#746810 (C++17) No.1879 How many matchings?

• 問題: No.1879 How many matchings?
• ユーザー: milanis48663220
• 提出日時: 2022-03-18 22:27:08
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 5,329 bytes
• コンパイル時間: 1,288 ms
• コンパイル使用メモリ: 121,084 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-04-14 10:20:31
• 合計ジャッジ時間: 2,115 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,816 KB
testcase_01	AC	2 ms; 6,940 KB
testcase_02	AC	2 ms; 6,944 KB
testcase_03	AC	2 ms; 6,940 KB
testcase_04	AC	2 ms; 6,944 KB
testcase_05	AC	2 ms; 6,944 KB
testcase_06	AC	2 ms; 6,944 KB
testcase_07	AC	2 ms; 6,940 KB
testcase_08	AC	2 ms; 6,940 KB
testcase_09	AC	2 ms; 6,944 KB
testcase_10	AC	2 ms; 6,944 KB
testcase_11	AC	2 ms; 6,940 KB
testcase_12	AC	2 ms; 6,944 KB
testcase_13	AC	2 ms; 6,940 KB
testcase_14	AC	2 ms; 6,940 KB

ソースコード

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using namespace std;
typedef long long ll;

template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
    return vector<vector<T>>(n, vector<T>(m, v));
}

template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}

template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
    if(v.empty()) {
        cout << endl;
        return;
    }
    for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << endl;
}

const ll MOD = 1000000007;

class ModInt{
    public:
    ll v;
    ModInt(ll _v = 0){
        if(_v < 0) _v = (_v%MOD)+MOD;
        if(_v >= MOD) _v %= MOD;
        v = _v;
    }
    ModInt operator+(ll n){
        return ModInt((v+n)%MOD);
    }
    ModInt operator-(ll n){
        return ModInt((v-n+MOD)%MOD);
    }
    ModInt operator*(ll n){
        if(n >= MOD) n %= MOD;
        return ModInt((v*n)%MOD);
    }
    ModInt operator/(ll n){
        return ModInt((ModInt(n).inv()*v).v%MOD);
    }

    ModInt &operator+=(ll n){
        v = (v+n)%MOD;
        return *this;
    }
    ModInt &operator-=(ll n){
        v = (v-n+MOD)%MOD;
        return *this;
    }
    ModInt &operator*=(ll n){
        v = (v*n+MOD)%MOD;
        return *this;
    }
    
    
    ModInt operator+(ModInt n){
        return ModInt((v+n.v)%MOD);
    }
    ModInt operator-(ModInt n){
        return ModInt((v-n.v+MOD)%MOD);
    }
    ModInt operator*(ModInt n){
        return ModInt((v*n.v)%MOD);
    }
    ModInt operator/(ModInt n){
        return ModInt((n.inv()*v).v%MOD);
    }

    ModInt &operator+=(ModInt n){
        v = (v+n.v)%MOD;
        return *this;
    }
    ModInt &operator-=(ModInt n){
        v = (v-n.v+MOD)%MOD;
        return *this;
    }
    ModInt &operator*=(ModInt n){
        v = (v*n.v)%MOD;
        return *this;
    }

    bool operator==(ModInt n){
        return v == n.v;
    }
    bool operator!=(ModInt n){
        return v != n.v;
    }
    ModInt &operator=(ll n){
        v = n%MOD;
        return *this;
    }

    ModInt inv(){
        if(v == 1) return ModInt(1);
        else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
    }
};

ostream& operator<<(ostream& os, const ModInt& m){
    os << m.v;
    return os;
}

istream & operator >> (istream &in,  ModInt &m){
    in >> m.v;
    return in;
}

ModInt pow(ModInt a, ll n) {
    assert(n >= 0);
	ModInt ans = 1;
    while (n > 0) {
        if (n&1) ans = ans*a;
        a = a*a;
        n >>= 1;
    }
	return ans;
}

using mint = ModInt;


template<typename T, int N, int M>
class Matrix {
    public:
    array<array<T, M>, N> dat;
    Matrix(T val) {
        for(int i = 0; i < N; i++){
            for(int j = 0; j < M; j++){
                dat[i][j] = val;
            }
        }
    }

    Matrix(array<array<T, M>, N> dat): dat(dat){  }
    array<T, M>& operator[](int x) {
        return dat[x];
	}
};

template<typename T, int N, int M, int K>
Matrix<T, N, K> operator*(Matrix<T, N, M> a, Matrix<T, M, K> b){
    Matrix<T, N, K> c(T(0));
    for(int i = 0; i < N; i++){
        for(int j = 0; j < K; j++){
            for(int k = 0; k < M; k++){
                c.dat[i][j] += a.dat[i][k]*b.dat[k][j];
            }
        }
    }
    return c;
}

template<typename T, int N>
Matrix<T, N, N> operator^(Matrix<T, N, N> m, long long r){
    Matrix<T, N, N> ans(T(0));
    for(int i = 0; i < N; i++) ans[i][i] = T(1);
    while (r > 0) {
        if (r&1) ans = (ans*m);
        m = (m*m);
        r >>= 1;
    }
    return ans;
}

template <typename T, int N, int M>
void print_mat(Matrix<T, N, M> a){
    for(int i = 0; i < N; i++){
        for(int j = 0; j < M; j++){
            cout << a.dat[i][j] << ' ';
        }
        cout << endl;
    }
}

template <typename T, int N, int M>
ostream& operator<<(ostream& os, const Matrix<T, N, M>& m){
    print_mat<T, N, M>(m);
    return os;
}

mint fib_kth(ll k){
    Matrix<mint, 2, 2> A(mint(0));
    Matrix<mint, 2, 1> a(mint(0));
    a[0][0] = 0;
    a[1][0] = 1;
    A[0][1] = 1;
    A[1][0] = 1; A[1][1] = 1;
    auto u = (A^k)*a;
    return u[0][0];
}

void test(int n){
    mint sum = 0;
    for(int i = 0; i <= n; i++){
        sum += fib_kth(i)*fib_kth(n-i);
    }
    cout << sum << endl;
    cout << (fib_kth(n+1)*n-fib_kth(n)+fib_kth(n-1)*n)/5 << endl;
}

mint calc(ll n){
    return (fib_kth(n+1)*mint(n)-fib_kth(n)+fib_kth(n-1)*mint(n))/5;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    ll n; cin >> n;
    if(n%2 == 0){
        cout << fib_kth(n/2+1) << endl;
    }else{
        cout << calc(n/2+2)+calc(n/2+1) << endl;
    }
}