test/aoj0399.test.cpp

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• Last update: 2021-06-21 15:24:20+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0399

Depends on

• math/squarematrix.cpp
• modint(固定MOD) (util/modint.cpp)

Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0399"
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

#include "../util/modint.cpp"

#include "../math/squarematrix.cpp"

struct SemiRing {
    using T = mint;
    static inline T mul(T x, T y){ return x * y; }
    static inline void add(T &x, T y){ x += y; }
    static inline T one(){ return 1; }
    static inline T zero(){ return 0; }
};

using ar = array<SemiRing::T, 101>;
using mat = SquareMatrix<SemiRing, 101>;

ar x;
mat A;
int main() {
    int n, m; ll d;
    cin >> n >> m >> d;
    vector<int> s(n), t(n), f(m);
    for (auto &&i : s) scanf("%d", &i);
    for (auto &&i : t) scanf("%d", &i);
    for (auto &&i : f) scanf("%d", &i);
    A[0][0] = 1;
    for (int i = 0; i < n; ++i) x[i+1] = s[i], A[i+1][0] = t[i], A[i+1][(i+n-1)%n+1] = 1;
    for (int i = 0; i < m; ++i) x[n+i+1] = f[i],  A[n+i+1][(i+m-1)%m+n+1] = 1;
    A[n+1][n] = 1;
    A = A.pow(d);
    cout << (x*A)[0].val << "\n";
    return 0;
}

#line 1 "test/aoj0399.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0399"
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

#line 1 "util/modint.cpp"
template <uint M>
struct modint {
    uint val;
public:
    static modint raw(int v) { modint x; x.val = v; return x; }
    modint() : val(0) {}
    template <class T>
    modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = uint(x); }
    modint(bool v) { val = ((unsigned int)(v) % M); }
    modint& operator++() { val++; if (val == M) val = 0; return *this; }
    modint& operator--() { if (val == 0) val = M; val--; return *this; }
    modint operator++(int) { modint result = *this; ++*this; return result; }
    modint operator--(int) { modint result = *this; --*this; return result; }
    modint& operator+=(const modint& b) { val += b.val; if (val >= M) val -= M; return *this; }
    modint& operator-=(const modint& b) { val -= b.val; if (val >= M) val += M; return *this; }
    modint& operator*=(const modint& b) { ull z = val; z *= b.val; val = (uint)(z % M); return *this; }
    modint& operator/=(const modint& b) { return *this = *this * b.inv(); }
    modint operator+() const { return *this; }
    modint operator-() const { return modint() - *this; }
    modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; }
    modint inv() const { return pow(M-2); }
    friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; }
    friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; }
    friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; }
    friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; }
    friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; }
    friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; }
};
using mint = modint<MOD>;

/**
 * @brief modint(固定MOD)
 * @docs _md/modint.md
 */
#line 21 "test/aoj0399.test.cpp"

#line 1 "math/squarematrix.cpp"
template<class H, size_t SIZE>
struct SquareMatrix {
    using T = typename H::T;
    using ar = array<T, SIZE>;
    using mat = array<ar, SIZE>;
    mat A;
    SquareMatrix() {
        for (int i = 0; i < SIZE; ++i) {
            for (int j = 0; j < SIZE; ++j) {
                A[i][j] = H::zero();
            }
        }
    }
    static SquareMatrix I(){
        SquareMatrix X;
        for (int i = 0; i < SIZE; ++i) {
            for (int j = 0; j < SIZE; ++j) {
                if(i == j) X[i][j] = H::one();
                else X[i][j] = H::zero();
            }
        }
        return X;
    }

    friend ar operator*=(ar &x, const SquareMatrix &Y) {
        ar ans;
        fill(begin(ans), end(ans), mint(0));
        for (int i = 0; i < SIZE; ++i) {
            for (int j = 0; j < SIZE; ++j) {
                H::add(ans[j], H::mul(x[i], Y[i][j]));
            }
        }
        x.swap(ans);
        return x;
    }
    friend ar operator*(ar x, const SquareMatrix &Y) { return x *= Y; }

    inline const ar &operator[](int k) const{ return (A.at(k)); }
    inline ar &operator[](int k) { return (A.at(k)); }
    SquareMatrix &operator+= (const SquareMatrix &B){
        for (int i = 0; i < SIZE; ++i) {
            for (int j = 0; j < SIZE; ++j) {
                H::add((*this)[i][j], B[i][j]);
            }
        }
        return (*this);
    }

    SquareMatrix &operator-= (const SquareMatrix &B){
        for (int i = 0; i < SIZE; ++i) {
            for (int j = 0; j < SIZE; ++j) {
                H::add((*this)[i][j], -B[i][j]);
            }
        }
        return (*this);
    }

    SquareMatrix &operator*=(const SquareMatrix &B) {
        SquareMatrix C{};
        for (int i = 0; i < SIZE; ++i) {
            for (int k = 0; k < SIZE; ++k) {
                for (int j = 0; j < SIZE; ++j) {
                    H::add(C[i][j],  H::mul((*this)[i][k], B[k][j]));
                }
            }
        }
        A.swap(C.A);
        return (*this);
    }

    SquareMatrix pow(ll n) const {
        SquareMatrix a = (*this), res = I();

        while(n > 0){
            if(n & 1) res *= a;
            a *= a;
            n >>= 1;
        }
        return res;
    }
    SquareMatrix operator+(const SquareMatrix &B) const {return SquareMatrix(*this) += B;}
    SquareMatrix operator-(const SquareMatrix &B) const {return SquareMatrix(*this) -= B;}
    SquareMatrix operator*(const SquareMatrix &B) const {return SquareMatrix(*this) *= B;}
};
#line 23 "test/aoj0399.test.cpp"

struct SemiRing {
    using T = mint;
    static inline T mul(T x, T y){ return x * y; }
    static inline void add(T &x, T y){ x += y; }
    static inline T one(){ return 1; }
    static inline T zero(){ return 0; }
};

using ar = array<SemiRing::T, 101>;
using mat = SquareMatrix<SemiRing, 101>;

ar x;
mat A;
int main() {
    int n, m; ll d;
    cin >> n >> m >> d;
    vector<int> s(n), t(n), f(m);
    for (auto &&i : s) scanf("%d", &i);
    for (auto &&i : t) scanf("%d", &i);
    for (auto &&i : f) scanf("%d", &i);
    A[0][0] = 1;
    for (int i = 0; i < n; ++i) x[i+1] = s[i], A[i+1][0] = t[i], A[i+1][(i+n-1)%n+1] = 1;
    for (int i = 0; i < m; ++i) x[n+i+1] = f[i],  A[n+i+1][(i+m-1)%m+n+1] = 1;
    A[n+1][n] = 1;
    A = A.pow(d);
    cout << (x*A)[0].val << "\n";
    return 0;
}

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