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 + ... + 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

hide comments
shivamojha99: 2020-07-11 15:41:31

it took me 3 hours to identify and correct it...guidance for everyone=> *learn the importance and necessity of 3 states of dp :) .... Happy Coding

ujjwalmittal: 2020-07-03 20:09:44

AC in one go !!

geekymanas_: 2020-06-27 17:28:33

2D DP with O(n*k)

killer_ash: 2020-06-27 01:36:42

AC in one go likhne walo beginners ka dhyaan karo
morale down hota h bhai
bhai dil se bura lagta h bhai

ayush01: 2020-06-25 18:05:52

Can somebody help me out with its code in java.
I'm getting array index out of bounds exception, but the same logic works absolutely fine in c++.

Last edit: 2020-06-25 18:06:19
black_shroud: 2020-03-30 09:23:21

did it with 2-D dp, with O(n^2) complexity

tanav_shah1: 2019-08-08 14:12:50

AC in 1 go!!!
Nice 3D dp!
Loving dp...

spojwithsaurav: 2019-04-30 18:49:11

Got accepted in one go...))
started loving DP

Last edit: 2019-04-30 18:53:23
vikash_2016: 2018-12-20 15:34:18

What is max value of k ?

leonardopaes: 2018-05-30 03:41:57

Finalmente fiz aeeeeeeee


Added by:Tamer
Date:2009-11-14
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