Hdoj/hdu 1297 Children ' s Queue (derivation ~ large number)

Problem Description
There is many students in PHT School. One day, the headmaster whose name was Pigheader wanted all students stand in a line. He prescribed that girl can is in a single. In other words, either no girl in the queue or more than one girl stands side by side. The case n=4 (n was the number of children) is like
FFFF, FFFM, Mfff, FFMM, MFFM, MMFF, MMMM
Here F stands for a girl and M stands for a boy. The total number of the queue satisfied the headmaster ' s needs is 7. Can do a program to find the total number of the queue with n children?

Input
There is multiple cases in this problem and ended by the EOF. In each case, there are only one integer n means the number of children (1<=n<=1000)

Output
For each test case, there was only one integer means the number of the queue satisfied the headmaster ' s needs.

Sample Input
1
2
3

Sample Output
1
2
4

Test instructions
Just n people, stand in a row.
There is a requirement that (F) girls cannot stand alone between boys.
There can be no girls.

The output of the number of station method;
(regardless of the difference between people, only the location and the difference between men and women)
(If a row ends in MF is not legal)

Analysis:
If n person's station law is db[n];
Deduced from the previous db[n].
Db[n-1] Add a m to the end, it is certain to be possible.
Db[n-2] At the end of the add FF, it is also sure to.
Add MF can not, add mm is also possible (but this case and db[n-1], add FM also and Db[n-1]+m repeat.

After the sequence can not be added FF (MF can not, plus FF), become legal,
So db[n-4] back +mfff can, in fact, add an F can also constitute a legal, but this situation is contained in db[n-2] (quite and +ff) inside;

So the recursive equation Db[n] =db[n-1] + db[n-2] + db[n-4];

Db[i] is the number of legal sequences saved.

Java large number of seconds a~~~

Import Java.math.biginteger;import Java.util.Scanner; Public classmain{StaticBigInteger db[] =Newbiginteger[1001]; Public Static void Main(string[] args)        {Dabiao (); Scanner sc =NewScanner (System.inch); while(Sc.hasnext ()) {intn =sc.nextint (); System. out. println (Db[n]); }    }Private Static void Dabiao() {db[0]=NewBigInteger ("1"); db[1]=NewBigInteger ("1"); db[2]=NewBigInteger ("2"); db[3]=NewBigInteger ("4"); db[4]=NewBigInteger ("7"); for(intI=5; i<db.length;i++) {db[i]=db[i-1].add (db[i-2]). Add (db[i-4]); }    }}

Hdoj/hdu 1297 Children ' s Queue (derivation ~ large number)