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

Given a positive integer n. The problem is to 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 

Approach: If (n & (n >> 1)) == 0, then ‘n’ is a fibbinary number Else not.

// C++ implementation to check whether a number
// is fibbinary or not
#include <bits/stdc++.h>
using namespace std;

// function to check whether a number
// is fibbinary or not
bool isFibbinaryNum(unsigned int n) {

  // if the number does not contain adjacent ones
  // then (n & (n >> 1)) operation results to 0
  if ((n & (n >> 1)) == 0)
    return true;

  // not a fibbinary number
  return false;

// Driver program to test above
int main() {
  unsigned int n = 10;
  if (isFibbinaryNum(n))
    cout << "Yes";
    cout << "No";
  return 0;



Time Complexity: O(1).

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