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.

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

// 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;
}

Java

// Java program to check if a number 
// is fibinnary number or not
class GFG {
      
    // function to check if binary 
    // representation of an integer 
    // has consecutive 1s
    static boolean checkFibinnary(int n) 
    {
  
        // stores the previous last bit
        // initially as 0
        int prev_last = 0;
          
        while (n != 0
        {
              
            // if current last bit and 
            // previous last bit is 1
            if ((n & 1) != 0 && prev_last != 0)
              
                return false;
          
            // stores the last bit
            prev_last = n & 1;
          
            // right shift the number
            n >>= 1;
        }
      
        return true;
    }
      
    // Driver code to check above function
    public static void main(String[] args)
    {
        int n = 10;
  
        if (checkFibinnary(n) == true)
            System.out.println("YES");
        else
            System.out.println("NO");
    }
}
  
// This code is contributed by
// Smitha Dinesh Semwal

Python3

# Python 3 program to check if a
# number is fibinnary number or 
# not
  
# function to check if binary 
# representation of an integer 
# has consecutive 1s
def checkFibinnary(n): 
  
    # stores the previous last bit
    # initially as 0
    prev_last = 0
      
    while (n): 
      
        # if current last bit and 
        # previous last bit is 1
        if ((n & 1) and prev_last):
            return False
      
        # stores the last bit
        prev_last = n & 1
      
        # right shift the number
        n >>= 1
      
  
    return True
  
# Driver code
n = 10
  
if (checkFibinnary(n)):
    print("YES")
else:
    print("NO")
  
# This code is contributed by Smitha Dinesh Semwal

C#

// C# program to check if a number 
// is fibinnary number or not
using System;
  
class GFG {
      
    // function to check if binary 
    // representation of an integer 
    // has consecutive 1s
    static bool checkFibinnary(int n) 
    {
  
        // stores the previous last bit
        // initially as 0
        int prev_last = 0;
          
        while (n != 0) 
        {
              
            // if current last bit and 
            // previous last bit is 1
            if ((n & 1) != 0 && prev_last != 0)
              
                return false;
          
            // stores the last bit
            prev_last = n & 1;
          
            // right shift the number
            n >>= 1;
        }
      
        return true;
    }
      
    // Driver code to check above function
    public static void Main()
    {
        int n = 10;
  
        if (checkFibinnary(n) == true)
            Console.WriteLine("YES");
        else
            Console.WriteLine("NO");
    }
}
  
// This code is contributed by vt_m.

PHP

<?php
// PHP program to check if a number 
// is fibinnary number or not
  
// function to check if binary 
// representation of an integer 
// has consecutive 1s
function checkFibinnary($n
{
    // stores the previous last bit
    // initially as 0
    $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
$n = 10;
if (checkFibinnary($n))
    echo "YES";
else
    echo "NO";
  
// This code is contributed by mits 
?>


Output :

YES

Time Complexity: O( log(n) )

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



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Striver(underscore)79 at Codechef and codeforces D

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