#869847 (C++14) No.510 二次漸化式

• 問題: No.510 二次漸化式
• ユーザー: t98slider
• 提出日時: 2023-05-17 01:04:39
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 99 ms / 3,000 ms
• コード長: 8,649 bytes
• コンパイル時間: 2,298 ms
• コンパイル使用メモリ: 180,576 KB
• 実行使用メモリ: 25,856 KB
• 最終ジャッジ日時: 2024-12-14 22:24:35
• 合計ジャッジ時間: 7,130 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
sample	AC * 2
other	AC * 34

ソースコード

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

template<const unsigned int MOD> struct prime_modint {
    using mint = prime_modint;
    unsigned int v;
    prime_modint() : v(0) {}
    prime_modint(unsigned int a) { a %= MOD; v = a; }
    prime_modint(unsigned long long a) { a %= MOD; v = a; }
    prime_modint(int a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
    prime_modint(long long a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
    static constexpr int mod() { return MOD; }
    mint& operator++() {v++; if(v == MOD)v = 0; return *this;}
    mint& operator--() {if(v == 0)v = MOD; v--; return *this;}
    mint operator++(int) { mint result = *this; ++*this; return result; }
    mint operator--(int) { mint result = *this; --*this; return result; }
    mint& operator+=(const mint& rhs) { v += rhs.v; if(v >= MOD) v -= MOD; return *this; }
    mint& operator-=(const mint& rhs) { if(v < rhs.v) v += MOD; v -= rhs.v; return *this; }
    mint& operator*=(const mint& rhs) {
        v = (unsigned int)((unsigned long long)(v) * rhs.v % MOD);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint r = 1, x = *this;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const { assert(v); return pow(MOD - 2); }
    friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint& lhs, const mint& rhs) { return (lhs.v == rhs.v); }
    friend bool operator!=(const mint& lhs, const mint& rhs) { return (lhs.v != rhs.v); }
    friend std::ostream& operator << (std::ostream &os, const mint& rhs) noexcept { return os << rhs.v; }
};
using mint = prime_modint<1000000007>;
//using mint = prime_modint<998244353>;

template <class T, size_t N> struct Matrix {
    std::array<std::array<T, N>, N> A{};
    Matrix() {}
    Matrix(const std::array<std::array<T, N>, N> &M) : A(M){}
    Matrix(const std::vector<std::vector<T>> &M)  {
        for(size_t i = 0; i < N; i++){
            for(size_t j = 0; j < N; j++){
                A[i][j] = M[i][j];
            }
        }
    }
    const std::array<T, N>& operator[](int i) const { return A[i]; }
    std::array<T, N>& operator[](int i) { return A[i]; }

    Matrix& operator+=(const Matrix& rhs) {
        for(size_t i = 0; i < N; i++){
            for(size_t j = 0; j < N; j++){
                A[i][j] += rhs[i][j];
            }
        }
        return *this;
    }
    Matrix& operator-=(const Matrix& rhs) {
        for(size_t i = 0; i < N; i++){
            for(size_t j = 0; j < N; j++){
                A[i][j] -= rhs[i][j];
            }
        }
        return *this;
    }
    Matrix& operator*=(const Matrix& rhs) {
        std::array<std::array<T, N>, N> res{};
        for(size_t i = 0; i < N; i++){
            for(size_t j = 0; j < N; j++){
                for(size_t k = 0; k < N; k++){
                    res[i][j] += A[i][k] * rhs[k][j];
                }
            }
        }
        swap(A, res);
        return *this;
    }
    Matrix& operator+() const { return *this; }
    Matrix& operator-() const { return Matrix() - *this; }
    friend Matrix operator+(const Matrix& lhs, const Matrix& rhs) {
        return Matrix(lhs) += rhs;
    }
    friend Matrix operator-(const Matrix& lhs, const Matrix& rhs) {
        return Matrix(lhs) -= rhs;
    }
    friend Matrix operator*(const Matrix& lhs, const Matrix& rhs) {
        return Matrix(lhs) *= rhs;
    }
    friend bool operator==(const Matrix& lhs, const Matrix& rhs) {
        return (lhs.A == rhs.A);
    }
    friend bool operator!=(const Matrix& lhs, const Matrix& rhs) {
        return (lhs.A != rhs.A);
    }
    Matrix pow(long long v){
        Matrix res, temp = A;
        for(size_t i = 0; i < N; i++)res[i][i] = 1;
        while(v){
            if(v & 1)res *= temp;
            temp *= temp;
            v >>= 1;
        }
        return res;
    }
    friend std::ostream& operator << (std::ostream &os, const Matrix& rhs) noexcept {
        for(size_t i = 0; i < N; i++){
            if(i) os << '\n';
            for(size_t j = 0; j < N; j++){
                os << (j ? " " : "") << rhs[i][j];
            }
        }
        return os;
    }
};

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
    public:
    segtree() : segtree(0) {}
    segtree(int n) : segtree(std::vector<S>(n, e())) {}
    segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        return d[p + size];
    }
    const S operator[](int p) const { return get(p); }
    S operator[](int p) { return get(p); }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    private:
    int _n, size, log;
    std::vector<S> d;
    int ceil_pow2(int n) {
        int x = 0;
        while ((1U << x) < (unsigned int)(n)) x++;
        return x;
    }
    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

using S = Matrix<mint, 4>;
S op(S lhs, S rhs){return lhs * rhs;}
S e(){
    S a{};
    a[0][0] = a[1][1] = a[2][2] = a[3][3] = 1;
    return a;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, Q, i, v;
    char c;
    cin >> n >> Q;
    S Mt{{{1,0,0,0},{0,0,0,0},{0,0,0,0},{0,1,1,1}}};
    segtree<S, op, e> seg(vector<S>(n, Mt));
    while(Q--){
        cin >> c >> i;
        if(c == 'a'){
            auto temp = seg.prod(0, i);
            mint ans;
            for(int i = 0; i < 4; i++) ans += temp[i][0];
            cout << ans << '\n';
        }else if(c == 'x'){
            cin >> v;
            auto temp = seg.get(i);
            temp[1][0] = v;
            seg.set(i, temp);
        }else{
            cin >> v;
            auto temp = seg.get(i);
            temp[1][1] = mint(v) * v;
            temp[2][1] = 2 * v;
            temp[2][2] = v;
            seg.set(i, temp);
        }
    }
}