Sphere Online Judge

SPOJ Problem Set (classical)

5295. Adjacent Bit Counts

Problem code: GNYR09F


For a string of n bits x1,x2,x3,...,Xn the adjacent bit count of the string (AdjBC(x)) is given by


X1*X2 + X2*X3 + X3*X4 + ... + Xn-1 * Xn


which counts the number of times a 1 bit is adjacent to another 1 bit. For example:
AdjBC(011101101) = 3
AdjBC(111101101) = 4
AdjBC(010101010) = 0

Write a program which takes as input integers n and k and returns the number of bit strings x of n bits (out of 2ⁿ) that satisfy AdjBC(x) = k. For example, for 5 bit strings, there are 6 ways of getting AdjBC(x) = 2:
11100, 01110, 00111, 10111, 11101, 11011

Input

The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number (n) of bits in the bit strings, followed by a single space, followed by a decimal integer (k) giving the desired adjacent bit count. The number of bits (n) will not be greater than 100 and the parameters n and k will be chosen so that the result will fit in a signed 32-bit integer.

Output

For each data set there is one line of output. It contains the data set number followed by a single space, followed by the number of n-bit strings with adjacent bit count equal to k.

Example

Input:
10
1 5 2
2 20 8
3 30 17
4 40 24
5 50 37
6 60 52
7 70 59
8 80 73
9 90 84
10 100 90
Output:
1 6
2 63426
3 1861225
4 168212501
5 44874764
6 160916
7 22937308
8 99167
9 15476
10 23076518

Added by:Tamer
Date:2009-11-14
Time limit:3s
Source limit:50000B
Memory limit:256MB
Cluster: Pyramid (Intel Pentium III 733 MHz)
Languages:All except: NODEJS PERL 6
Resource:ACM Greater New York Regional Contest 2009

hide comments
2014-10-30 16:24:06 abhijeet gusain
if u have those eyes u can see the answer in the bits .... :)
2014-08-16 16:31:29 manoj kumar regar
@Sahil Sethi for n=1 ,k =0..it would 2 bcz string can be "0" or "1" ...
2014-05-17 21:05:21 BLANKRK
nice one :D
2014-03-21 09:49:01 Sahil Sethi
What should be the answer for n=1,k=0 ... I believe it should be undefined.

But the recurrence that I have worked out will depend upon (1,0) for certain cases. help !!


Last edit: 2014-03-21 09:53:39
2014-02-12 12:22:23 Pritam Prakash
nice question.
solved using 3D DP.
2014-02-11 20:46:56 Vipul Pandey
good one! Feeling great to have solved this in first go. Not an easy one. You need to think a bit.

Last edit: 2014-02-11 20:48:26
2014-02-01 12:15:42 manoj
Leave a Comment

Last edit: 2014-02-01 12:16:29
2014-01-17 18:26:10 Rishab Kalra
accepted in 1 go :D
2013-12-16 15:22:02 meAnon
nice problem my 100th on spoj! :D
2013-10-31 08:32:34 mystique_blue
This is what should be done:
1) Come up with a brute force solution..
2) Alanlyze the recurisve statement to be used..
3)Memoize it..

A few simpler test cases..
1 5 1 --> 10
2 7 3 --> 16
3 7 4 --> 8
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