洛谷 [P1939] 矩阵加速数列

矩阵快速幂模版

#include <iostream>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <cstdio>
#include <cmath>
#define ll long long
using namespace std;
const int MOD = (int) 1e9+7;
struct Matrix {
	static const int MAXN = 3;
	ll num[MAXN][MAXN], col, row;
	void clear() {
		memset(num, 0, sizeof(num));
		col = row = 0;
	}
	void unit() {
		col = row = 3;
		for(int i = 0; i < MAXN; i++) num[i][i] = 1;
	}
	void build(){
		col = row = 3;
		num[1][0] = num[2][1] = num[0][2] = num[2][2] = 1;
	}
};
Matrix operator * (const Matrix & a, const Matrix & b){
	Matrix res;
	res.clear();
	for(int i = 0; i < 3; i++) {
		for(int j = 0; j < 3; j++) {
			for(int k = 0; k < 3; k++) {
				(res.num[i][j] += a.num[i][k] * b.num[k][j]) %= MOD;
			}
		}
	}
	return res;
}
Matrix operator ^ (Matrix a, ll k) {
	Matrix res;
	res.clear(); res.unit();
	while(k) {
		if(k & 1ll) res = res * a;
		a = a * a;
		k >>= 1;
	}
	return res;
}
ll T, n;
int main() {
	cin>>T;
	while(T--) {
		cin>>n;
		if(n <= 3) {cout<<1<<endl;continue;}
		n -= 3;
		Matrix a;
		a.clear(); a.build();
		a = a ^ n;
		ll ans = 0;
		for(int i = 0; i < 3; i++)  ans += a.num[i][2];
		ans %= MOD;
		cout<<ans<<endl;
	}
	return 0;
}