#569398 (C++14) No.510 二次漸化式

• 問題: No.510 二次漸化式
• ユーザー: 🍮かんプリン
• 提出日時: 2020-10-21 20:12:07
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 669 ms / 3,000 ms
• コード長: 9,555 bytes
• コンパイル時間: 2,019 ms
• コンパイル使用メモリ: 191,352 KB
• 実行使用メモリ: 87,296 KB
• 最終ジャッジ日時: 2024-07-21 09:01:59
• 合計ジャッジ時間: 16,976 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

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

ソースコード

/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2020.10.21 20:12:00
**/

#include "bits/stdc++.h" 
using namespace std; 
typedef long long ll;

template< int MOD >
struct mint {
public:
    long long x;
    mint(long long x = 0) :x((x%MOD+MOD)%MOD) {}
    mint(std::string &s) {
        long long z = 0;
        for (int i = 0; i < s.size(); i++) {
            z *= 10;
            z += s[i] - '0';
            z %= MOD;
        }
        this->x = z;
    }
    mint& operator+=(const mint &a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator-=(const mint &a) {
        if ((x += MOD - a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator*=(const mint &a) {
        (x *= a.x) %= MOD;
        return *this;
    }
    mint& operator/=(const mint &a) {
        long long n = MOD - 2;
        mint u = 1, b = a;
        while (n > 0) {
            if (n & 1) {
                u *= b;
            }
            b *= b;
            n >>= 1;
        }
        return *this *= u;
    }
    mint operator+(const mint &a) const {
        mint res(*this);
        return res += a;
    }
    mint operator-() const {return mint() -= *this; }
    mint operator-(const mint &a) const {
        mint res(*this);
        return res -= a;
    }
    mint operator*(const mint &a) const {
        mint res(*this);
        return res *= a;
    }
    mint operator/(const mint &a) const {
        mint res(*this);
        return res /= a;
    }
    friend std::ostream& operator<<(std::ostream &os, const mint &n) {
        return os << n.x;
    }
    friend std::istream &operator>>(std::istream &is, mint &n) {
        long long x;
        is >> x;
        n = mint(x);
        return is;
    }
    bool operator==(const mint &a) const {
        return this->x == a.x;
    }
    bool operator!=(const mint &a) const {
        return this->x != a.x;
    }
    mint pow(long long k) const {
        mint ret = 1;
        mint p = this->x;
        while (k > 0) {
            if (k & 1) {
                ret *= p;
            }
            p *= p;
            k >>= 1;
        }
        return ret;
    }
};
constexpr int MOD = 1e9 + 7;
template< class T >
struct Matrix {
    std::vector< std::vector< T > > A;
    Matrix() {}
    Matrix(size_t n, size_t m) : A(n, std::vector< T >(m, 0)) {}
    Matrix(size_t n) : A(n, std::vector< T >(n, 0)) {};
    size_t height() const {
        return (A.size());
    }
    size_t width() const {
        return (A[0].size());
    }
    inline const std::vector< T > &operator[](int k) const {
        return (A.at(k));
    }
    inline std::vector< T > &operator[](int k) {
        return (A.at(k));
    }
    static Matrix I(size_t n) {
        Matrix mat(n);
        for (int i = 0; i < (int)n; i++) mat[i][i] = 1;
        return (mat);
    }
    Matrix &operator+=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                (*this)[i][j] += B[i][j];
        return (*this);
    }
    Matrix &operator-=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                (*this)[i][j] -= B[i][j];
        return (*this);
    }
    Matrix &operator*=(const Matrix &B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        std::vector< std::vector< T > > C(n, std::vector< T >(m, 0));
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                for (int k = 0; k < p; k++)
                    C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        A.swap(C);
        return (*this);
    }
    Matrix operator+(const Matrix &B) const {
        return (Matrix(*this) += B);
    }
    Matrix operator-(const Matrix &B) const {
        return (Matrix(*this) -= B);
    }
    Matrix operator*(const Matrix &B) const {
        return (Matrix(*this) *= B);
    }
    bool operator==(const Matrix &B) const {
        assert(this->A.size() == B.A.size() && this->A[0].size() == B.A[0].size());
        int n = this->A.size();
        int m = this->A[0].size();
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                if (this->A[i][j] != B.A[i][j]) return false;
        return true;
    }
    bool operator!=(const Matrix &B) const {
        return !(*this == B);
    }
    friend std::ostream &operator<<(std::ostream &os, Matrix &p) {
        size_t n = p.height(), m = p.width();
        for (int i = 0; i < n; i++) {
            os << "[";
            for (int j = 0; j < m; j++) {
                os << p[i][j] << (j + 1 == m ? "]\n" : ",");
            }
        }
        return (os);
    }
    
