Fibbinary Numbers (No consecutive 1s in binary)


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


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 

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";
        cout << "NO";
    return 0;



Time Complexity: O( log(n) )

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

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