zoj 2317 Nice Patterns Strike Back(矩阵乘法)

problemId=1317">http://acm.zju.edu.cn/onlinejudge/showProblem.do?

problemId=1317

给出一个n*m的矩阵(n <= 10^100, m <= 5)，对于2*2的子方格若全是黑色或全是白色的是非法的，用黑白两色去染n*m的方格，问共同拥有多少种合法的染色方案。

构造出转移矩阵，上一行向下一行的转移矩阵。由于m<=5，每行最多有32个状态。能够进行状态压缩构造出一个32*32的转移矩阵A。A[i][j] = 1表示上一行i状态能够向下一行的j状态转移。否则不能转移。要求最后的合法方案数，就再构造一个B矩阵，是一个32*1的矩阵，表示了到达第一行每个状态的方案数。那么A*B就表示到达第二行每个状态的方案数。以此类推。A^n-1 * B表示到达第n行每个状态的合法方案数，那么全部状态相应方案数的和就是总的方案数。

由于n特别大。要用到大数。我存矩阵的时候開始定义的大数类，一直T。改成了int型才A，1s+，难道大数类这么慢么，5s都过不了。

import java.io.*;
import java.math.BigInteger;
import java.util.Scanner;

class Matrix
{
	public int [][] mat = new int[35][35];
	public Matrix()
	{

	}
	public void init()
	{
		for(int i = 0; i < 35; i++)
		{
			for(int j = 0; j < 35; j++)
			{
				if(i == j)
					mat[i][j] = 1;
				else mat[i][j] = 0;
			}
		}
	}
}

public class Main {
	public static Matrix A,B,res;
	public static BigInteger n;
	public static int m,p,test,mm;
	static Scanner cin = new Scanner(System.in);

	public static void buildA()
	{
		for(int i = 0; i < mm; i++)
		{
			for(int j = 0; j < mm; j++)
			{
				String s1 = Integer.toBinaryString(i);
				String s2 = Integer.toBinaryString(j);
				String ss1 = new String();
				String ss2 = new String();
				for(int k = 0; k < m-s1.length(); k++)
					ss1 += '0';
				ss1 += s1;
				for(int k = 0; k < m-s2.length(); k++)
					ss2 += '0';
				ss2 += s2;

				int flag = 0;
				for(int k = 0; k < m-1; k++)
				{
					if(ss1.charAt(k)-'0' == 0 && ss1.charAt(k+1)-'0' == 0
					&& ss2.charAt(k)-'0' == 0 && ss2.charAt(k+1)-'0' == 0)
					{flag = 1;break;}
					if(ss1.charAt(k)-'0' == 1 && ss1.charAt(k+1)-'0' == 1
					&& ss2.charAt(k)-'0' == 1 && ss2.charAt(k+1)-'0' == 1)
					{flag = 1;break;}
				}
				if(flag == 1)
					A.mat[i][j] = 0;
				else A.mat[i][j] = 1;
			}
		}
	}

	public static Matrix Mul(Matrix x,Matrix y)
	{
		Matrix ans = new Matrix();
		for(int i = 0; i < mm; i++)
		{
			for(int k = 0; k < mm; k++)
			{
				if(x.mat[i][k] == 0)
					continue;
				for(int j = 0; j < mm; j++)
				{
					ans.mat[i][j] = (ans.mat[i][j]+x.mat[i][k]*y.mat[k][j])%p;
				}
			}
		}
		return ans;
	}

	public static Matrix Pow(Matrix tmp,BigInteger nn)
	{
		Matrix ans = new Matrix();
		ans.init();
		while(nn.compareTo(BigInteger.ZERO) > 0)
		{
			if( nn.remainder(BigInteger.valueOf(2)).compareTo(BigInteger.ONE) == 0)
				ans = Mul(ans,tmp);
			nn = nn.divide(BigInteger.valueOf(2));
			tmp = Mul(tmp,tmp);
		}
		return ans;
	}

	public static void main(String[] args) throws IOException
	{
		int test = cin.nextInt();
		while((test--) > 0)
		{
			n = cin.nextBigInteger();
			m = cin.nextInt();
			p = cin.nextInt();
			mm = (1<<m);

			A = new Matrix();
			B = new Matrix();

			buildA();
			for(int i = 0; i < mm; i++)
				B.mat[i][0] = 1;

			res = Pow(A,n.subtract(BigInteger.ONE));
			res = Mul(res,B);

			int anw = 0;
			for(int i = 0; i < mm; i++)
			{
				anw = (anw+res.mat[i][0])%p;
			}
			System.out.println(anw);
			if(test > 0)
				System.out.println();
		}
	}
}