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Check if binary representation of a number is palindrome

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  • Difficulty Level : Medium
  • Last Updated : 28 Jun, 2022

Given an integer ‘x’, write a C function that returns true if binary representation of x is palindrome else return false.
For example a numbers with binary representation as 10..01 is palindrome and number with binary representation as 10..00 is not palindrome.
The idea is similar to checking a string is palindrome or not. We start from leftmost and rightmost bits and compare bits one by one. If we find a mismatch, then return false. 

Method#1:  We follow the following logic to check binary of number is Palindrome or not:

  •  Find number of bits in x using sizeof() operator. 
  • Initialize left and right positions as 1 and n respectively. 
  • Do following while left ‘l’ is smaller than right ‘r’. 
    • If bit at position ‘l’ is not same as bit at position ‘r’, then return false. 
    • Increment ‘l’ and decrement ‘r’, i.e., do l++ and r–-. 
  •  If we reach here, it means we didn’t find a mismatching bit.
  • To find the bit at a given position, we can use the idea similar to this post. The expression “x & (1 << (k-1))” gives us non-zero value if bit at k’th position from right is set and gives a zero value if if k’th bit is not set.

Following is the implementation of the above algorithm.
 

C++




// C++ Program to Check if binary representation
// of a number is palindrome
#include<iostream>
using namespace std;
 
// This function returns true if k'th bit in x
// is set (or 1). For example if x (0010) is 2
// and k is 2, then it returns true
bool isKthBitSet(unsigned int x, unsigned int k)
{
    return (x & (1 << (k - 1))) ? true : false;
}
 
// This function returns true if binary
// representation of x is palindrome.
// For example (1000...001) is palindrome
bool isPalindrome(unsigned int x)
{
    int l = 1; // Initialize left position
    int r = sizeof(unsigned int) * 8; // initialize right position
 
    // One by one compare bits
    while (l < r)
    {
        if (isKthBitSet(x, l) != isKthBitSet(x, r))
            return false;
        l++; r--;
    }
    return true;
}
 
// Driver Code
int main()
{
    unsigned int x = 1 << 15 + 1 << 16;
    cout << isPalindrome(x) << endl;
    x = 1 << 31 + 1;
    cout << isPalindrome(x) << endl;
    return 0;
}

Java




// Java Program to Check if binary representation
// of a number is palindrome
class GFG
{
 
    // This function returns true if k'th bit in x
    // is set (or 1). For example if x (0010) is 2
    // and k is 2, then it returns true
    static int isKthBitSet(long x, long k)
    {
        int rslt = ((x & (1 << (k - 1))) != 0) ? 1 : 0;
        return rslt;
    }
     
    // This function returns true if binary
    // representation of x is palindrome.
    // For example (1000...001) is palindrome
    static int isPalindrome( long x)
    {
        long l = 1; // Initialize left position
        long r = (Integer.SIZE/8 )* 8; // initialize right position
     
        // One by one compare bits
        while (l < r)
        {
            if (isKthBitSet(x, l) != isKthBitSet(x, r))
            {
                return 0;
            }
            l++; r--;
        }
        return 1;
    }
     
    // Driver Code
    public static void main (String[] args)
    {
        long x = 1 << 15 + 1 << 16 ;
        System.out.println(isPalindrome(x));
         
        x = (1 << 31) + 1 ;
        System.out.println(isPalindrome(x));
    }
}
 
// This code is contributed by AnkitRai01

Python3




# python 3 Program to Check if binary representation
# of a number is palindrome
import sys
# This function returns true if k'th bit in x
# is set (or 1). For example if x (0010) is 2
# and k is 2, then it returns true
def isKthBitSet(x, k):
    if ((x & (1 << (k - 1))) !=0):
        return True
    else:
        return False
 
# This function returns true if binary
# representation of x is palindrome.
# For example (1000...001) is palindrome
def isPalindrome(x):
    l = 1 # Initialize left position
    r = 2 * 8 # initialize right position
 
