結果

問題 No.720 行列のできるフィボナッチ数列道場 (2)
ユーザー algon_320algon_320
提出日時 2018-07-28 04:13:28
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,030 bytes
コンパイル時間 2,112 ms
コンパイル使用メモリ 181,876 KB
実行使用メモリ 4,384 KB
最終ジャッジ日時 2023-09-19 05:57:21
合計ジャッジ時間 3,057 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge14
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,376 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 1 ms
4,376 KB
testcase_03 AC 2 ms
4,376 KB
testcase_04 AC 1 ms
4,376 KB
testcase_05 AC 2 ms
4,380 KB
testcase_06 AC 1 ms
4,376 KB
testcase_07 AC 2 ms
4,376 KB
testcase_08 AC 1 ms
4,380 KB
testcase_09 AC 1 ms
4,376 KB
testcase_10 AC 2 ms
4,376 KB
testcase_11 AC 2 ms
4,376 KB
testcase_12 AC 1 ms
4,380 KB
testcase_13 AC 2 ms
4,376 KB
testcase_14 AC 2 ms
4,384 KB
testcase_15 AC 1 ms
4,380 KB
testcase_16 AC 2 ms
4,376 KB
testcase_17 AC 1 ms
4,384 KB
testcase_18 AC 2 ms
4,380 KB
testcase_19 AC 1 ms
4,380 KB
testcase_20 AC 2 ms
4,376 KB
testcase_21 AC 2 ms
4,376 KB
testcase_22 AC 2 ms
4,380 KB
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>
using namespace std;
#define int long long
using ll=long long;
using vi=vector<int>;
using pii=pair<int,int>;
#define ALL(c) begin(c),end(c)
#define RALL(c) rbegin(c),rend(c)
#define ITR(i,b,e) for(auto i=(b);i!=(e);++i)
#define FORE(x,c) for(auto &x:c)
#define REPF(i,a,n) for(int i=a,i##len=(int)(n);i<i##len;++i)
#define REP(i,n) REPF(i,0,n)
#define REPR(i,n) for(int i=(int)(n);i>=0;--i)
#define SZ(c) ((int)c.size())
#define CONTAIN(c,x) (c.find(x)!=end(c))
#define OUTOFRANGE(y,x,h,w) ((y)<0||(x)<0||(y)>=(h)||(x)>=(w))
#define dump(...)
#define pb push_back
const signed INF_=1001001001; const long long INF=1001001001001001001LL;
const int DX[9]={0,1,0,-1,1,1,-1,-1,0},DY[9]={-1,0,1,0,-1,1,1,-1,0};
template<class T> ostream& operator<<(ostream &os,const vector<T> &v) {
    ITR(i,begin(v),end(v))os<<*i<<(i==end(v)-1?"":" ");return os;}
template<class T> istream& operator>>(istream &is,vector<T> &v) {
    ITR(i,begin(v),end(v)) is>>*i;return is;}
template<class T,class U> istream& operator>>(istream &is, pair<T,U> &p) {
    is>>p.first>>p.second;return is;}
template<class T, class U> bool chmax(T &a,const U &b){return a<b?a=b,1:0;}
template<class T, class U> bool chmin(T &a,const U &b){return a>b?a=b,1:0;}
template<class T> using heap=priority_queue<T,vector<T>,greater<T>>;
struct before_main_function {
    before_main_function() {
        cin.tie(0); ios::sync_with_stdio(false);
        cout << setprecision(15) << fixed;
        #define endl "\n"
    }
} before_main_function;
//------------------8<------------------------------------8<--------------------

template<typename T>
void resize_matrix(vector<vector<T>> &A, int h, int w, T fill) {
    A.resize(h);
    for (int i = 0; i < h; i++) {
        A[i].resize(w, fill);
    }
}
template<typename T>
vector<vector<T>> multiple_matrix(vector<vector<T>> &A, vector<vector<T>> &B,
  function<T(T, T)> add = [](T a, T b){return a + b;},
  function<T(T, T)> mul = [](T a, T b){return a * b;},
  T zero = 0) {
    int m = A.size();
    int n = A[0].size();
    assert(n == B.size());
    int l = B[0].size();
    vector<vector<T>> res;
    resize_matrix(res, m, l, zero);
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < l; j++) {
            T tmp = zero;
            for (int k = 0; k < n; k++) {
                T p = mul(A[i][k], B[k][j]);
                tmp = add(tmp, p);
            }
            res[i][j] = tmp;
        }
    }
    return res;
}
template <typename T>
vector<vector<T>> pow_matrix(vector<vector<T>> A, int k,
  function<T(T, T)> add = [](T a, T b){return a + b;},
  function<T(T, T)> mul = [](T a, T b){return a * b;},
  T e = 1, T zero = 0) {
    int n = A.size();
    assert(n == A[0].size());

    vector<vector<T>> res;
    resize_matrix(res, n, n, zero);
    for (int i = 0; i < n; i++) res[i][i] = e;
    while (k > 0) {
        if (k & 1) res = multiple_matrix(res, A, add, mul, zero);
        A = multiple_matrix(A, A, add, mul, zero);
        k >>= 1;
    }
    return res;
}

template <int mod = 1000000007>
class ModInt {
public:
    ModInt() : v(0) {}
    ModInt(int x) : v((x+mod)%mod) {}
    int value() const {return v;}
    const ModInt operator+(const ModInt &r) const { return ModInt(this->v + r.v); }
    const ModInt operator-(const ModInt &r) const { return ModInt(this->v + mod - r.v); }
    const ModInt operator*(const ModInt &r) const { return ModInt(this->v * r.v); }
    const ModInt operator/(const ModInt &r) const { return (*this * (~r)); }
    const ModInt operator~() const { return ModInt(bpow(this->v, mod-2)); }
    bool operator==(const ModInt &r) const { return this->v == r.v; }
    bool operator!=(const ModInt &r) const { return this->v != r.v; }
    ModInt& operator+=(const ModInt &r) { return *this = *this + r; }
    ModInt& operator-=(const ModInt &r) { return *this = *this - r; }
    ModInt& operator*=(const ModInt &r) { return *this = *this * r; }
    ModInt& operator/=(const ModInt &r) { return *this = *this * (~r); }
private:
    int v;
    int bpow(int a, int b) const {
        int ret = 1;
        while (b > 0) {
            if (b & 1) ret = (ret * a) % mod;
            a = (a * a) % mod;
            b >>= 1;
        }
        return ret;
    }
};
using Mint = ModInt<>;

signed main() {
    int N, M;
    cin >> N >> M;
    vector<vector<Mint>> A = {{0, 1}, {1, 1}};
    A = pow_matrix(A, M);
    vector<vector<Mint>> B = {
        {A[0][0], A[0][1], 0},
        {A[1][0], A[1][1], 0},
        {A[1][0], A[1][1], 1},
    };
    B = pow_matrix(B, N - 1);

    auto fib = [](int n) {
        if (n == 1 || n == 2) return Mint(1);
        vector<vector<Mint>> A = {{0, 1}, {1, 1}};
        auto B = pow_matrix(A, n - 2);
        vector<vector<Mint>> v = {{1}, {1}};
        v = multiple_matrix(B, v);
        return v[1][0];
    };

    Mint fib_m_1 = fib(M - 1), fib_m = fib(M);
    vector<vector<Mint>> v = {
        {fib_m_1}, {fib_m}, {fib_m}
    };
    v = multiple_matrix(B, v);
    cout << v[2][0].value() << endl;
    return 0;
}
0