Check if a given number is sparse or not - GeeksforGeeks

18 Jan, 2022
A number is said to be a sparse number if in binary representation of the number no two or more consecutive bits are set. Write a function to check if a given number is Sparse or not.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.
 
If we observer carefully, then we can notice that if we can use bitwise AND of binary representation of the “given number its “right shifted number”(i.e., half the given number) to figure out whether the number is sparse or not. Result of AND operator would be 0 if number is sparse and non-zero if not sparse. 
Below is the implementation of above idea.  
C++
Java
Python3
C#
PHP
Javascript
// C++ program to check if n is sparse or not#include<iostream>using namespace std; // Return true if n is sparse, else falsebool checkSparse(int n){    // n is not sparse if there is set    // in AND of n and n/2    if (n & (n>>1))        return false;     return true;} // Driver programint main(){    cout << checkSparse(72) << endl;    cout << checkSparse(12) << endl;    cout << checkSparse(2) << endl;    cout << checkSparse(3) << endl;    return 0;}
// JAVA Code to Check if a// given number is sparse or notimport java.util.*; class GFG {         // Return true if n is    // sparse,else false    static int checkSparse(int n)    {         // n is not sparse if there        // is set in AND of n and n/2        if ((n & (n>>1)) >=1)            return 0;              return 1;    }         // Driver code    public static void main(String[] args)    {        System.out.println(checkSparse(72)) ;        System.out.println(checkSparse(12)) ;        System.out.println(checkSparse(2)) ;        System.out.println(checkSparse(3)) ;        }    } //This code is contributed by Arnav Kr. Mandal.
# Python program to check# if n is sparse or not # Return true if n is# sparse, else falsedef checkSparse(n):     # n is not sparse if there is set    # in AND of n and n/2    if (n & (n>>1)):        return 0      return 1     # Driver codeprint(checkSparse(72))print(checkSparse(12))print(checkSparse(2))print(checkSparse(30)) # This code is contributed# by Anant Agarwal.
// C# Code to Check if a given// number is sparse or notusing System; class GFG {         // Return true if n is    // sparse,else false    static int checkSparse(int n)    {         // n is not sparse if there        // is set in AND of n and n/2        if ((n & (n >> 1)) >= 1)            return 0;             return 1;    }         // Driver code    public static void Main()    {        Console.WriteLine(checkSparse(72));        Console.WriteLine(checkSparse(12));        Console.WriteLine(checkSparse(2));        Console.WriteLine(checkSparse(3));    }} // This code is contributed by Sam007.
<?php// PHP program to check if// n is sparse or not// Return true if n is sparse,// else false function checkSparse($n){    // n is not sparse if    // there is set in AND    // of n and n/2    if ($n & ($n >> 1))        return 0;     return 1;} // Driver Codeecho checkSparse(72), "\n";echo checkSparse(12), "\n";echo checkSparse(2), "\n";echo checkSparse(3), "\n"; // This code is contributed by Ajit.?>
<script>     // Javascript program to check if n is sparse or not         // Return true if n is sparse, else false    function checkSparse(n)    {        // n is not sparse if there is set        // in AND of n and n/2        if ((n & (n>>1)) > 0)            return 0;         return 1;    }         document.write(checkSparse(72) + "</br>");    document.write(checkSparse(12) + "</br>");    document.write(checkSparse(2) + "</br>");    document.write(checkSparse(3) + "</br>");     </script>
Output : 
1
0
1
0
Time Complexity: O(1)
Auxiliary Space: O(1)
Note: Instead of right shift, we could have used left shift also, but left shift might lead to overflow in some cases.This article is contributed by Vimal Vestron. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above 
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