Check whether the number has only first and last bits set

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:

1. If n == 1, return “Yes”.
2. 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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