結果

問題 No.3031 曲面の向き付け
ユーザー zawakasu
提出日時 2025-02-21 23:46:49
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 381 ms / 2,000 ms
コード長 4,821 bytes
コンパイル時間 1,987 ms
コンパイル使用メモリ 137,148 KB
実行使用メモリ 39,112 KB
最終ジャッジ日時 2025-02-21 23:46:57
合計ジャッジ時間 8,455 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 29
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <iostream>
#include <iomanip>
#include <cassert>
#include <vector>
#include <algorithm>
#include <utility>
#include <set>
#include <cstdint>
#include <cstddef>
namespace zawa {
using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;
using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using usize = std::size_t;
} // namespace zawa
#include <iterator>
#include <limits>
namespace zawa {
template <class T>
class CompressedSequence {
private:
    std::vector<T> comped_;
    std::vector<u32> f_;
    
public:
    static constexpr u32 NotFound = std::numeric_limits<u32>::max();
    CompressedSequence() = default;
    template <class InputIterator>
    CompressedSequence(InputIterator first, InputIterator last) : comped_(first, last), f_{} {
        std::sort(comped_.begin(), comped_.end());
        comped_.erase(std::unique(comped_.begin(), comped_.end()), comped_.end());
        comped_.shrink_to_fit();
        f_.reserve(std::distance(first, last));
        for (auto it{first} ; it != last ; it++) {
            f_.emplace_back(std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), *it)));
        }
    }
    CompressedSequence(const std::vector<T>& A) : CompressedSequence(A.begin(), A.end()) {}
    inline usize size() const noexcept {
        return comped_.size();
    }
    u32 operator[](const T& v) const {
        return std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v));
    }
    u32 find(const T& v) const {
        u32 i = std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v));
        return i == comped_.size() or comped_[i] != v ? NotFound : i;
    }
    bool contains(const T& v) const {
        u32 i = std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v));
        return i < comped_.size() and comped_[i] == v;
    }
    u32 at(const T& v) const {
        u32 res{(*this)[v]};
        assert(res < size() and comped_[res] == v);
        return res;
    }
    inline u32 map(u32 i) const noexcept {
        assert(i < f_.size());
        return f_[i];
    }
    inline T inverse(u32 i) const noexcept {
        assert(i < size());
        return comped_[i];
    }
};
} // namespace zawa
std::ostream& operator<<(std::ostream& os, std::pair<int, int> p) {
    os << '[' << p.first << ',' << p.second << ']';
    return os;
}
using namespace zawa;
int N, A[100010], B[100010], C[100010];
std::vector<std::pair<int, std::pair<int, int>>> g[100010];
bool solve() {
    std::vector<std::pair<int, int>> app;
    for (int i = 0 ; i < N ; i++) {
        app.push_back({A[i], B[i]});
        app.push_back({B[i], C[i]});
        app.push_back({A[i], C[i]});
    }
    CompressedSequence comp{app};
    std::vector<std::vector<int>> vals(comp.size());
    for (int i = 0 ; i < N ; i++) {
        for (const auto& p : {std::pair{A[i], B[i]}, std::pair{B[i], C[i]}, std::pair{A[i], C[i]}}) {
            assert(p.first < p.second);
            auto it = comp.at(p);
            vals[it].push_back(i);
        }
    }
    for (int i = 0 ; i < (int)comp.size() ; i++) {
        if (vals[i].size() >= 3u) return false;
        if (vals[i].size() == 1u) continue;
        g[vals[i][0]].push_back({vals[i][1], comp.inverse(i)});  
        g[vals[i][1]].push_back({vals[i][0], comp.inverse(i)});  
    }
    std::vector<int> col(comp.size(), -1);
    auto assign = [&](int i, int c) -> bool {
        assert(0 <= i and i < (int)comp.size());
        // std::cout << "try " << comp.inverse(i) << ' ' << c << std::endl;
        if (col[i] == -1) col[i] = c;
        else {
            if (col[i] == c) return false;
        }
        return true;
    };
    // 0 hueru
    // 1 heru
    std::vector<bool> vis(N);
    auto dfs = [&](auto dfs, int v, int c) -> bool {
        // std::cout << "dfs " << A[v] << ' ' << B[v] << ' ' << C[v] << " col " << c << std::endl;
        if (!assign(comp.find({A[v], B[v]}), c)) return false;
        if (!assign(comp.find({B[v], C[v]}), c)) return false;
        if (!assign(comp.find({A[v], C[v]}), c ^ 1)) return false;
        vis[v] = true;
        for (const auto& [x, e] : g[v]) if (!vis[x]) {
            auto it = comp.at(e);
            int nc = col[it] ^ 1;
            if (e == std::pair{A[x], C[x]}) nc ^= 1;
            if (!dfs(dfs, x, nc)) return false;
        }
        return true;
    };
    for (int i = 0 ; i < N ; i++) if (!vis[i]) {
        if (!dfs(dfs, i, 0)) return false;
    }
    return true;
}
int main() {
    std::cin.tie(nullptr)->sync_with_stdio(false);
    std::cin >> N;
    for (int i = 0 ; i < N ; i++) std::cin >> A[i] >> B[i] >> C[i];
    std::cout << (solve() ? "YES\n" : "NO\n");
}
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