【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('\n')

#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;

    }

}