hdu5642 King's Order（数位dp）

King's Order

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 625 Accepted Submission(s): 361

[align=left]Problem Description[/align]
After the king's speech , everyone is encouraged. But the war is not over. The king needs to give orders from time to time. But sometimes he can not speak things well. So in his order there are some ones
like this: "Let the group-p-p three come to me". As you can see letter 'p' repeats for 3 times. Poor king!

Now , it is war time , because of the spies from enemies , sometimes it is pretty hard for the general to tell which orders come from the king. But fortunately the general know how the king speaks: the king never repeats a letter for more than 3 times continually
.And only this kind of order is legal. For example , the order: "Let the group-p-p-p three come to me" can never come from the king. While the order:" Let the group-p three come to me" is a legal statement.

The general wants to know how many legal orders that has the length of n

To make it simple , only lower case English Letters can appear in king's order , and please output the answer modulo
1000000007


We regard two strings are the same if and only if each charactor is the same place of these two strings are the same.

[align=left]Input[/align]
The first line contains a number
T(T≤10)

——The
number of the testcases.

For each testcase, the first line and the only line contains a positive number
n(n≤2000)

.

[align=left]Output[/align]
For each testcase, print a single number as the answer.

[align=left]Sample Input[/align]

2
2
4

[align=left]Sample Output[/align]

676
456950

hint:
All the order that  has length 2 are legal. So the answer is 26*26.

For the order that has length 4. The illegal order are : "aaaa" , "bbbb"…….."zzzz" 26 orders in total. So the answer for n == 4 is 26^4-26 = 456950

[align=left]Source[/align]
BestCoder Round #75

题意：一个长度为n的字符串，每个字符不能连续出现3次以上（不包含3次）；求有多少种情况。
分析：一道数位dp，很久没做数位dp了，尽然完全不会了- -。

<span style="font-size:18px;">#include <iostream>
#include <cstdio>
#include <cstring>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <vector>
#include <cmath>
#include <algorithm>
using namespace std;
const double eps = 1e-6;
const double pi = acos(-1.0);
const int INF = 0x3f3f3f3f;
const int MOD = 1000000007;
#define ll long long
#define CL(a,b) memset(a,b,sizeof(a))
#define lson (i<<1)
#define rson ((i<<1)|1)
#define MAXN 100010

ll dp[2010][4];///dp[i][j]表示第i个位置，j表示当前连续字符出现了j次

int main()
{
int T,n;
cin>>T;
dp[0][1] = 26;
for(int i=1; i<2002; i++)
{
dp[i][2] = dp[i-1][1]%MOD;
dp[i][3] = dp[i-1][2]%MOD;
dp[i][1] = (dp[i-1][1]+dp[i-1][2]+dp[i-1][3])*25%MOD;
}
while(T--)
{
cin>>n;
cout<<(dp[n-1][1]+dp[n-1][2]+dp[n-1][3])%MOD<<endl;
}
return 0;
}
</span>