#611516 (C++17) No.1370 置換門松列

提出ソース
結果

問題	No.1370 置換門松列
ユーザー	iiljj
提出日時	2021-01-29 23:04:42
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	16,507 bytes
コンパイル時間	3,502 ms
コンパイル使用メモリ	243,748 KB
実行使用メモリ	23,216 KB
最終ジャッジ日時	2024-11-08 04:17:23
合計ジャッジ時間	7,984 ms
ジャッジサーバーID （参考情報）	judge5 / judge2
このコードへのチャレンジ
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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 10,496 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	3 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	2 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	AC	2 ms 5,248 KB
testcase_14	AC	2 ms 5,248 KB
testcase_15	AC	2 ms 5,248 KB
testcase_16	AC	3 ms 5,248 KB
testcase_17	AC	2 ms 5,248 KB
testcase_18	AC	2 ms 5,248 KB
testcase_19	AC	2 ms 5,248 KB
testcase_20	AC	2 ms 5,248 KB
testcase_21	AC	73 ms 20,940 KB
testcase_22	AC	64 ms 23,216 KB
testcase_23	AC	72 ms 21,736 KB
testcase_24	TLE	-
testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
testcase_28	--	-
testcase_29	--	-
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ソースコード

raw source code
/* #region Head */

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))

#define endl '\n'

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
    REP(i, 0, SIZE(arr)) is >> arr[i];
    return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&... tail) {
    cout << head;
    if (sizeof...(Tail) > 0) cout << ' ';
    pprint(move(tail)...);
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

#define VAR(type, ...)                                                                                                 \
    type __VA_ARGS__;                                                                                                  \
    cin >> __VA_ARGS__;

template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

// #include <atcoder/all>
// using namespace atcoder;

/* #region Graph */

// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
template <class weight_t = int, class flow_t = int> struct Edge {
    ll src;          // エッジ始点となる頂点
    ll dst;          // エッジ終点となる頂点
    weight_t weight; // 重み
    flow_t cap;
    Edge() : src(0), dst(0), weight(0) {}
    Edge(ll src, ll dst, weight_t weight) : src(src), dst(dst), weight(weight) {}
    Edge(ll src, ll dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {}
    // Edge 標準出力
    friend ostream &operator<<(ostream &os, Edge &edge) {
        os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
        return os;
    }
};
// 同じ頂点を始点とするエッジ集合
template <class weight_t = int, class flow_t = int> class Node : public vc<Edge<weight_t, flow_t>> {
  public:
    ll idx;
    Node() : vc<Edge<weight_t, flow_t>>() {}
    // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); };
};
// graph[i] := 頂点 i を始点とするエッジ集合
template <class weight_t = int, class flow_t = int> class Graph : public vc<Node<weight_t, flow_t>> {
  public:
    Graph() : vc<Node<weight_t, flow_t>>() {}
    Graph(int n) : vc<Node<weight_t, flow_t>>(n) { REP(i, 0, n)(*this)[i].idx = i; }
    // 単方向
    void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); }
    // 双方向
    void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); }
};
// using Array = vc<Weight>;
// using Matrix = vc<Array>;

/* #endregion */

/* #region scc */

// 強連結成分分解
template <class weight_t, class flow_t> vll scc(const Graph<weight_t, flow_t> &g) {
    ll n = SIZE(g);                // ノード数
    Graph<weight_t, flow_t> rg(n); // 逆向きのグラフ
    for (const Node<weight_t, flow_t> &es : g)
        for (Edge<weight_t, flow_t> e : es) {
            swap(e.src, e.dst);
            rg[e.src].emplace_back(e);
        }

    vll order;
    order.reserve(n);

    { // dfs 1回目
        vc<bool> visited(n), added(n);
        REP(i, 0, n) {
            if (visited[i]) continue;
            stack<ll> stk;
            stk.push(i);
            while (!stk.empty()) {
                ll cur = stk.top();
                visited[cur] = true;
                bool pushed = false;
                for (const Edge<weight_t, flow_t> &e : g[cur])
                    if (!visited[e.dst]) {
                        stk.push(e.dst);
                        pushed = true;
                    }
                if (!pushed) { // カレントノードからは未訪問ノードへ到達できない
                    ll t = stk.top();
                    stk.pop(); // 未訪問ノードへ到達できないノードは除いていく
                    if (!added[t]) {
                        added[t] = true;
                        order.push_back(t);
                    }
                }
            }
        }
        reverse(ALL(order));
    }

    vll ret(n, -1);
    { // dfs 2回目
        ll groupnum = 0;
        for (ll &v : order) {
            if (ret[v] != -1) continue;
            stack<ll> stk;
            stk.push(v);
            while (!stk.empty()) {
                ll cur = stk.top();
                stk.pop();
                ret[cur] = groupnum;
                for (Edge<weight_t, flow_t> &e : rg[cur])
                    if (ret[e.dst] == -1) stk.push(e.dst);
            }
            ++groupnum;
        }
    }
    return ret;
}

