Uva10862-connect the Cable Wires (recursive + large number of Java)

Uva10862-connect the Cable Wires (recursive + large number of Java)

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Title: give you n house in a straight line, and then just give you a cable service. Each house is required to be wired, indirectly through the direct neighbor of the House (provided that its neighbor is connected to the cable), and the second is the ability to connect directly to the cable service.

Problem-solving ideas: The back of the house is numbered 1, the front is N. If we're going to have a house number 1th, then it's three possible.

1, direct and cable service connection, then is to add f (n-1) species (front of the n-1 house of the Combination way).

2, and 2nd House connection does not and cable service connection, then again f (n-1) species.

3, and 2nd House link and Cable service connection, then this means that the 2nd House can not and cable service link, otherwise formed ring. This will allow numbers 1th and 2nd to be considered as a whole, and have an edge over the cable service. This situation can be divided into two types: (1), No and third, plus F (n-2).

(2) and number third, so that the situation goes back to 3, indicating that this is recursive.

So f (n) = 2 f (n-1) + f (n-2) + f (n-3) +: + F (1) + 1. (recursion to 1 only when there is no connection with the number 1th and 1th and then 1th and cable service both)
The same writes out F (n-1), subtracting: f (n) = 3 $*$ f (n-1)-F (n-2); (n > 2).
The boundary f (2) = 3, f (1) = 1;3 2000 will exceed long long, so use a large number.

Code:

Import Java.util.*;import Java.math.*;import java.io.*; Public classMain {StaticBigInteger f[] =Newbiginteger[2005]; Public Static voidInit () {f[1] = biginteger.valueof (1); f[2] = biginteger.valueof (3); for(inti =3; I <= -; i++) F[i] = biginteger.valueof (3). Multiply (F[i-1]). Subtract (F[i-2]); } Public Static voidMain (String args[]) {ScannerCin=NewScanner (system.in);intN Init (); while(true) {n =Cin. Nextint ();if(n = =0) Break;        System.out.println (F[n]); }    }}

Uva10862-connect the Cable Wires (recursive + large number of Java)