結果

問題 No.1848 Long Prefixes
コンテスト
ユーザー rin204
提出日時 2024-05-05 17:01:35
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 41 ms / 2,000 ms
コード長 9,796 bytes
コンパイル時間 3,401 ms
コンパイル使用メモリ 258,608 KB
実行使用メモリ 14,504 KB
最終ジャッジ日時 2024-11-27 16:23:50
合計ジャッジ時間 6,540 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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ファイルパターン 結果
other AC * 40
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ソースコード

diff #
raw source code 

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

using ll = long long;

template <int MOD>
struct Modint {
    int x;
    Modint() : x(0) {}
    Modint(int64_t y) {
        if (y >= 0)
            x = y % MOD;
        else
            x = (y % MOD + MOD) % MOD;
    }

    Modint &operator+=(const Modint &p) {
        x += p.x;
        if (x >= MOD) x -= MOD;
        return *this;
    }

    Modint &operator-=(const Modint &p) {
        x -= p.x;
        if (x < 0) x += MOD;
        return *this;
    }

    Modint &operator*=(const Modint &p) {
        x = int(1LL * x * p.x % MOD);
        return *this;
    }

    Modint &operator/=(const Modint &p) {
        *this *= p.inverse();
        return *this;
    }

    Modint &operator%=(const Modint &p) {
        assert(p.x == 0);
        return *this;
    }

    Modint operator-() const {
        return Modint(-x);
    }

    Modint &operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }

    Modint &operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }

    Modint operator++(int) {
        Modint result = *this;
        ++*this;
        return result;
    }

    Modint operator--(int) {
        Modint result = *this;
        --*this;
        return result;
    }

    friend Modint operator+(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) += rhs;
    }

    friend Modint operator-(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) -= rhs;
    }

    friend Modint operator*(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) *= rhs;
    }

    friend Modint operator/(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) /= rhs;
    }

    friend Modint operator%(const Modint &lhs, const Modint &rhs) {
        assert(rhs.x == 0);
        return Modint(lhs);
    }

    bool operator==(const Modint &p) const {
        return x == p.x;
    }

    bool operator!=(const Modint &p) const {
        return x != p.x;
    }

    bool operator<(const Modint &rhs) const {
        return x < rhs.x;
    }

    bool operator<=(const Modint &rhs) const {
        return x <= rhs.x;
    }

    bool operator>(const Modint &rhs) const {
        return x > rhs.x;
    }

    bool operator>=(const Modint &rhs) const {
        return x >= rhs.x;
    }

    Modint inverse() const {
        int a = x, b = MOD, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            a -= t * b;
            u -= t * v;
            std::swap(a, b);
            std::swap(u, v);
        }
        return Modint(u);
    }

    Modint pow(int64_t k) const {
        Modint ret(1);
        Modint y(x);
        while (k > 0) {
            if (k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }

    friend std::ostream &operator<<(std::ostream &os, const Modint &p) {
        return os << p.x;
    }

    friend std::istream &operator>>(std::istream &is, Modint &p) {
        int64_t y;
        is >> y;
        p = Modint<MOD>(y);
        return (is);
    }

    static int get_mod() {
        return MOD;
    }
};

struct Arbitrary_Modint {
    int x;
    static int MOD;

    static void set_mod(int mod) {
        MOD = mod;
    }

    Arbitrary_Modint() : x(0) {}
    Arbitrary_Modint(int64_t y) {
        if (y >= 0)
            x = y % MOD;
        else
            x = (y % MOD + MOD) % MOD;
    }

    Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {
        x += p.x;
        if (x >= MOD) x -= MOD;
        return *this;
    }

    Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {
        x -= p.x;
        if (x < 0) x += MOD;
        return *this;
    }

    Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {
        x = int(1LL * x * p.x % MOD);
        return *this;
    }

    Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {
        *this *= p.inverse();
        return *this;
    }

    Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {
        assert(p.x == 0);
        return *this;
    }

    Arbitrary_Modint operator-() const {
        return Arbitrary_Modint(-x);
    }

    Arbitrary_Modint &operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }

    Arbitrary_Modint &operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }

    Arbitrary_Modint operator++(int) {
        Arbitrary_Modint result = *this;
        ++*this;
        return result;
    }

