Snapper chain (Time
limit : 45 min)
The Snapper is a clever little device that, on one side,
plugs into an output socket, and, on the other side, exposes an output socket
for plugging in a light or other device.
When a Snapper is the ON state and is receiving power from
its input plug, then the device connected to its output socket is receiving power
as well. When you Snap your finger – making a clicking sound – any Snapper receiving
power at the time of the snap toggles between the ON and OFF states.
In hopes of destroying the universe by means of a
singularity, I have purchased N Snapper
devices and chained them together by plugging the first one into power socket,
the second one into the first one, and so on. The light is plugged into the Nth snapper.
Initially, all the Snappers are in the OFF state, so only
the first one is receiving power from the socket and the light is off. I snap
my finger once, which toggles the first snapper into ON state and gives power
at the second one, I snap my fingers again, which toggles both Snappers and
promptly cut power off from the second one, leaving it in the ON state, but
with no power. I snap my fingers the third time, which toggles the first
Snapper again and gives power to second one. Now both Snappers are in the ON
state, and if my light is plugged into the second Snapper it will be on.
I keep doing this for hours. Will the light be on or off after
I have snapped my fingers K times?
The light is on if and only if it’s receiving power from the Snapper it’s
plugged into.
Input
The first line of the input gives the number of test cases, T. T
lines follow. Each one containing two integers, N and K.
Output
For each test case, output one line containing “Case #x:y”,where
x is the case number starting from 1 and y is either ON or OFF, indicating
state of light bulb.
Limits 1<=T<=10000 ,1<=N<=30,0<=K<=10^8
Sample:
Input
4
1 0
1 1
4 0
4 47
Output
Case#1:OFF
Case#2: ON
Case#3:OFF
Case#4:ON
For my Solution see the comment....
