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hello guys welcome to algorithms made easy my name is rajat and today we will be discussing the question non-negative integers without consecutive ones in this question we are given a positive integer n and we need to return the number of integers in the range 0 to n whose binary representation do not contain the consecutive ones in the first example as we can see that n is equals to 5 and we have 5 numbers in between 0 and 5 which do not have consecutive ones in their binary representation and similarly in the rest of the example now the n can range from 1 to 10 raised to power 9. so in no way we can do a brute force approach or even a off and approach won't suffice over here as the input is very large so now let's first understand what the problem is all about and how we can solve that so suppose the queries that we have with us is n 8 10 12 and 15 we have taken all these numbers in order to understand what all the different variations of this particular problem that can exist so if...