    Arbitrary_Modint operator--(int) {
        Arbitrary_Modint result = *this;
        --*this;
        return result;
    }

    friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) += rhs;
    }

    friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) -= rhs;
    }

    friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) *= rhs;
    }

    friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) /= rhs;
    }

    friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        assert(rhs.x == 0);
        return Arbitrary_Modint(lhs);
    }

    bool operator==(const Arbitrary_Modint &p) const {
        return x == p.x;
    }

    bool operator!=(const Arbitrary_Modint &p) const {
        return x != p.x;
    }

    bool operator<(const Arbitrary_Modint &rhs) {
        return x < rhs.x;
    }

    bool operator<=(const Arbitrary_Modint &rhs) {
        return x <= rhs.x;
    }

    bool operator>(const Arbitrary_Modint &rhs) {
        return x > rhs.x;
    }

    bool operator>=(const Arbitrary_Modint &rhs) {
        return x >= rhs.x;
    }

    Arbitrary_Modint inverse() const {
        int a = x, b = MOD, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            a -= t * b;
            u -= t * v;
            std::swap(a, b);
            std::swap(u, v);
        }
        return Arbitrary_Modint(u);
    }

    Arbitrary_Modint pow(int64_t k) const {
        Arbitrary_Modint ret(1);
        Arbitrary_Modint y(x);
        while (k > 0) {
            if (k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }

    friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) {
        return os << p.x;
    }

    friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) {
        int64_t y;
        is >> y;
        p = Arbitrary_Modint(y);
        return (is);
    }

    static int get_mod() {
        return MOD;
    }
};
int Arbitrary_Modint::MOD = 998244353;

using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint  = Arbitrary_Modint;

std::vector<int> Z_algorithm(const std::string &S) {
    int n = S.size();
    std::vector<int> Z(n);
    Z[0]  = n;
    int i = 1;
    int j = 0;
    while (i < n) {
        while (i + j < n && S[j] == S[i + j]) j++;
        Z[i] = j;
        if (j == 0) {
            i++;
            continue;
        }
        int k = 1;
        while (i + k < n && k + Z[k] < j) {
            Z[i + k] = Z[k];
            k++;
        }
        i += k;
        j -= k;
    }
    return Z;
}

template <typename T>
std::vector<int> Z_algorithm(const std::vector<T> &S) {
    int n = S.size();
    std::vector<int> Z(n);
    Z[0]  = n;
    int i = 1;
    int j = 0;
    while (i < n) {
        while (i + j < n && S[j] == S[i + j]) j++;
        Z[i] = j;
        if (j == 0) {
            i++;
            continue;
        }
        int k = 1;
        while (i + k < n && k + Z[k] < j) {
            Z[i + k] = Z[k];
            k++;
        }
        i += k;
        j -= k;
    }
    return Z;
}
using mint = modint1;

void solve() {
    int n;
    cin >> n;
    vector<ll> A(n);
    for (auto &a : A) cin >> a;
    string S;
    cin >> S;
    mint ans = 0;

    vector<pair<long long, char>> B;
    char b        = S[0];
    long long row = 0;
    for (int i = 0; i < n; i++) {
        if (b == S[i]) {
            row += A[i];
        } else {
            B.emplace_back(row, b);
            b   = S[i];
            row = A[i];
        }
    }
    B.emplace_back(row, b);

    n = B.size();
    if (n == 1) {
        mint ans = B[0].first * (B[0].first + 1) / 2;
        cout << ans << endl;
        return;
    }
    vector<ll> cum(n + 1, 0);
    for (int i = 0; i < n; i++) {
        cum[i + 1] = cum[i] + B[i].first;
    }

    auto Z = Z_algorithm(B);

    auto B2 = B;
    B2.erase(B2.begin());
    auto Z2 = Z_algorithm(B2);

    for (int i = 0; i < n; i++) {
        int z = Z[i];
        ans += cum[i + z] - cum[i];
        if (i + z < n and B[z].second == B[i + z].second) {
            ans += min(B[z].first, B[i + z].first);
        }
        if (B[0].second == B[i].second) {
            ll x = B[0].first;
            ll y = B[i].first - 1;
            if (x < y) {
                ans += x * (y - x);
                y = x;
            }
            ans += y * (y + 1) / 2;

            if (B[0].first < B[i].first) {
                ll z     = Z2[i];
                mint tmp = cum[i + 1 + z] - cum[i + 1];
                if (B[z + 1].second == B[i + z + 1].second) {
                    tmp += min(B[z + 1].first, B[i + z + 1].first);
                }
                ans += tmp;
            }
        }
        // cout << i << " " << ans << endl;
    }

    cout << ans << endl;
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    cout << fixed << setprecision(12);
    int t;
    t = 1;
    // cin >> t;
    while (t--) solve();
    return 0;
}
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