N -ROOM LIGHTS PROBLEM

[ALIABBAS J PETIWALA]

N -ROOM LIGHTS PROBLEM
========================

THERE IS A BIG SQURE ROOM OF SIDE N WHICH CONSISTS OF N X N SMALLER
SQUARE ROOMS(ARRANGED LIKE CHESS BOARD)
EACH ROOM HAS A LIGHT.

WHEN the light of a smaller room k is toggled then all the
neighboring room's lights get toggled (max 5 lights get toggled
including the kth room if center room gets clicked )
THE PROBLEM IS to formulate an algorithm which will generate an order
in which the lights have to be toggled such that
all the n X n rooms get lit, initially no room is lit.
(toggle means that if the light is on then it is toggled of & if it is
off then it is switched on)
(question asked by Microsoft at IIT)
me>CAN a divide and conquer strategy work?
Me>I think that dynamic programming techniq can be used to solve this
problem?


Dear wade u got it wrong as u said " A light is On iff the number of
Up switches in the room and its horizontal/vertical (not diagonal)
neighbors is odd."

If u toggle a light near the wall of the room as shown:





if its possible I am attaching a sample program.

 

[Michael Mair]

N -ROOM LIGHTS PROBLEM
========================

THERE IS A BIG SQURE ROOM OF SIDE N WHICH CONSISTS OF N X N SMALLER
SQUARE ROOMS(ARRANGED LIKE CHESS BOARD)
EACH ROOM HAS A LIGHT.

WHEN the light of a smaller room k is toggled then all the
neighboring room's lights get toggled (max 5 lights get toggled
including the kth room if center room gets clicked )
THE PROBLEM IS to formulate an algorithm which will generate an order
in which the lights have to be toggled such that
all the n X n rooms get lit, initially no room is lit.
(toggle means that if the light is on then it is toggled of & if it is
off then it is switched on)
(question asked by Microsoft at IIT)
me>CAN a divide and conquer strategy work?
Me>I think that dynamic programming techniq can be used to solve this
problem?

Dear wade u got it wrong as u said " A light is On iff the number of
Up switches in the room and its horizontal/vertical (not diagonal)
neighbors is odd."

If u toggle a light near the wall of the room as shown:

if its possible I am attaching a sample program.

This is not a C question; if you have found an algorithm
and have problems implementing it in C, you can show it
to us. If you do, then describe your expectations, your
problems, and copy&paste the program.

<OT>
Hints:
- Does order matter?
- N=1 and N=2 are special cases
- What happens if you toggle each room's switch exactly once?
</OT>


Cheers
Michael