Contador de bits adyacente

F • 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
B B B B B B B B

x1*x2 + x2*x3+ x3*x4 + … + xn-1*xn
B B B B B B B B B B B B B B B B

which counts the number of times a 1 bit is adjacent to another 1 bit. For example: AdjBC(011101101) = 3AdjBC(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 ofinput 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 setnumber, 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 willfit 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 thenumber of n-bit strings with adjacent bit count equal to k. Sample 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
GreaterNew York Regional

Sample Output 1 6 2 63426 3 1861225 4 168212501 5 44874764 6 160916 7 22937308 8 99167 9 15476 10 23076518
F • Adjacent Bit Counts