結果

問題 No.1370 置換門松列
ユーザー hitonanodehitonanode
提出日時 2021-01-29 21:48:54
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 44 ms / 2,000 ms
コード長 9,225 bytes
コンパイル時間 2,423 ms
コンパイル使用メモリ 212,568 KB
実行使用メモリ 12,928 KB
最終ジャッジ日時 2024-09-14 19:19:04
合計ジャッジ時間 3,920 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 2 ms
5,376 KB
testcase_15 AC 2 ms
5,376 KB
testcase_16 AC 2 ms
5,376 KB
testcase_17 AC 2 ms
5,376 KB
testcase_18 AC 2 ms
5,376 KB
testcase_19 AC 2 ms
5,376 KB
testcase_20 AC 2 ms
5,376 KB
testcase_21 AC 33 ms
12,928 KB
testcase_22 AC 24 ms
11,932 KB
testcase_23 AC 27 ms
11,264 KB
testcase_24 AC 10 ms
5,376 KB
testcase_25 AC 44 ms
12,800 KB
testcase_26 AC 42 ms
12,800 KB
testcase_27 AC 17 ms
11,168 KB
testcase_28 AC 18 ms
11,008 KB
testcase_29 AC 12 ms
5,376 KB
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 # 

#include <bits/stdc++.h>
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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const 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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#else
#define dbg(x) (x)
#endif

// Directed graph library to find strongly connected components （強連結成分分解）
// 0-indexed directed graph
// Complexity: O(V + E)
struct DirectedGraphSCC {
    int V; // # of Vertices
    std::vector<std::vector<int>> to, from;
    std::vector<int> used; // Only true/false
    std::vector<int> vs;
    std::vector<int> cmp;
    int scc_num = -1;

    DirectedGraphSCC(int V = 0) : V(V), to(V), from(V), cmp(V) {}

    void _dfs(int v) {
        used[v] = true;
        for (auto t : to[v])
            if (!used[t]) _dfs(t);
        vs.push_back(v);
    }
    void _rdfs(int v, int k) {
        used[v] = true;
        cmp[v] = k;
        for (auto t : from[v])
            if (!used[t]) _rdfs(t, k);
    }

    void add_edge(int from_, int to_) {
        assert(from_ >= 0 and from_ < V and to_ >= 0 and to_ < V);
        to[from_].push_back(to_);
        from[to_].push_back(from_);
    }

    // Detect strongly connected components and return # of them.
    // Also, assign each vertex `v` the scc id `cmp[v]` (0-indexed)
    int FindStronglyConnectedComponents() {
        used.assign(V, false);
        vs.clear();
        for (int v = 0; v < V; v++)
            if (!used[v]) _dfs(v);
        used.assign(V, false);
        scc_num = 0;
        for (int i = (int)vs.size() - 1; i >= 0; i--)
            if (!used[vs[i]]) _rdfs(vs[i], scc_num++);
        return scc_num;
    }

    // Find and output the vertices that form a closed cycle.
    // output: {v_1, ..., v_C}, where C is the length of cycle,
    //         {} if there's NO cycle (graph is DAG)
    int _c, _init;
    std::vector<int> _ret_cycle;
    bool _dfs_detectcycle(int now, bool b0) {
        if (now == _init and b0) return true;
        for (auto nxt : to[now])
            if (cmp[nxt] == _c and !used[nxt]) {
                _ret_cycle.emplace_back(nxt), used[nxt] = 1;
                if (_dfs_detectcycle(nxt, true)) return true;
                _ret_cycle.pop_back();
            }
        return false;
    }
    std::vector<int> DetectCycle() {
        int ns = FindStronglyConnectedComponents();
        if (ns == V) return {};
        std::vector<int> cnt(ns);
        for (auto x : cmp) cnt[x]++;
        _c = std::find_if(cnt.begin(), cnt.end(), [](int x) { return x > 1; }) - cnt.begin();
        _init = std::find(cmp.begin(), cmp.end(), _c) - cmp.begin();
        used.assign(V, false);
        _ret_cycle.clear();
        _dfs_detectcycle(_init, false);
        return _ret_cycle;
    }

    // After calling `FindStronglyConnectedComponents()`, generate a new graph by uniting all vertices
    // belonging to the same component(The resultant graph is DAG).
    DirectedGraphSCC GenerateTopologicalGraph() {
        DirectedGraphSCC newgraph(scc_num);
        for (int s = 0; s < V; s++)
            for (auto t : to[s]) {
                if (cmp[s] != cmp[t]) newgraph.add_edge(cmp[s], cmp[t]);
            }
        return newgraph;
    }
};

// 2-SAT solver: Find a solution for  `(Ai v Aj) ^ (Ak v Al) ^ ... = true`
// - `nb_sat_vars`: Number of variables
// - Considering a graph with `2 * nb_sat_vars` vertices
// - Vertices [0, nb_sat_vars) means `Ai`
// - vertices [nb_sat_vars, 2 * nb_sat_vars) means `not Ai`
struct SATSolver : DirectedGraphSCC {
    int nb_sat_vars;
    std::vector<int> solution;
    SATSolver(int nb_variables = 0) : DirectedGraphSCC(nb_variables * 2), nb_sat_vars(nb_variables), solution(nb_sat_vars) {}
    void add_x_or_y_constraint(bool is_x_true, int x, bool is_y_true, int y) {
        assert(x >= 0 and x < nb_sat_vars);
        assert(y >= 0 and y < nb_sat_vars);
        if (!is_x_true) x += nb_sat_vars;
        if (!is_y_true) y += nb_sat_vars;
        add_edge((x + nb_sat_vars) % (nb_sat_vars * 2), y);
        add_edge((y + nb_sat_vars) % (nb_sat_vars * 2), x);
    }
    // Solve the 2-SAT problem. If no solution exists, return `false`.
    // Otherwise, dump one solution to `solution` and return `true`.
    bool run() {
        FindStronglyConnectedComponents();
        for (int i = 0; i < nb_sat_vars; i++) {
            if (cmp[i] == cmp[i + nb_sat_vars]) return false;
            solution[i] = cmp[i] > cmp[i + nb_sat_vars];
        }
        return true;
    }
};

template <typename T> bool kado(T a, T b, T c) {
    if (a == b or b == c or a == c) return false;
    if (a < b and b > c) return true;
    if (a > b and b < c) return true;
    return false;
}
int main() {
    int N, M;
    cin >> N >> M;
    vector<int> A(N);
    cin >> A;
    for (auto &a : A) a--;
    DirectedGraphSCC graph(M);
    REP(i, N - 1) {
        if (i % 2 == 0) graph.add_edge(A[i], A[i + 1]);
        else graph.add_edge(A[i + 1], A[i]);
    }
    int s = graph.FindStronglyConnectedComponents();
    if (s < M) {
        puts("No");
        return 0;
    }
    dbg(A);
    dbg(graph.cmp);
    FOR(i, 1, N - 1) if (!kado(graph.cmp[A[i - 1]], graph.cmp[A[i]], graph.cmp[A[i + 1]])) {
        puts("No");
        return 0;
    }
    cout << "Yes\n";
    for (auto x : graph.cmp) cout << x + 1 << '\n';
}
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