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Check whether the number has only first and last bits set | Set 2

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  • Difficulty Level : Easy
  • Last Updated : 04 Jun, 2022

Given a positive integer n, check whether only the first and last bits are set in the binary representation of n. Print ‘Yes’ or ‘No’.
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. 
 

 

We have already discussed a solution here.
In this post, a simpler solution is discussed.

Any number with first and last bits set are of the form (1+2^n):
    2^n     =>  10000… (n zeroes)
+ 1               +        1
 ————————————-
(1 + 2^n) => 10000….1 (n-1 zeroes)

For any given number ‘N’ of the form (1 + 2^n), we have: ((N-1) & (N-2)) = 0

    ((1 + 2^n) – 1) =>    (2^n)        => 10000…. (n zeroes) 
& ((1 + 2^n) – 2) => &((2^n) – 1) => 01111…. (n 1’s)
————————————————————–
                                                            00000….

For example: ‘9’ is of the form (1 + 2^3)
(9)10 => (1001)2
   (8)10 =>    (1000)2
&(7)10 =>& (0111)2
———————–
                     (0000)2

Hence for any given number ‘N’, if ((N-1) & (N-2)) == 0, then we can say ‘N’ has only first and last bits set.

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 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 (((n - 1) & (n - 2)) == 0);
}
 
// Driver program to test above
int main()
{
    unsigned int n = 9;
    if (onlyFirstAndLastAreSet(n))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java




// Java to check whether
// the number has only
// first and last bits set
 
class GFG
{
// function to check whether
// the number has only
// first and last bits set
static boolean onlyFirstAndLastAreSet(int n)
{
    if (n == 1)
        return true;
    if (n == 2)
        return false;
    return (((n - 1) &
             (n - 2)) == 0);
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 9;
    if (onlyFirstAndLastAreSet(n))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
 
// This code is contributed
// by Smitha

Python3




# Python 3 to check whether
# the number has only
# first and last bits set
 
# function to check whether
# the number has only
# first and last bits set
def onlyFirstAndLastAreSet(n):
 
    if (n == 1):
        return True
    if (n == 2):
        return False
 
    return (((n - 1) &
             (n - 2)) == 0)
 
# Driver Code
n = 9
if (onlyFirstAndLastAreSet(n)):
    print("Yes")
else:
    print("No")
     
# This code is contributed
# by Smitha

C#




// C# to check whether
// the number has only
// first and last bits set
using System;
 
class GFG
{
// function to check whether
// the number has only
// first and last bits set
static bool onlyFirstAndLastAreSet(int n)
{
    if (n == 1)
        return true;
    if (n == 2)
        return false;
    return (((n - 1) &
             (n - 2)) == 0);
}
 
// Driver Code
public static void Main()
{
    int n = 9;
    if (onlyFirstAndLastAreSet(n))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}
 
// This code is contributed
// by Smitha

PHP




<?php
// PHP to check whether the
// number has only first and
// last bits set
 
// function to check whether
// the number has only first
// and last bits set
function onlyFirstAndLastAreSet($n)
{
    if ($n == 1)
        return true;
    if ($n == 2)
        return false;
    return ((($n - 1) &
             ($n - 2)) == 0);
}
 
// Driver Code
$n = 9;
if (onlyFirstAndLastAreSet($n))
    echo "Yes";
else
    echo "No";
     
// This code is contributed
// by Smitha
?>

Javascript




<script>
 
// javascript to check whether
// the number has only
// first and last bits set
 
// 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 (((n - 1) &
             (n - 2)) == 0);
}
 
// Driver Code
 
var n = 9;
if (onlyFirstAndLastAreSet(n))
    document.write("Yes");
else
    document.write("No");
 
// This code contributed by shikhasingrajput
 
</script>

Output: 

Yes

 


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