Check if a given number is sparse or not

Write a function to check if a given number is Sparse or not.

A number is said to be a sparse number if in the binary representation of the number no two or more consecutive bits are set.

Example: 

Input:  x  = 72
Output: true
Explanation:  Binary representation of 72 is 01001000. 
There are no two consecutive 1's in binary representation

Input:  x  = 12
Output: false
Explanation:  Binary representation of 12 is 1100. 
Third and fourth bits (from end) are set.

Naive Approach:  The idea is to check the consecutive bits of the number until the number becomes 0.

Not Sparse

Time Complexity: O(Log₂n)
Auxiliary Space: O(1)

Efficient Approach: To solve the problem follow the below idea:

If we observe carefully, then we can notice that if we can use bitwise AND of the binary representation of the "given number, then it's "right-shifted number"(i.e., half the given number) to figure out whether the number is sparse or not. The result of AND operator would be 0 if the number is sparse and non-zero if not sparse.

Below is the implementation of the above approach:

1
0
1
0

Time Complexity: O(1)
Auxiliary Space: O(1)

Note: Instead of the right shift, we could have used the left shift also, but the left shift might lead to an overflow in some cases.