XOR and OR of all N-digit palindrome number

Given an integer N. The task is to find the XOR and OR of all N digit palindromic numbers.
Examples

Input: 3 
Output: XOR = 714 and OR = 1023
Input: 4 
Output: XOR = 4606 and OR = 16383

Approach:

• Find the starting and ending number of N-digit palindromic number by: 
  

  starting number = pow(10, n - 1)
  ending number = pow(10, n) - 1

• Iterate over starting number till ending number and check whether that number is palindromic or not.
• If the number is palindromic, then take XOR and OR of that number separately.
• Else proceed for next iteration and print the value of XOR and OR after all iterations.

Below is the implementation of the above approach: 

C++

// C++ program to find the XOR
// and OR of all palindrome numbers
// of N digits
#include <bits/stdc++.h>
using namespace std;

// Function to check if a number
// is palindrome or not
bool ispalin(int num)
{
    // Convert the num n to string
    string s = to_string(num);

    int st = 0, ed = s.size() - 1;

    // Iterate over string to
    // check whether it is
    // palindromic or not
    while (st <= ed) {
        if (s[st] != s[ed])
            return false;
        st++;
        ed--;
    }
    return true;
}

// Function to find XOR of all
// N-digits palindrome number
void CalculateXORandOR(int n)
{
    // To store the XOR and OR of all
    // palindromic number
    int CalculateXOR = 0;
    int CalculateOR = 0;

    // Starting N-digit
    // palindromic number
    int start = pow(10, n - 1);

    // Ending N-digit
    // palindromic number
    int end = pow(10, n) - 1;

    // Iterate over starting and
    /// ending number
    for (int i = start; i <= end; i++) {

        // To check if i is
        // palindromic or not
        if (ispalin(i)) {
            CalculateXOR = CalculateXOR ^ i;
            CalculateOR = CalculateOR | i;
        }
    }

    // Print the XOR and OR of all
    // palindromic number
    cout << "XOR = " << CalculateXOR;
    cout << " OR = " << CalculateOR;
}

// Driver Code
int main()
{
    int n = 4;
    CalculateXORandOR(n);
    return 0;
}

Java

// Java program to find the XOR
// and OR of all palindrome numbers
// of N digits
class GFG
{

// Function to check if a number
// is palindrome or not
static boolean ispalin(int num)
{
    // Convert the num n to string
    String s = Integer.toString(num);

    int st = 0, ed = s.length() - 1;

    // Iterate over string to
    // check whether it is
    // palindromic or not
    while (st <= ed) {
        if (s.charAt(st) != s.charAt(ed))
            return false;
        st++;
        ed--;
    }
    return true;
}

// Function to find XOR of all
// N-digits palindrome number
static void CalculateXORandOR(int n)
{
    // To store the XOR and OR of all
    // palindromic number
    int CalculateXOR = 0;
    int CalculateOR = 0;

    // Starting N-digit
    // palindromic number
    int start = (int)Math.pow(10, n - 1);

    // Ending N-digit
    // palindromic number
    int end = (int)Math.pow(10, n) - 1;

    // Iterate over starting and
    /// ending number
    for (int i = start; i <= end; i++) {

        // To check if i is
        // palindromic or not
        if (ispalin(i)) {
            CalculateXOR = CalculateXOR ^ i;
            CalculateOR = CalculateOR | i;
        }
    }

    // Print the XOR and OR of all
    // palindromic number
    System.out.print("XOR = " + CalculateXOR);
    System.out.println(" OR = " + CalculateOR);
}

// Driver Code
public static void main (String[] args)
{
    int n = 4;
    CalculateXORandOR(n);
}

}

// This code is contributed by AnkitRai01

Python3

# Python3 program to find the XOR
# and OR of all palindrome numbers
# of N digits

# Function to check if a number
# is palindrome or not
def ispalin(num) :

    # Convert the num n to string
    s = str(num);

    st = 0;
    ed = len(s) - 1;

    # Iterate over string to
    # check whether it is
    # palindromic or not
    while (st <= ed) :
        if (s[st] != s[ed]) :
            return False;
        st += 1;
        ed -= 1;

    return True;