    T determinant() {
        Matrix B(*this);
        assert(width() == height());
        T ret = 1;
        for (int i = 0; i < width(); i++) {
            int idx = -1;
            for (int j = i; j < width(); j++) {
                if (B[j][i] != 0) idx = j;
            }
            if (idx == -1) return (0);
            if (i != idx) {
                ret *= -1;
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T vv = B[i][i];
            for (int j = 0; j < width(); j++) {
                B[i][j] /= vv;
            }
            for (int j = i + 1; j < width(); j++) {
                T a = B[j][i];
                for (int k = 0; k < width(); k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return (ret);
    }
    
    
    Matrix pow(ll k) const {
        auto res = I(A.size());
        auto M = *this;
        while (k > 0) {
            if (k & 1) {
                res *= M;
            }
            M *= M;
            k >>= 1;
        }
        return res;
    }
};

template < class Monoid >
struct SegmentTree {
private:
    using Func = std::function< Monoid(Monoid, Monoid) >;
    Func F;
    Monoid UNITY;
    int n;
    std::vector< Monoid > node;
    int _binary_search(int a, int b, const std::function<bool(Monoid)> &f, Monoid &s, int k = 0, int l = 0, int r = -1) {
        if (r < 0) r = n;
        if (r <= a || b <= l) return n;
        if (a <= l && r <= b && !f(F(s,node[k]))) {
            s = F(s,node[k]);
            return n;
        }
        if (l == r - 1) {s = F(s,node[k]); return l;}
        int ret = _binary_search(a, b, f, s, 2 * k + 1, l, (r - l) / 2 + l);
        return ret != n ? ret : _binary_search(a, b, f, s, 2 * k + 2, (r - l) / 2 + l, r);
    }
public:
    SegmentTree() {}
    SegmentTree(const std::vector< Monoid > &v, const Func f, const Monoid &unity) {
        F = f;
        UNITY = unity;
        int sz = v.size();
        n = 1;
        while (n < sz) n <<= 1;
        node.resize(n * 2 - 1, UNITY);
        for (int i = 0; i < sz; i++) node[i + n - 1] = v[i];
        build();
    }
    
    SegmentTree(int m, const Monoid &val, const Func f, const Monoid &unity) {
        F = f;
        UNITY = unity;
        n = 1;
        while (n < m) n <<= 1;
        node.resize(n * 2 - 1, UNITY);
        if (val != UNITY) {
            for (int i = 0; i < m; i++) node[i + n - 1] = val;
            build();
        }
    }
    
    void set(int k, const Monoid &x) {
        node[n + k - 1] = x;
    }
    void build() {
        for (int i = n - 2; i >= 0; i--) node[i] = F(node[2 * i + 1], node[2 * i + 2]);
    }
    void update_query(int x, const Monoid &val) {
        if (x >= n || x < 0) return;
        x += n - 1;
        node[x] = val;
        while (x > 0) {
            x = (x - 1) >> 1;
            node[x] = F(node[2 * x + 1], node[2 * x + 2]);
        }
    }
    
    Monoid get_query(int l, int r) {
        Monoid L = UNITY, R = UNITY;
        if (l < 0) l = 0;
        if (r < 0) return UNITY;
        if (l >= n) return UNITY;
        if (r >= n) r = n;
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if (l & 1) L = F(L, node[l++ - 1]);
            if (r & 1) R = F(node[--r - 1], R);
        }
        return F(L, R);
    }
    
    
    int binary_search(int l, int r, const std::function<bool(Monoid)> &f) {
        Monoid s = UNITY;
        int ret = _binary_search(l,r,f,s);
        return ret != n ? ret : -1;
    }
    Monoid operator[](int x) const {
        return node[n + x - 1];
    }
    int size() {
        return n;
    }
    void print() {
        for (int i = 0; i < n; i++) {
            std::cout << i << "\t: " << node[n + i - 1] << std::endl;
        }
    }
};
int main() {
    int n,q;cin >> n >> q;
    using M = Matrix<mint<MOD>>;
    M shoki(4);
    shoki[0][0] = 1;
    shoki[1][3] = 1;
    shoki[2][3] = 1;
    shoki[3][3] = 1;
    SegmentTree<M> seg(n,shoki,[](M a, M b){return b*a;},M::I(4));
    while(q--) {
        string c;cin >> c;
        if (c == "x") {
            int i,v;cin >> i >> v;
            M mat = seg[i];
            mat[0][1] = v;
            seg.update_query(i,mat);
        }
        else if (c == "y") {
            int i,v;cin >> i >> v;
            M mat = seg[i];
            mat[1][1] = mint<MOD>(v) * v;
            mat[1][2] = mint<MOD>(2) * v;
            mat[2][2] = v;
            seg.update_query(i,mat);
        }
        else {
            int i;cin >> i;
            M mat = seg.get_query(0,i);
            cout << mat[0][0] + mat[0][1] + mat[0][2] + mat[0][3] << endl;
        }
    }
    return 0;
}