Coutn_of_binary_strings problem

#1

sir i mnot able to understand the top down approach of this question plz share the code.

#2

hi anuj
his problem can be solved using Dynamic Programming. Let a[i] be the number of binary strings of length i which do not contain any two consecutive 1’s and which end in 0. Similarly, let b[i] be the number of such strings which end in 1. We can append either 0 or 1 to a string ending in 0, but we can only append 0 to a string ending in 1. This yields the recurrence relation:

a[i] = a[i - 1] + b[i - 1]
b[i] = a[i - 1]
The base cases of above recurrence are a[1] = b[1] = 1. The total number of strings of length i is just a[i] + b[i].
And another interesting hack of the problem is the number of binary strings are related to some fibbonacci sequence as well.
the count is actually (n+2)’th Fibonacci number for n >= 1.

#3

But sir this is bottom up approach.

#4

i want top down approach how can i do with the help of recurssion

#5

you can refer this

#6

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