    # One by one compare bits
    while (l < r):
        if (isKthBitSet(x, l) != isKthBitSet(x, r)):
            return False
        l += 1
        r -= 1
     
    return True
 
# Driver Code
if __name__ =='__main__':
    x = 1 << 15 + 1 << 16
    print(int(isPalindrome(x)))
    x = 1 << 31 + 1
    print(int(isPalindrome(x)))
 
# This code is contributed by
# Surendra_Gangwar

C#




// C# Program to Check if binary representation
// of a number is palindrome
using System;
 
class GFG
{
 
    // This function returns true if k'th bit in x
    // is set (or 1). For example if x (0010) is 2
    // and k is 2, then it returns true
    static int isKthBitSet(long x, long k)
    {
        int rslt = ((x & (1 << (int)(k - 1))) != 0) ? 1 : 0;
        return rslt;
    }
     
    // This function returns true if binary
    // representation of x is palindrome.
    // For example (1000...001) is palindrome
    static int isPalindrome( long x)
    {
        long l = 1; // Initialize left position
        long r = 4 * 8; // initialize right position
     
        // One by one compare bits
        while (l < r)
        {
            if (isKthBitSet(x, l) != isKthBitSet(x, r))
            {
                return 0;
            }
            l++; r--;
        }
        return 1;
    }
     
    // Driver Code
    public static void Main ()
    {
        long x = 1 << 15 + 1 << 16 ;
        Console.WriteLine(isPalindrome(x));
         
        x = (1 << 31) + 1 ;
        Console.WriteLine(isPalindrome(x));
    }
}
 
// This code is contributed by AnkitRai01

PHP




<?php
// PHP Program to Check if binary representation
// of a number is palindrome
 
// This function returns true if k'th bit in x
// is set (or 1). For example if x (0010) is 2
// and k is 2, then it returns true
function isKthBitSet($x, $k)
{
    return ($x & (1 << ($k - 1))) ? true : false;
}
 
// This function returns true if binary
// representation of x is palindrome.
// For example (1000...001) is palindrome
function isPalindrome($x)
{
    $l = 1; // Initialize left position
    $r = sizeof(4) * 8; // initialize right position
 
    // One by one compare bits
    while ($l < $r)
    {
        if (isKthBitSet($x, $l) != isKthBitSet($x, $r))
            return false;
        $l++;
        $r--;
    }
    return true;
}
 
// Driver Code
$x = 1 << 15 + 1 << 16;
echo isPalindrome($x), "\n";
$x = 1 << 31 + 1;
echo isPalindrome($x), "\n";
 
// This code is contributed by ajit.
?>

Javascript




<script>
 
// Javascript program to Check if binary
// representation of a number is palindrome
 
// This function returns true if k'th bit in x
// is set (or 1). For example if x (0010) is 2
// and k is 2, then it returns true
function isKthBitSet(x, k)
{
    let rslt = ((x & (1 << (k - 1))) != 0) ? 1 : 0;
    return rslt;
}
   
// This function returns true if binary
// representation of x is palindrome.
// For example (1000...001) is palindrome
function isPalindrome(x)
{
     
    // Initialize left position
    let l = 1;
     
    // initialize right position
    let r = 4 * 8;
   
    // One by one compare bits
    while (l < r)
    {
        if (isKthBitSet(x, l) !=
            isKthBitSet(x, r))
        {
            return 0;
        }
        l++; r--;
    }
    return 1;
}
 
// Driver code
let x = 1 << 15 + 1 << 16;
document.write(isPalindrome(x) + "</br>");
 
x = (1 << 31) + 1;
document.write(isPalindrome(x));
 
// This code is contributed by divyesh072019
 
</script>

Output: 

1
1

Time Complexity: O(x)

Auxiliary Space: O(1)

Method#2: Using reverse() function: 

  • When user inputs an integer, it is passed to method which will evaluate the result. 
  • Actual logic inside the method focuses on following: 
    • It first convert the integer to binary form of integer in string format. 
    • It reverse the string using reverse method. 
    • It is palindrome if both the string is equal else not. 

