結果
| 問題 |
No.2675 KUMA
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2024-03-15 23:15:07 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 12 ms / 2,000 ms |
| コード長 | 12,199 bytes |
| コンパイル時間 | 2,674 ms |
| コンパイル使用メモリ | 218,888 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-09-30 02:48:19 |
| 合計ジャッジ時間 | 3,799 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 47 |
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 <iostream>
#include <vector>
// Bipartite matching of undirected bipartite graph (Hopcroft-Karp)
// https://ei1333.github.io/luzhiled/snippets/graph/hopcroft-karp.html
// Comprexity: O((V + E)sqrtV)
// int solve(): enumerate maximum number of matching / return -1 (if graph is not bipartite)
struct BipartiteMatching {
int V;
std::vector<std::vector<int>> to; // Adjacency list
std::vector<int> dist; // dist[i] = (Distance from i'th node)
std::vector<int> match; // match[i] = (Partner of i'th node) or -1 (No parter)
std::vector<int> used, vv;
std::vector<int> color; // color of each node(checking bipartition): 0/1/-1(not determined)
BipartiteMatching() = default;
BipartiteMatching(int V_) : V(V_), to(V_), match(V_, -1), used(V_), color(V_, -1) {}
void add_edge(int u, int v) {
assert(u >= 0 and u < V and v >= 0 and v < V and u != v);
to[u].push_back(v);
to[v].push_back(u);
}
void _bfs() {
dist.assign(V, -1);
std::vector<int> q;
int lq = 0;
for (int i = 0; i < V; i++) {
if (!color[i] and !used[i]) q.push_back(i), dist[i] = 0;
}
while (lq < int(q.size())) {
int now = q[lq++];
for (auto nxt : to[now]) {
int c = match[nxt];
if (c >= 0 and dist[c] == -1) q.push_back(c), dist[c] = dist[now] + 1;
}
}
}
bool _dfs(int now) {
vv[now] = true;
for (auto nxt : to[now]) {
int c = match[nxt];
if (c < 0 or (!vv[c] and dist[c] == dist[now] + 1 and _dfs(c))) {
match[nxt] = now, match[now] = nxt;
used[now] = true;
return true;
}
}
return false;
}
bool _color_bfs(int root) {
color[root] = 0;
std::vector<int> q{root};
int lq = 0;
while (lq < int(q.size())) {
int now = q[lq++], c = color[now];
for (auto nxt : to[now]) {
if (color[nxt] == -1) {
color[nxt] = !c, q.push_back(nxt);
} else if (color[nxt] == c) {
return false;
}
}
}
return true;
}
int solve() {
for (int i = 0; i < V; i++) {
if (color[i] == -1 and !_color_bfs(i)) return -1;
}
int ret = 0;
while (true) {
_bfs();
vv.assign(V, false);
int flow = 0;
for (int i = 0; i < V; i++) {
if (!color[i] and !used[i] and _dfs(i)) flow++;
}
if (!flow) break;
ret += flow;
}
return ret;
}
template <class OStream> friend OStream &operator<<(OStream &os, const BipartiteMatching &bm) {
os << "{N=" << bm.V << ':';
for (int i = 0; i < bm.V; i++) {
if (bm.match[i] > i) os << '(' << i << '-' << bm.match[i] << "),";
}
return os << '}';
}
};
int main() {
int N;
cin >> N;
vector<pint> xys(N);
for (auto &[x, y] : xys) cin >> x >> y;
sort(xys.begin(), xys.end());
vector<pint> dxdys{{2, -1}, {2, 1}, {1, 2}, {-1, 2}, {-2, 1}, {-2, -1}, {-1, -2}, {1, -2}};
int ret = N + 1;
auto rec = [&](auto &&self, int rem_mask, vector<vector<int>> groups) -> void {
if (!rem_mask) {
if ((int)groups.size() >= ret) return;
vector<vector<pint>> to;
vector<pint> all_vs;
for (const auto &is : groups) {
vector<pint> targets;
for (auto dxy : dxdys) {
pint target = xys.at(is.at(0)) + dxy;
if (binary_search(xys.begin(), xys.end(), target)) continue;
targets.push_back(target);
}
sort(targets.begin(), targets.end());
for (int i : is) {
vector<pint> next_targets;
for (auto dxy : dxdys) {
pint target = xys.at(i) + dxy;
if (binary_search(targets.begin(), targets.end(), target)) next_targets.push_back(target);
}
targets = sort_unique(next_targets);
}
to.push_back(targets);
all_vs.insert(all_vs.end(), targets.begin(), targets.end());
}
all_vs = sort_unique(all_vs);
BipartiteMatching bm(groups.size() + all_vs.size());
REP(m, groups.size()) {
for (const auto &v : to.at(m)) {
const int j = arglb(all_vs, v);
bm.add_edge(m, groups.size() + j);
}
}
if (bm.solve() == (int)groups.size()) chmin(ret, (int)groups.size());
return;
}
const int i = __builtin_ctz(rem_mask);
assert(rem_mask & (1 << i));
groups.push_back({i});
self(self, rem_mask - (1 << i), groups);
for (int j = i + 1; j < N; ++j) {
if (!((rem_mask >> j) & 1)) continue;
auto dxy = xys.at(j) - xys.at(i);
if ((dxy.first == 0 and abs(dxy.second) == 2) or (dxy.second == 0 and abs(dxy.first) == 2)) {
groups.back().push_back(j);
self(self, rem_mask - (1 << i) - (1 << j), groups);
groups.back().pop_back();
}
}
};
rec(rec, (1 << N) - 1, {});
cout << (ret <= N ? ret : -1) << '\n';
}