Recurrence Relation-Self Doubt(Discrete Math+Algo)

Question

Let $A(n)$ denotes the number of $n$ bit binary strings which have no pair of consecutive $1’s.$ what will be recurrence relation for it and what will be it’s Time Complexity??

Comments

similar problem from Rosen

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@ankitgupta.1729

yes base condition will be

$T(0)=0$

$T(1)=01$

right??

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You can use dynamic programming to get the answer in $O(n)$ , since the recurrence is same as that of the Fibonacci one.

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@srestha mam, $a_1=2$ because 0 and 1 are possible strings of size 1 where no consecutive 1 occurs 

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but then it just a count of elements

Here we want how recurrence grows

right??

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recurrence is defined  for 'no. of n bit strings where no two consecutive 1s occur'

Please check the given pic and understand the meaning of $a_n, a_{n-1},a_{n-2}$