {
std::vector<std::pair<int, int>> result;
result.reserve(cardinality);
for (int u = 0; u < n; ++u) if (u < mate[u]) result.emplace_back(u, mate[u]);
return result;
}
};
#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 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>
#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 4 "test/general_matching.test.cpp"
int main() {
FastInput in;
FastOutput out;
int n = 0, m = 0;
in.read(n);
in.read(m);
GeneralMatching g(n);
g.reserve(m);
for (int i = 0, u = 0, v = 0; i < m; ++i) {
in.read(u);
in.read(v);
g.add_edge(u, v);
}
out.write(g.build());
out.write('\n');
for (auto [u, v] : g.edges()) {
out.write(u);
out.write(' ');
out.write(v);
out.write('\n');
}
}