Below is the implementation of the above approach: 

C++




// C++ program to to check if binary representation
// of a number is palindrome
#include <bits/stdc++.h>
using namespace std;
 
// This function return the binary form of integer in string format
string bin(unsigned n)
{   string ans;
    while(n > 0){
        ans = (to_string(n&1)) + ans;
        n >>= 1;
    }
     
    return ans;
}
 
// This function returns true if binary
// representation of x is palindrome
bool checkPalindrome( unsigned int n){
    string s1 = bin(n);
    string s2 = s1;
     
    // reversing the string 1
    reverse(s2.begin(), s2.end());
     
    return s1 == s2;
}
 
// Driver code
int main() {
    unsigned int x = 1 << 15 + 1 << 16;
    cout << checkPalindrome(x) << endl;
    x = 10;
    cout << checkPalindrome(x) << endl;
    return 0;
}

Java




// Java program to to check if binary representation
// of a number is palindrome
class GFG
{
   
  // This function return the binary form of integer in string format
  static String bin(int n)
  {  
    String ans = "";
    while(n > 0){
      ans = (Integer.toString(n&1)) + ans;
      n >>= 1;
    }
 
    return ans;
  }
 
  // This function returns true if binary
  // representation of x is palindrome
  static int checkPalindrome(int n){
    String s1 = bin(n);
 
    // reversing the string 1
    StringBuilder s2 = new StringBuilder(s1);
    s2 = s2.reverse();
 
 
    return s1.equals(s2.toString()) ? 1 : 0;
  }
 
  public static void main(String[] args) {
    int x = 9;
    System.out.println(checkPalindrome(x));
    x = 10;
    System.out.println(checkPalindrome(x)); 
  }
}
 
// This code is contributed by phasing17.

Python




def bin(n):
    ans="";
    while n > 0:
        ans = (str(n&1)) + ans;
        n >>= 1;
    return ans;
 
def checkPalindrome(x):
    s1 = bin(x)
    s2 = s1[::-1]
    return 1 if s1 == s2 else 0
 
# Some test cases....
x = 9
print(checkPalindrome(x)) #  output 1
 
x = 10
print(checkPalindrome(x)) # output 0

C#




// C# program to to check if binary representation
// of a number is palindrome
using System;
 
public class GFG
{
 
  // This function returns the binary form of integer in
  // string format
  static string bin(int n)
  {
    string ans = "";
    while (n > 0) {
      ans = (Convert.ToString(n & 1)) + ans;
      n >>= 1;
    }
 
    return ans;
  }
 
  // This function returns true if binary
  // representation of x is palindrome
  static int checkPalindrome(int n)
  {
    string s1 = bin(n);
 
    // reversing the string 1
    char[] charArray = s1.ToCharArray();
    Array.Reverse(charArray);
    string s2 = new string(charArray);
 
    return s1.Equals(s2) ? 1 : 0;
  }
 
  // Driver Code
  public static void Main(string[] args)
  {
    int x = 9;
    Console.WriteLine(checkPalindrome(x));
    x = 10;
    Console.WriteLine(checkPalindrome(x));
  }
}
 
// This code is contributed by phasing17.

Javascript




// JavaScript program to to check if binary representation
// of a number is palindrome
 
// This function return the binary form of integer in string format
function bin(n)
{   let ans="";
    while(n > 0){
        ans = ((n&1).toString()) + ans;
        n >>= 1;
    }
     
    return ans;
}
 
// This function returns true if binary
// representation of x is palindrome
function checkPalindrome(x){
    let s1 = bin(x);
    // reversing the string s1
    let s2 = s1.split("").reverse().join("");
    return s1 === s2 ? 1 :0;
}
 
// Some test case
let x = 1 << 15 + 1 << 16 ;
console.log(checkPalindrome(x));
 
x = 10;
console.log(checkPalindrome(x));

Output

1
0

Time Complexity: O(log(x))

Auxiliary Space: O(1)

This article is contributed by Saurabh Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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