Interesting number (dynamic planning)

Problem description

We call a number interesting when and only if:

1. Its numbers contain only 0, 1, 2, 3, and these four numbers appear at least once.

2. All 0 appear before all 1, and all 2 appear before all 3.

3. The maximum number of digits is not 0.

Therefore, the smallest interesting number that conforms to our definition is 2013. In addition, the 4-bit interesting number also has two: 2031 and 2301.

Please calculate the number of interesting numbers that happen to have n bits. Because the answer can be very large, only the remainder of the output answer divided by 1000000007 is required.

Input format

The input has only one row, including exactly a positive integer n (4≤n≤1000).

Output format

The output has only one row, including the number of interesting numbers in the exact n-bit integer divided by the remainder of 1000000007.

Sample input

4

Sample output

3

Dynamic Programming Solution:

import java.util.*;p ublic class main {      public  Static void main (String[] args)  {      new main (). Run () ;} Public void run ()  {      Scanner fin = new  Scanner (system.in);       int n = fin.nextint ();    &NBSP;&NBSP;&NBSP;LONG[]&NBSP;COUNT&NBSP;=&NBSP;NEW&NBSP;LONG[8];&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;COUNT[6]  = 0;      count[7] = 1;       long mod = 1000000007;      for  (int i = 2;  i <= n; ++i)  {          long[]  newCount = new long[8];           newcount[0] = (Count[0] * 2 + count[1] + count[3])  % mod;           newCount[1] =  (count[1] * 2 + count[2]  +&NBSP;COUNT[5])  % mod;          newCount[2]  =  (Count[2] + count[6])  % mod;           newCount[3] =  (count[3] * 2 + count[4] + count[5])  %  mod;          newcount[4] =  (count[4] +  COUNT[7])  % mod;          newCount[5] =  (Count[5] * 2 + count[6] + count[7])  % mod;           newCount[6] = 0;           newcount[7] = 1;          count = newcount;       }     system.out.println (count[0]);    }}

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Interesting number (dynamic planning)