Given N, check if the number is Fibbinary Number or not. Fibbinary numbers are integers whose binary representation contains no consecutive ones.

Examples:

Input : 10 Output : YES Explanation: 1010 is the binary representation of 10 which does not contains any consecutive 1's. Input : 11 Output : NO Explanation: 1011 is the binary representation of 11, which contains consecutive 1's

The idea to do this is to right shift the number, till n!=0. For every binary representation of 1, check if the last bit found was 1 or not. Get the last bit of binary representation of the integer by doing a (n&1). If the last bit of the binary representation is 1 and the previous bit before doing a right shift was also one, we encounter consecutive 1’s. So we come to the conclusion that it is not a fibonnary number.

Some of the first few Fibonnary numbers are:

0, 2, 4, 8, 10, 16, 18, 20.......

// CPP program to check if a number // is fibinnary number or not #include <iostream> using namespace std; // function to check if binary // representation of an integer // has consecutive 1s bool checkFibinnary(int n) { // stores the previous last bit // initially as 0 int prev_last = 0; while (n) { // if current last bit and // previous last bit is 1 if ((n & 1) && prev_last) return false; // stores the last bit prev_last = n & 1; // right shift the number n >>= 1; } return true; } // Driver code to check above function int main() { int n = 10; if (checkFibinnary(n)) cout << "YES"; else cout << "NO"; return 0; }

Output:

YES

**Time Complexity:** O( log(n) )

Fibbinary Numbers (No consecutive 1s in binary) – O(1) Approach

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