Check whether the number has only first and last bits set

0 0 3 minutes read

Given a positive integer n. The problem is to check whether only the first and last bits are set in the binary representation of n.
Examples:

Input : 9
Output : Yes
(9)₁₀ = (1001)₂, only the first and
last bits are set.

Input : 15
Output : No
(15)₁₀ = (1111)₂, except first and last
there are other bits also which are set.

Approach: Following are the steps:

If n == 1, return “Yes”.
Else check whether n-1 is a power of 2. Refer this post.

C++

// C++ to check whether the number has only 
// first and last bits set
#include <bits/stdc++.h>
 
using namespace std;
 
// function to check whether 'n'
// is a power of 2 or not
bool powerOfTwo(unsigned int n)
{
    return (!(n & n-1));
}
 
// function to check whether the number has only 
// first and last bits set
bool onlyFirstAndLastAreSet(unsigned int n)
{
    if (n == 1)
        return true;
    if (n == 2)
        return false;
    return powerOfTwo(n-1);    
}
 
// Driver program to test above
int main()
{
    unsigned int n = 9;
     
    if (onlyFirstAndLastAreSet(n))
        cout << "Yes";
    else
        cout << "No";    
     
    return 0;
} 

Java

// Java program to check whether the 
// number has only first and last 
// bits set
import java.util.*;
 
class GFG
{
    // function to check whether 'n'
    // is a power of 2 or not
    static boolean powerOfTwo(int n)
    {
        return ((n & n - 1) == 0);
    }
 
    // function to check whether the number has  
    // only first and last bits set
    static boolean onlyFirstAndLastAreSet(int n)
    {
        if (n == 1)
            return true;
     
        return powerOfTwo(n-1); 
    }
 
    // Driver program to test above
    public static void main (String[] args) {
        
       int n = Integer.parseUnsignedInt("9");
     
        if (onlyFirstAndLastAreSet(n))
            System.out.println("Yes");
        else
            System.out.println("No"); 
    }
} 
 
/* This code is contributed by Mr. Somesh Awasthi */

Python3

# Python3 program to check whether number 
# has only first and last bits set
 
# function to check whether 'n'
# is a power of 2 or not
def powerOfTwo (n):
    return (not(n & n-1))
 
 
# function to check whether number  
# has only first and last bits set
def onlyFirstAndLastAreSet (n):
 
    if (n == 1):
        return True
    return powerOfTwo (n-1)
 
# Driver program to test above
n = 9
if (onlyFirstAndLastAreSet (n)):
    print('Yes')
else:
    print('No')
 
# This code is contributed by Shariq Raza

C#

// C# program to check whether the
// number has only first and last
// bits set
using System;
 
class GFG {
 
    // function to check whether 'n'
    // is a power of 2 or not
    static bool powerOfTwo(uint n)
    {
        return ((n & n - 1) == 0);
    }
 
    // function to check whether the number has
    // only first and last bits set
    static bool onlyFirstAndLastAreSet(uint n)
    {
        if (n == 1)
            return true;
 
        return powerOfTwo(n - 1);
    }
 
    // Driver program to test above
    public static void Main()
    {
 
        uint n = (uint)9;
 
        if (onlyFirstAndLastAreSet(n))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
 
}
 
// This code is contributed by Sam007

PHP

<?php
// PHP to check whether the number 
// has only first and last bits set 
 
// function to check whether 'n' 
// is a power of 2 or not 
function powerOfTwo($n) 
{ 
    return (!($n & $n - 1)); 
} 
 
// function to check whether 
// the number has only first
// and last bits set 
function onlyFirstAndLastAreSet($n) 
{ 
    if ($n == 1) 
        return true; 
    if ($n == 2) 
        return false; 
    return powerOfTwo($n - 1);     
} 
 
// Driver Code
$n = 9; 
 
if (onlyFirstAndLastAreSet($n)) 
    echo "Yes"; 
else
    echo "No"; 
 
// This code is contributed
// by Sach_Code
?>

Javascript

<script>
 
// Javascript to check whether the number has only 
// first and last bits set 
 
// function to check whether 'n' 
// is a power of 2 or not 
function powerOfTwo(n) 
{ 
    return (!(n & n-1)); 
} 
 
// function to check whether the number has only 
// first and last bits set 
function onlyFirstAndLastAreSet(n) 
{ 
    if (n == 1) 
        return true; 
    if (n == 2) 
        return false; 
    return powerOfTwo(n-1);     
} 
 
// Driver program to test above 
var n = 9; 
 
if (onlyFirstAndLastAreSet(n)) 
    document.write("Yes"); 
else
    document.write("No");     
     
</script>

Output:

Yes

Time Complexity – O(1)

Space Complexity – O(1)
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