cp-library
競技プログラミング用 C++ ライブラリ
test/hungarian.test.cpp
test/hungarian.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/assignment"
#include "../graph/hungarian.hpp"
#include "../components/fast_io.hpp"
#include <vector>
int main() {
FastInput in;
FastOutput out;
int n;
in.read(n);
std::vector<int> a(std::size_t(n) * n);
for (auto &x : a) in.read(x);
Hungarian res(n, n, a.data());
out.write(res.cost);
out.write('\n');
for (int i = 0; i < n; ++i) {
if (i) out.write(' ');
out.write(res.row_to_col[i]);
}
out.write('\n');
}
#line 1 "test/hungarian.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/assignment"
#line 1 "graph/hungarian.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <iterator>
#include <limits>
#include <numeric>
#include <type_traits>
#include <utility>
#include <vector>
template <class Cost = long long>
struct Hungarian {
static_assert(std::numeric_limits<Cost>::is_integer && std::numeric_limits<Cost>::is_signed);
Cost cost = 0;
std::vector<int> row_to_col, col_to_row;
template <class Matrix>
explicit Hungarian(const Matrix &a, bool maximize = false) {
int n = int(a.size()), m = n ? int(a[0].size()) : 0;
using T = std::remove_cvref_t<decltype(a[0][0])>;
std::vector<const T *> rows(n);
for (int i = 0; i < n; ++i) {
assert(int(a[i].size()) == m);
rows[i] = std::data(a[i]);
}
if (maximize) solve<true>(n, m, rows);
else solve<false>(n, m, rows);
}
template <class T>
Hungarian(int n, int m, const T *a, int stride = -1, bool maximize = false) {
assert(0 <= n && n <= m);
if (stride == -1) stride = m;
assert(stride >= m);
std::vector<const T *> rows(n);
for (int i = 0; i < n; ++i) rows[i] = a + std::size_t(i) * stride;
if (maximize) solve<true>(n, m, rows);
else solve<false>(n, m, rows);
}
private:
template <bool maximize, class T>
void solve(int n, int m, const std::vector<const T *> &a) {
assert(n <= m);
row_to_col.assign(n, -1);
col_to_row.assign(m, -1);
if (!n) return;
auto value = [&](int i, int j) -> Cost {
if constexpr (maximize) return -Cost(a[i][j]);
else return Cost(a[i][j]);
};
auto finish = [&] {
for (int i = 0; i < n; ++i) cost += Cost(a[i][row_to_col[i]]);
};
if (n == m) {
using Wide = std::conditional_t<(sizeof(T) < 8), long long, __int128_t>;
int order = 3;
for (int i = 1; i < n && order; ++i)
for (int j = 1; j < m; ++j) {
Wide x = Wide(a[i - 1][j - 1]) + Wide(a[i][j]);
Wide y = Wide(a[i - 1][j]) + Wide(a[i][j - 1]);
if (x > y) order &= 2;
if (x < y) order &= 1;
if (!order) break;
}
if (order) {
bool reverse = maximize ? bool(order & 1) : !(order & 1);
for (int i = 0; i < n; ++i) {
int j = reverse ? n - 1 - i : i;
row_to_col[i] = j;
col_to_row[j] = i;
}
finish();
return;
}
}
std::vector<Cost> price(m), dist(m);
std::vector<int> columns(m), pred(m);
if (n == m) {
std::vector<T> minimum(a[0], a[0] + m);
std::vector<int> owner(m), count(n);
for (int i = 1; i < n; ++i)
for (int j = 0; j < m; ++j) {
T x = a[i][j];
bool better = maximize ? x > minimum[j] : x < minimum[j];
minimum[j] = better ? x : minimum[j];
owner[j] = better ? i : owner[j];
}
for (int j = 0; j < m; ++j) price[j] = maximize ? -Cost(minimum[j]) : Cost(minimum[j]);
for (int j = m - 1; j >= 0; --j) {
int i = owner[j];
if (!count[i]++) row_to_col[i] = j, col_to_row[j] = i;
}
for (int i = 0; i < n; ++i) if (count[i] == 1) {
Cost delta = std::numeric_limits<Cost>::max();
int matched = row_to_col[i];
for (int j = 0; j < m; ++j)
if (j != matched) delta = std::min(delta, Cost(value(i, j) - price[j]));
price[matched] -= delta;
}
for (int pass = 0; pass < 2; ++pass)
for (int i = 0; i < n; ++i) if (row_to_col[i] == -1) {
int best_col = 0;
Cost best = value(i, 0) - price[0], second = std::numeric_limits<Cost>::max();
for (int j = 1; j < m; ++j) {
Cost x = value(i, j) - price[j];
if (x < best) second = best, best = x, best_col = j;
else if (x == best && col_to_row[best_col] != -1 && col_to_row[j] == -1) second = best, best_col = j;
else second = std::min(second, x);
}
if (best < second) price[best_col] -= second - best;
int old = col_to_row[best_col];
if (old != -1) row_to_col[old] = -1;
row_to_col[i] = best_col;
col_to_row[best_col] = i;
}
} else {
for (int i = 0; i < n; ++i) {
int best_col = 0;
Cost best = value(i, 0);
for (int j = 1; j < m; ++j) {
Cost x = value(i, j);
if (x < best || (x == best && col_to_row[best_col] != -1 && col_to_row[j] == -1)) best = x, best_col = j;
}
if (col_to_row[best_col] == -1) row_to_col[i] = best_col, col_to_row[best_col] = i;
}
}
std::iota(columns.begin(), columns.end(), 0);
for (int root = 0; root < n; ++root) if (row_to_col[root] == -1) {
for (int j = 0; j < m; ++j) dist[j] = value(root, j) - price[j], pred[j] = root;
int scanned = 0, queued = 0, target = -1;
Cost level = 0;
while (target == -1) {
if (scanned == queued) {
level = dist[columns[scanned]];
for (int k = scanned; k < m; ++k) {
int j = columns[k];
if (dist[j] > level) continue;
if (dist[j] < level) level = dist[j], queued = scanned, target = -1;
std::swap(columns[k], columns[queued++]);
if (col_to_row[j] == -1) target = j;
}
if (target != -1) break;
}
int j0 = columns[scanned++], i = col_to_row[j0];
Cost offset = value(i, j0) - price[j0] - level;
for (int k = queued; k < m; ++k) {
int j = columns[k];
Cost candidate = value(i, j) - price[j] - offset;
if (candidate >= dist[j]) continue;
dist[j] = candidate;
pred[j] = i;
if (candidate == level) {
if (col_to_row[j] == -1) { target = j; break; }
std::swap(columns[k], columns[queued++]);
}
}
}
for (int k = 0; k < scanned; ++k) {
int j = columns[k];
price[j] += dist[j] - level;
}
while (target != -1) {
int i = pred[target], next = row_to_col[i];
row_to_col[i] = target;
col_to_row[target] = i;
target = next;
}
}
finish();
}
};
#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>
#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 5 "test/hungarian.test.cpp"
int main() {
FastInput in;
FastOutput out;
int n;
in.read(n);
std::vector<int> a(std::size_t(n) * n);
for (auto &x : a) in.read(x);
Hungarian res(n, n, a.data());
out.write(res.cost);
out.write('\n');
for (int i = 0; i < n; ++i) {
if (i) out.write(' ');
out.write(res.row_to_col[i]);
}
out.write('\n');
}