/* #endregion */

template <class weight_t, class flow_t> bool has_cycle_directed(Graph<weight_t, flow_t> &graph) {
    ll n = SIZE(graph);
    vc<bool> visited(n, false);
    function<bool(ll, ll)> dfs = [&](ll idx, ll par) {
        if (visited[idx]) return true;
        visited[idx] = true;
        for (Edge<weight_t, flow_t> &edge : graph[idx])
            if (edge.dst != par && dfs(edge.dst, idx)) return true;
        return false;
    };
    vll indegrees(n, 0); // 入次数
    REP(i, 0, n) REP(j, 0, SIZE(graph[i])) indegrees[graph[i][j].dst]++;
    // 入次数が 0 になるような頂点が存在しない場合，閉路は必ず存在する（ほんと？）
    if (find(ALL(indegrees), 0LL) == indegrees.end()) return true;
    dump(111);
    REP(i, 0, n) {
        fill(ALL(visited), false);
        if (indegrees[i] == 0)
            if (dfs(i, -1)) return true;
    }
    return false;
}

template <class weight_t, class flow_t> vll get_cycle_directed(Graph<weight_t, flow_t> &graph) {
    ll n = SIZE(graph);
    vll group = scc(graph);

    um<ll, vll> mp;
    REP(i, 0, n) {
        if (mp.find(group[i]) == mp.end()) mp[group[i]] = vll();
        mp[group[i]].emplace_back(i);
    }
    REPI(itr, mp) {
        ll sz = SIZE(itr->second);
        if (sz > 1) {
            // cout << sz << endl;
            // REP(i, 0, sz) cout << itr->second[i] << endl;
            // ぐるっと1周するようなパスが複数存在する場合，すべてを出力するのは駄目
            // ぐるっと1周する閉路を横切るようなパスが存在しないような閉路を出力しないといけない
            // まずはぐるっと1周するパスを探し，それを横切るエッジがあるなら，そのエッジの終点から始点までのパスを探す
            set<ll> st;
            REP(i, 0, sz) st.insert(itr->second[i]);

            ll start = itr->second[0], term = -1;
            while (true) {
                vll visited(n, -1);
                ll visitcnt = 0;
                visited[start] = visitcnt++;

                queue<Node<weight_t, flow_t>> que; // 「訪問予定」頂点リスト

                que.push(graph[start]);
                Graph<weight_t, flow_t> g2(n);
                vc<pll> shortcut;
                while (!que.empty()) { // bfs
                    Node<weight_t, flow_t> cur = que.front();
                    que.pop();

                    for (Edge<weight_t, flow_t> &e : cur) {
                        if (st.find(e.dst) == st.end()) continue;
                        if (visited[e.dst] == 0) {
                            // dump(e.src, e.dst);
                            term = e.src;
                            continue;
                        } else if (visited[e.dst] != -1) {
                            shortcut.emplace_back(e.src, e.dst);
                            continue;
                        }
                        g2.add_arc(e.dst, e.src);
                        visited[e.dst] = visitcnt++;
                        que.push(graph[e.dst]);
                    }
                    if (term != -1) break;
                }
                vll nodes = {term};
                set<ll> st2;
                st2.insert(term);
                ll cur = term;
                while (cur != start) {
                    // なるべく番号が若いノードを辿っていく
                    ll num = INF, par = -1;
                    for (Edge<weight_t, flow_t> &e : g2[cur]) {
                        if (chmin(num, visited[e.dst])) par = e.dst;
                    }
                    nodes.push_back(par);
                    st2.insert(par);
                    cur = par;
                }
                reverse(ALL(nodes));
                if (SIZE(shortcut) == 0) return nodes;
                // ショートカットが存在しても，その両端点が nodes に入っていなければセーフ
                bool safe = true;
                for (pll &sc : shortcut) {
                    if (st2.find(sc.first) != st2.end() && st2.find(sc.second) != st2.end()) {
                        safe = false;
                        break;
                    }
                }
                if (safe) return nodes;
                start = shortcut[0].second, term = -1;
            }
        }
    }
    return vll(0);
}

// Problem
void solve() {
    VAR(ll, n, m); //
    vll a(n);
    cin >> a;
    REP(i, 0, n) a[i]--;

    // <><>...
    Graph<> graph(m);
    vll h(m, 0);       // 入ってくるエッジの本数
    REP(i, 0, n - 1) { // 小さい方から大きい方へ辺を張る
        if (a[i] == a[i + 1]) {
            Yn(false);
            return;
        }
        if (i % 2 == 0) {
            graph.add_arc(a[i], a[i + 1]);
            h[a[i + 1]]++;
            // dump(a[i], a[i + 1]);
        } else {
            graph.add_arc(a[i + 1], a[i]);
            h[a[i]]++;
            // dump(a[i + 1], a[i]);
        }
    }
    REP(i, 0, n - 2) {
        if (a[i] == a[i + 2]) {
            Yn(false);
            return;
        }
    }
    vll cycle = get_cycle_directed(graph);
    // if (has_cycle_directed(graph)) {
    //     Yn(false);
    //     return;
    // }
    if (SIZE(cycle) > 0) {
        Yn(false);
        return;
    }

    stack<ll> st;
    REP(i, 0, m) if (h[i] == 0) st.push(i);

    vll ans;
    while (st.size()) {
        ll node_idx = st.top();
        st.pop();
        ans.push_back(node_idx);
        for (Edge<> &edge : graph[node_idx]) {
            h[edge.dst]--;
            if (h[edge.dst] == 0) st.push(edge.dst);
        }
    }
    // dump(ans);

    vll ret(m, 1);
    REP(i, 0, SIZE(ans)) ret[ans[i]] = i + 1;
    Yn(true);
    cout >> ret;
}

// entry point
int main() {
    solve();
    return 0;
}
yukicoder

結果

テストケース

ソースコード
