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The Goddess Of The Moon

Chang’e （嫦娥） is a well-known character in Chinese ancient mythology. She’s the goddess of the Moon. There are many tales about Chang‘e, but there‘s a well-known story regarding the origin of the Mid-Autumn Moon Festival. In a very distant past, ten suns had risen together to the heavens, thus causing hardship for the people. The archer Yi shot down nine of them and was given the elixir of immortality as a reward, but he did not consume it as he did not want to gain immortality without his beloved wife Chang‘e. 



However, while Yi went out hunting, Fengmeng broke into his house and forced Chang‘e to give up the elixir of immortality to him, but she refused to do so. Instead, Chang‘e drank it and flew upwards towards the heavens, choosing the moon as residence to be nearby her beloved husband.



Yi discovered what had transpired and felt sad, so he displayed the fruits and cakes that his wife Chang‘e had liked, and gave sacrifices to her. Now, let’s help Yi to the moon so that he can see his beloved wife. Imagine the earth is a point and the moon is also a point, there are n kinds of short chains in the earth, each chain is described as a number, we can also take it as a string, the quantity of each kind of chain is infinite. The only condition that a string A connect another string B is there is a suffix of A , equals a prefix of B, and the length of the suffix(prefix) must bigger than one(just make the joint more stable for security concern), Yi can connect some of the chains to make a long chain so that he can reach the moon, but before he connect the chains, he wonders that how many different long chains he can make if he choose m chains from the original chains.

2
10 50
12 1213 1212 1313231 12312413 12312 4123 1231 3 131
5 50
121 123 213 132 321

86814837
797922656
Hint
11 111 is different with 111 11
 

/* ***********************************************
Author        :CKboss
Created Time  :2015年07月29日 星期三 09时55分36秒
File Name     :HDOJ5318.cpp
************************************************ */

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;

typedef long long int LL;

const LL mod=1000000007;

int n,m;

string str[55];

bool check(int a,int b)
{
	if(a==b) return true;

	int n1=str[a].length();
	int n2=str[b].length();

	for(int i=2,ml=min(n1,n2);i<=ml;i++)
	{
		int p1=n1-i,p2=0;

		bool flag=true;
		for(int j=0;j<i&&flag;j++,p1++,p2++)
		{
			if(str[a][p1]==str[b][p2]) continue;
			else flag=false;
		}

		if(flag==true) return flag;
	}

	return false;

}


struct Matrix
{
	LL m[52][52];

	Matrix()
	{
		memset(m,0,sizeof(m));
	}

	void getE()
	{
		for(int i=0;i<n;i++) m[i][i]=1;
	}

	void toString()
	{
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<n;j++)
				cout<<m[i][j]<<" ";
			cout<<endl;
		}
		cout<<endl;
	}
};

Matrix Muilt(Matrix a,Matrix b)
{
	Matrix mat;

	for(int i=0;i<n;i++)
	{
		for(int j=0;j<n;j++)
		{
			LL temp=0;
			for(int k=0;k<n;k++)
			{
				temp=(temp+(a.m[i][k]*b.m[k][j])%mod)%mod;
			}
			mat.m[i][j]=temp;
		}
	}

	return mat;
}

Matrix Pow(Matrix& m,int k)
{
	Matrix e;
	e.getE();

	while(k)
	{
		if(k&1) e=Muilt(e,m);
		m=Muilt(m,m);
		k/=2;
	}
	return e;
}

LL Solve(Matrix& e)
{
	LL ans=0;
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<n;j++)
		{
			ans=(ans+e.m[i][j])%mod;
		}
	}

	return ans;
}

set<string> ss;

int main()
{
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);

	int T_T;
	scanf("%d",&T_T);
	while(T_T--)
	{
		scanf("%d%d",&n,&m);

		ss.clear();

		int kut=0;
		string sss;

		for(int i=0;i<n;i++) 
		{
			cin>>sss;
			if(sss.length()<2) continue;
			if(ss.count(sss)==0) 
			{
				ss.insert(sss);
				str[kut++]=sss;
			}
		}
		n=kut;
		Matrix mt;
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<n;j++)
			{
				if(check(i,j)==true) mt.m[i][j]=1;
			}
		}

		Matrix e = Pow(mt,m-1);
		cout<<Solve(e)<<endl;;
	}
    
    return 0;
}

HDOJ 5318 The Goddess Of The Moon 矩阵快速幂

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原文地址：http://blog.csdn.net/ck_boss/article/details/47127839