結果

問題 No.3075 Mex Recurrence Formula
ユーザー Today03
提出日時 2025-03-28 22:08:03
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 389 ms / 2,000 ms
コード長 6,127 bytes
コンパイル時間 3,705 ms
コンパイル使用メモリ 296,688 KB
実行使用メモリ 22,708 KB
最終ジャッジ日時 2025-03-28 22:08:42
合計ジャッジ時間 12,615 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 * 3
other AC * 46
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>
#define ALL(x) (x).begin(), (x).end()
#define LB(v, x) (int)(lower_bound(ALL(v), x) - (v).begin())
#define UQ(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define IO ios::sync_with_stdio(false), cin.tie(nullptr);
#define chmax(a, b) (a) = (a) < (b) ? (b) : (a)
#define chmin(a, b) (a) = (a) < (b) ? (a) : (b)
using namespace std;
using ll = long long;
const int INF = 1e9 + 10;
const ll INFL = 4e18;

template <typename Monoid>
struct SegTree {
    using Type = typename Monoid::Type;

    SegTree() = default;
    SegTree(int n) {
        this->n = n;
        dat.assign(n << 1, Monoid::id());
        cand.reserve(100), cand_l.reserve(100), cand_r.reserve(100);
    }
    SegTree(const vector<Type>& v) {
        this->n = v.size();
        dat.assign(n << 1, Monoid::id());
        for (int i = 0; i < n; i++) dat[i + n] = v[i];
        for (int i = n - 1; i > 0; i--) dat[i] = Monoid::op(dat[i << 1], dat[i << 1 | 1]);
        cand.reserve(100), cand_l.reserve(100), cand_r.reserve(100);
    }

    void set(int i, Type x) {
        i += n;
        dat[i] = x;
        while (i >>= 1) dat[i] = Monoid::op(dat[i << 1], dat[i << 1 | 1]);
    }
    Type fold(int l, int r) {
        Type retl = Monoid::id(), retr = Monoid::id();
        l += n, r += n;
        while (l < r) {
            if (l & 1) retl = Monoid::op(retl, dat[l++]);
            if (r & 1) retr = Monoid::op(dat[--r], retr);
            l >>= 1, r >>= 1;
        }
        return Monoid::op(retl, retr);
    }
    template <typename F>
    int find_right(int l, F f) {
        assert(f(Monoid::id()));
        if (l == n) return n;
        l += n;
        int r = n + n;
        cand_l.clear(), cand_r.clear();
        while (l < r) {
            if (l & 1) cand_l.push_back(l++);
            if (r & 1) cand_r.push_back(--r);
            l >>= 1, r >>= 1;
        }
        cand = cand_l;
        reverse(cand_r.begin(), cand_r.end());
        cand.insert(cand.end(), cand_r.begin(), cand_r.end());
        Type val = Monoid::id();
        for (int i : cand) {
            if (f(Monoid::op(val, dat[i]))) {
                val = Monoid::op(val, dat[i]);
            } else {
                while (i < n) {
                    i <<= 1;
                    if (f(Monoid::op(val, dat[i]))) {
                        val = Monoid::op(val, dat[i]);
                        i |= 1;
                    }
                }
                return i - n;
            }
        }
        return n;
    }
    template <typename F>
    int find_left(int r, F f) {
        assert(f(Monoid::id()));
        if (r == 0) return 0;
        r += n;
        int l = n;
        cand_l.clear(), cand_r.clear();
        while (l < r) {
            if (l & 1) cand_l.push_back(l++);
            if (r & 1) cand_r.push_back(--r);
            l >>= 1, r >>= 1;
        }
        cand = cand_r;
        reverse(cand_l.begin(), cand_l.end());
        cand.insert(cand.end(), cand_l.begin(), cand_l.end());
        Type val = Monoid::id();
        for (int i : cand) {
            if (f(Monoid::op(dat[i], val))) {
                val = Monoid::op(dat[i], val);
            } else {
                while (i < n) {
                    i = (i << 1) | 1;
                    if (f(Monoid::op(dat[i], val))) {
                        val = Monoid::op(dat[i], val);
                        i ^= 1;
                    }
                }
                return i - n + 1;
            }
        }
        return 0;
    }

    int size() { return n; }
    Type operator[](int i) { return dat[i + n]; }

private:
    int n;
    vector<Type> dat;
    vector<int> cand, cand_l, cand_r;
};

namespace Monoid {
    template <typename T, T max_value = INF>
    struct Min {
        using Type = T;
        static Type id() { return max_value; }
        static Type op(const Type& a, const Type& b) { return min(a, b); }
    };

    template <typename T, T min_value = -INF>
    struct Max {
        using Type = T;
        static Type id() { return min_value; }
        static Type op(const Type& a, const Type& b) { return max(a, b); }
    };

    template <typename T>
    struct Sum {
        using Type = T;
        static Type id() { return 0; }
        static Type op(const Type& a, const Type& b) { return a + b; }
    };

    template <typename T>
    struct SumPair {
        using Type = pair<T, int>;
        static Type id() { return make_pair(T(0), 0); }
        static Type op(const Type& a, const Type& b) { return {a.first + b.first, a.second + b.second}; }
    };
}  // namespace Monoid

namespace RangeQuery {
    template <typename T, T max_value = INF>
    struct Min {
        using Type = struct SegTree<Monoid::Min<T, max_value>>;
    };

    template <typename T, T min_value = -INF>
    struct Max {
        using Type = struct SegTree<Monoid::Max<T, min_value>>;
    };

    template <typename T>
    struct Sum {
        using Type = struct SegTree<Monoid::Sum<T>>;
    };
}  // namespace RangeQuery

struct Mn {
    using Type = bool;
    static Type op(Type l, Type r) { return l & r; }
    static Type id() { return true; }
};

int main() {
    ll N, X;
    cin >> N >> X;
    X--;
    vector<ll> A(N);
    for (int i = 0; i < N; i++) cin >> A[i];

    if (X < N) {
        cout << A[X] << endl;
        return 0;
    }

    const int mx = 5e5;
    auto seg = SegTree<Mn>(vector<bool>(mx, false));
    vector<int> cnt(mx);
    for (int i = 0; i < N; i++)
        if (A[i] < mx) cnt[A[i]]++, seg.set(A[i], true);

    set<int> st;
    for (int i = N; i < 5 * N; i++) {
        int mex = seg.find_right(0, [&](bool x) { return x; });
        if (X >= 5 * N && st.count(mex)) {
            vector<int> B;
            for (int j = N; j < i; j++) B.push_back(A[j]);
            X -= N, X %= ssize(B);
            cout << B[X] << endl;
            return 0;
        }
        if (i == X) {
            cout << mex << endl;
            return 0;
        }
        st.insert(mex);
        A.push_back(mex);
        ++cnt[mex];
        seg.set(mex, true);
        if (A[i - N] < mx && --cnt[A[i - N]] == 0) seg.set(A[i - N], false);
    }
}
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