GNYR09F  Adjacent Bit Counts
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 + ... + Xn1 * 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 32bit 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 nbit 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
hide comments
gautam:
20170228 16:11:09
nailed it...;) 

singh1495:
20170223 05:03:39
nice problem 

taiken:
20170201 03:05:13
Hello, I can solve it just fine... in around 1 minute. Last edit: 20170201 03:05:54 

apurvgs:
20170124 16:54:36
Last edit: 20170124 16:56:24 

Shubham Agrawal:
20170116 14:18:31
Easy DP problem. Just try to observe a pattern and you will get the answer... 

prasoonbatham:
20170115 06:53:48
Easy dp :) 

tanmaysachan:
20161101 07:02:44
How to do this in 2d? took me a 3d dp


yash_18:
20161014 21:42:44
Good question!!


siddharth_0196:
20161008 20:38:36
A paper, a pen and a bit of observation will do the trick! ;)


hash7:
20160622 10:24:26
NYC QSN... 
Added by:  Tamer 
Date:  20091114 
Time limit:  3s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 NODEJS OBJC PERL6 SQLITE VB.NET 
Resource:  ACM Greater New York Regional Contest 2009 