XOR and OR of all N-digit palindrome number

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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)
Auxiliary Space: O(1)

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