結果
| 問題 |
No.3009 Union-Find でつながろう！
|
| ユーザー |
 hitonanode
|
| 提出日時 | 2025-01-17 22:17:33 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 246 ms / 2,000 ms |
| コード長 | 12,011 bytes |
| コンパイル時間 | 2,512 ms |
| コンパイル使用メモリ | 229,224 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2025-01-17 22:17:40 |
| 合計ジャッジ時間 | 6,124 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 27 |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <cassert>
#include <chrono>
#include <random>
// F_p, p = 2^61 - 1
// https://qiita.com/keymoon/items/11fac5627672a6d6a9f6
class ModIntMersenne61 {
static const long long md = (1LL << 61) - 1;
long long _v;
inline unsigned hi() const noexcept { return _v >> 31; }
inline unsigned lo() const noexcept { return _v & ((1LL << 31) - 1); }
public:
static long long mod() { return md; }
ModIntMersenne61() : _v(0) {}
// 0 <= x < md * 2
explicit ModIntMersenne61(long long x) : _v(x >= md ? x - md : x) {
assert(0 <= x and x < md * 2);
}
long long val() const noexcept { return _v; }
ModIntMersenne61 operator+(const ModIntMersenne61 &x) const {
return ModIntMersenne61(_v + x._v);
}
ModIntMersenne61 operator-(const ModIntMersenne61 &x) const {
return ModIntMersenne61(_v + md - x._v);
}
ModIntMersenne61 operator*(const ModIntMersenne61 &x) const {
using ull = unsigned long long;
ull uu = (ull)hi() * x.hi() * 2;
ull ll = (ull)lo() * x.lo();
ull lu = (ull)hi() * x.lo() + (ull)lo() * x.hi();
ull sum = uu + ll + ((lu & ((1ULL << 30) - 1)) << 31) + (lu >> 30);
ull reduced = (sum >> 61) + (sum & ull(md));
return ModIntMersenne61(reduced);
}
ModIntMersenne61 pow(long long n) const {
assert(n >= 0);
ModIntMersenne61 ans(1), tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
ModIntMersenne61 inv() const { return pow(md - 2); }
ModIntMersenne61 operator/(const ModIntMersenne61 &x) const { return *this * x.inv(); }
ModIntMersenne61 operator-() const { return ModIntMersenne61(md - _v); }
ModIntMersenne61 &operator+=(const ModIntMersenne61 &x) { return *this = *this + x; }
ModIntMersenne61 &operator-=(const ModIntMersenne61 &x) { return *this = *this - x; }
ModIntMersenne61 &operator*=(const ModIntMersenne61 &x) { return *this = *this * x; }
ModIntMersenne61 &operator/=(const ModIntMersenne61 &x) { return *this = *this / x; }
ModIntMersenne61 operator+(unsigned x) const { return ModIntMersenne61(this->_v + x); }
bool operator==(const ModIntMersenne61 &x) const { return _v == x._v; }
bool operator!=(const ModIntMersenne61 &x) const { return _v != x._v; }
bool operator<(const ModIntMersenne61 &x) const { return _v < x._v; } // To use std::map
template <class OStream> friend OStream &operator<<(OStream &os, const ModIntMersenne61 &x) {
return os << x._v;
}
static ModIntMersenne61 randgen(bool force_update = false) {
static ModIntMersenne61 b(0);
if (b == ModIntMersenne61(0) or force_update) {
std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());
std::uniform_int_distribution<long long> d(1, ModIntMersenne61::mod());
b = ModIntMersenne61(d(mt));
}
return b;
}
};
#include <algorithm>
#include <numeric>
#include <utility>
#include <vector>
// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
std::vector<int> par, cou;
UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
bool unite(int x, int y) {
x = find(x), y = find(y);
if (x == y) return false;
if (cou[x] < cou[y]) std::swap(x, y);
par[y] = x, cou[x] += cou[y];
return true;
}
int count(int x) { return cou[find(x)]; }
bool same(int x, int y) { return find(x) == find(y); }
std::vector<std::vector<int>> groups() {
std::vector<std::vector<int>> ret(par.size());
for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i);
ret.erase(std::remove_if(ret.begin(), ret.end(),
[&](const std::vector<int> &v) { return v.empty(); }),
ret.end());
return ret;
}
};
int main() {
int M, N;
cin >> M >> N;
// vector<ModIntMersenne61> a(N);
// REP(i, a.size()) a.at(i) = ModIntMersenne61::randgen(true);
// vector<ModIntMersenne61> sum(M);
UnionFind uf(N);
using BS = bitset<4097>;
vector<BS> bs(M);
REP(j, M) {
string S;
cin >> S;
dbg(S);
bs.at(j) = BS(S);
// dbg(bs.at(j));
// int last = -1;
// REP(i, N) {
// if (S.at(i) == '1') {
// if (last >= 0) uf.unite(last, i);
// last = i;
// sum.at(j) += a.at(i);
// }
// }
}
vector<int> c(N);
REP(i, N) {
BS b;
REP(j, N) b.set(j);
bool has = false;
for (const auto &v : bs) {
if (v.test(i)) {
b &= v;
has = true;
}
}
if (has) {
int last = -1;
for (int j = 0; j < N; ++j) {
if (b.test(j)) {
if (last >= 0) uf.unite(last, j);
dbg(make_tuple(i, last));
c.at(j)++;
last = j;
}
}
}
}
if (count(ALL(c), 0)) {
puts("1");
} else {
int ret = uf.groups().size();
cout << ret << '\n';
}
}