@All
I found a flaw in the recurrence provided above..
Correct recurrence is as follows:
F(n) = F(n - 1) + F(n - 2) + sum over all i ( 0 to (n-3) ) { F(i) }
F(0) = F(1) = 1;
On Jan 12, 12:03 am, Lucifer <sourabhd2...@gmail.com> wrote:
> @correction:
>
> F(2) = F(1) + F(0)..
>
> On Jan 11, 11:59 pm, Lucifer <sourabhd2...@gmail.com> wrote:
>
>
>
>
>
>
>
> > @ravi..
>
> > The recurrence would be :
> > F(N) = F(N-1) + F(N-2) + 2*F(N-3), for N>=3..
>
> > F(0) = F(1) = 1,
> > F(2) = F(1) + F(2) = 2
>
> > On Jan 11, 11:08 pm, Ravi Ranjan <ravi.cool2...@gmail.com> wrote:
>
> > > *Problem 1: Number of Tilings, (K Narayan Kumar, CMI)*
>
> > > You have to tile a room that is two units wide and *N* units long. You
> > > have
> > > with you two types of tiles: a rectangle that is one unit wide and two
> > > units long, and an L-shaped tile covering three square units. Here are
> > > pictures of the two types of tiles.
>
> > > [image: Figure 1]
>
> > > You are allowed to rotate the tiles when you lay them. You have an
> > > infinite
> > > supply of both types of tiles. Your objective is to calculate the number
> > > of
> > > different ways of tiling the room using these tiles.
>
> > > For instance, a 2×3 room can be tiled in 5 different ways, as follows:
>
> > > [image: Figure 2]
>
> > > Notice that a tiling can use both types of tiles. Consider, for instance,
> > > the following tiling of a 2×4 room.
>
> > > [image: Figure 3]
>
> > > Given *N*, your task is to determine the number of ways to tile a room of
> > > size 2×*N*. Since this number may be very large, it is sufficient to
> > > report
> > > the last four digits of the answer. For instance the number of ways to
> > > tile
> > > a 2×13 room is 13465. Your program should just print 3465. If the answer
> > > involves fewer than 4 digits then print the entire answer. For example,
> > > if *
> > > N* = 3 you should print 5.
>
> > > *Input format*
>
> > > A single integer *N*, indicating the size of the room.
>
> > > *Output format*
>
> > > The last four digits of the number of ways of tiling the 2×*N* room. If
> > > the
> > > answer involves fewer than 4 digits, print the entire answer.
>
> > > *Test Data:*
>
> > > You may assume *N* ≤ 1000000.
>
> > > *Example:*
>
> > > Here is the sample input and output corresponding to the example discussed
> > > above.
>
> > > *Sample Input*
>
> > > 13
>
> > > *Sample Output*
>
> > > 3465
>
> > > source::http://www.iarcs.org.in/inoi/2006/zio2006/zio2006-qpaper.pdf
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