【LOJ】#3086. 「GXOI / GZOI2019」逼死强迫症

LOJ#3086. 「GXOI / GZOI2019」逼死强迫症

这个就是设状态为(S,j)表示轮廓线为(S)，然后用的1×1个数为j

列出矩阵转移

这样会算重两个边相邻的，只要算出斐波那契数然后乘上N就是不合法的方案

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
#define pb push_back
#define space putchar(' ')
#define enter putchar('
')
#define eps 1e-10
#define MAXN 100005
#define ba 47
//#define ivorysi
using namespace std;
typedef long long int64;
typedef unsigned int u32;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;T f = 1;char c = getchar();
    while(c < '0' || c > '9') {
	if(c == '-') f = -1;
	c = getchar();
    }
    while(c >= '0' && c <= '9') {
	res = res * 10 +c - '0';
	c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) {
	out(x / 10);
    }
    putchar('0' + x % 10);
}
int N;
const int MOD = 1000000007;
int inc(int a,int b) {
    return a + b >= MOD ? a + b - MOD : a + b;
}
int mul(int a,int b) {
    return 1LL * a * b % MOD;
}
void update(int &x,int y) {
    x = inc(x,y);
}
int getid(int x,int y) {
    return y * 4 + x;
}
template<int T> 
struct Matrix {
    int f[T][T];
    Matrix(){memset(f,0,sizeof(f));}
    friend Matrix operator * (const Matrix &a,const Matrix &b) {
	Matrix c;
	for(int i = 0 ; i < T ; ++i) {
	    for(int j = 0 ; j < T; ++j) {
		for(int k = 0 ; k < T ; ++k) {
		    update(c.f[i][j],mul(a.f[i][k],b.f[k][j]));
		}
	    }
	}
	return c;
    }
    friend Matrix fpow(Matrix a,int c) {
	Matrix t = a,res;
	for(int i = 0 ; i < T ; ++i) res.f[i][i] = 1;
	while(c) {
	    if(c & 1) res = res * t;
	    t = t * t;
	    c >>= 1;
	}
	return res;
    }
};

Matrix<12> a,ansa;
Matrix<2> b,ansb;
void Init() {
    for(int j = 0 ; j <= 2 ; ++j) {
	update(a.f[getid(0,j)][getid(0,j)],1);
	update(a.f[getid(3,j)][getid(0,j)],1);
	update(a.f[getid(0,j)][getid(3,j)],1);
    }
    update(a.f[getid(0,0)][getid(0,2)],1);
    for(int j = 0 ; j < 2 ; ++j) {
	update(a.f[getid(0,j)][getid(1,j + 1)],1);
	update(a.f[getid(0,j)][getid(2,j + 1)],1);
	update(a.f[getid(2,j)][getid(0,j + 1)],1);
	update(a.f[getid(1,j)][getid(0,j + 1)],1);
    }
    for(int j = 0 ; j <= 2 ; ++j) {
	update(a.f[getid(2,j)][getid(1,j)],1);
	update(a.f[getid(1,j)][getid(2,j)],1);
    }
    update(b.f[0][0],1);update(b.f[0][1],1);
    update(b.f[1][0],1);
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    Init();
    int T,N;read(T);
    for(int i = 1 ; i <= T ; ++i) {
	read(N);
	ansa = fpow(a,N);ansb = fpow(b,N);
	out(inc(ansa.f[getid(0,0)][getid(0,2)],MOD - mul(N,ansb.f[0][0])));enter;
    }
}