# Function to find XOR of all
# N-digits palindrome number
def CalculateXORandOR(n) :

    # To store the XOR and OR of all
    # palindromic number
    CalculateXOR = 0;
    CalculateOR = 0;

    # Starting N-digit
    # palindromic number
    start = 10 ** (n - 1);

    # Ending N-digit
    # palindromic number
    end = (10**n) - 1;

    # Iterate over starting and
    # ending number
    for i in range( start, end + 1) :

        # To check if i is
        # palindromic or not
        if (ispalin(i)) :
            CalculateXOR = CalculateXOR ^ i;
            CalculateOR = CalculateOR | i;

    # Print the XOR and OR of all
    # palindromic number
    print("XOR =", CalculateXOR,end = " ");
    print("OR = ", CalculateOR);

# Driver Code
if __name__ == "__main__" :

    n = 4;
    CalculateXORandOR(n);

# This code is contributed by AnkitRai01

C#

// C# program to find the XOR
// and OR of all palindrome numbers
// of N digits

using System;

class GFG
{

// Function to check if a number
// is palindrome or not
static bool ispalin(int num)
{
    // Convert the num n to string
    string s = num.ToString();

    int st = 0;
    int ed = s.Length - 1;

    // Iterate over string to
    // check whether it is
    // palindromic or not
    while (st <= ed) {
        if (s[st] != s[ed])
            return false;
        st++;
        ed--;
    }
    return true;
}

// Function to find XOR of all
// N-digits palindrome number
static void CalculateXORandOR(int n)
{
    // To store the XOR and OR of all
    // palindromic number
    int CalculateXOR = 0;
    int CalculateOR = 0;

    // Starting N-digit
    // palindromic number
    int start = (int)Math.Pow(10, n - 1);

    // Ending N-digit
    // palindromic number
    int end = (int)Math.Pow(10, n) - 1;

    // Iterate over starting and
    /// ending number
    for (int i = start; i <= end; i++) {

        // To check if i is
        // palindromic or not
        if (ispalin(i)) {
            CalculateXOR = CalculateXOR ^ i;
            CalculateOR = CalculateOR | i;
        }
    }

    // Print the XOR and OR of all
    // palindromic number
    Console.Write("XOR = " + CalculateXOR);
    Console.WriteLine(" OR = " + CalculateOR);
}

// Driver Code
public static void Main (string[] args)
{
    int n = 4;
    CalculateXORandOR(n);
}

}

// This code is contributed by AnkitRai01

Javascript

<script>

// Javascript program to find the XOR
// and OR of all palindrome numbers
// of N digits

// Function to check if a number
// is palindrome or not
function ispalin(num)
{
    // Convert the num n to string
    let s = num.toString();

    let st = 0, ed = s.length - 1;

    // Iterate over string to
    // check whether it is
    // palindromic or not
    while (st <= ed) {
        if (s[st] != s[ed])
            return false;
        st++;
        ed--;
    }
    return true;
}

// Function to find XOR of all
// N-digits palindrome number
function CalculateXORandOR(n)
{
    // To store the XOR and OR of all
    // palindromic number
    let CalculateXOR = 0;
    let CalculateOR = 0;

    // Starting N-digit
    // palindromic number
    let start = Math.pow(10, n - 1);

    // Ending N-digit
    // palindromic number
    let end = Math.pow(10, n) - 1;

    // Iterate over starting and
    /// ending number
    for (let i = start; i <= end; i++) {

        // To check if i is
        // palindromic or not
        if (ispalin(i)) {
            CalculateXOR = CalculateXOR ^ i;
            CalculateOR = CalculateOR | i;
        }
    }

    // Print the XOR and OR of all
    // palindromic number
    document.write("XOR = " + CalculateXOR);
    document.write(" OR = " + CalculateOR);
}

// Driver Code
    let n = 4;
    CalculateXORandOR(n);

</script>

Output:

XOR = 4606 OR = 16383

Time Complexity: O(10ⁿ)