From 0340eaafe39e8d16630a9d340a9d72acbffe4db4 Mon Sep 17 00:00:00 2001
From: Yaswanth Naga Sai K <140506928+YASWANTH1976@users.noreply.github.com>
Date: Sat, 3 Jan 2026 11:12:46 +0530
Subject: [PATCH 1/3] Add palindrome number checker with user input

Adds a simple Python implementation to check whether a number is a palindrome using user input.
---
 maths/palindrome_number.py | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 maths/palindrome_number.py

diff --git a/maths/palindrome_number.py b/maths/palindrome_number.py
new file mode 100644
index 000000000000..1c85ea4a5442
--- /dev/null
+++ b/maths/palindrome_number.py
@@ -0,0 +1,27 @@
+def is_palindrome(number: int) -> bool:
+    """
+    Check whether a given integer is a palindrome.
+
+    A palindrome number reads the same forwards and backwards.
+
+    Examples:
+    >>> is_palindrome(121)
+    True
+    >>> is_palindrome(123)
+    False
+    """
+    number_str = str(number)
+    return number_str == number_str[::-1]
+
+
+if __name__ == "__main__":
+    user_input = input("Enter a number: ").strip()
+
+    if user_input.isdigit():
+        number = int(user_input)
+        if is_palindrome(number):
+            print("The number is a palindrome.")
+        else:
+            print("The number is not a palindrome.")
+    else:
+        print("Please enter a valid non-negative integer.")

From b1779c501a0f3cc0608d73313a6ccec1b15f2a48 Mon Sep 17 00:00:00 2001
From: Yaswanth Naga Sai K <140506928+YASWANTH1976@users.noreply.github.com>
Date: Wed, 7 Jan 2026 09:13:41 +0530
Subject: [PATCH 2/3] Refactor is_palindrome function for efficiency

Refactor palindrome check to avoid string conversion and improve logic.
---
 maths/palindrome_number.py | 33 ++++++++++++---------------------
 1 file changed, 12 insertions(+), 21 deletions(-)

diff --git a/maths/palindrome_number.py b/maths/palindrome_number.py
index 1c85ea4a5442..7ab3b0f98bee 100644
--- a/maths/palindrome_number.py
+++ b/maths/palindrome_number.py
@@ -1,27 +1,18 @@
 def is_palindrome(number: int) -> bool:
     """
-    Check whether a given integer is a palindrome.
+    Determines if an integer is a palindrome without string conversion.
 
-    A palindrome number reads the same forwards and backwards.
-
-    Examples:
-    >>> is_palindrome(121)
-    True
-    >>> is_palindrome(123)
-    False
+    Logic:
+    1. Filter out negative numbers and multiples of 10.
+    2. Reverse the second half of the number.
+    3. Compare the two halves.
     """
-    number_str = str(number)
-    return number_str == number_str[::-1]
-
+    if number < 0 or (number % 10 == 0 and number != 0):
+        return False
 
-if __name__ == "__main__":
-    user_input = input("Enter a number: ").strip()
+    reversed_half = 0
+    while number > reversed_half:
+        reversed_half = (reversed_half * 10) + (number % 10)
+        number //= 10
 
-    if user_input.isdigit():
-        number = int(user_input)
-        if is_palindrome(number):
-            print("The number is a palindrome.")
-        else:
-            print("The number is not a palindrome.")
-    else:
-        print("Please enter a valid non-negative integer.")
+    return number == reversed_half or number == reversed_half // 10

From 12bcdb858f58a5b0727c64cab9262ee70a43650a Mon Sep 17 00:00:00 2001
From: Yaswanth Naga Sai K <140506928+YASWANTH1976@users.noreply.github.com>
Date: Wed, 7 Jan 2026 09:22:00 +0530
Subject: [PATCH 3/3] Refactor palindrome check to O(1) space mathematical
 approach

---
 maths/palindrome_number.py | 20 ++++++++++++++++----
 1 file changed, 16 insertions(+), 4 deletions(-)

diff --git a/maths/palindrome_number.py b/maths/palindrome_number.py
index 7ab3b0f98bee..2febb6fafd30 100644
--- a/maths/palindrome_number.py
+++ b/maths/palindrome_number.py
@@ -1,11 +1,23 @@
 def is_palindrome(number: int) -> bool:
     """
-    Determines if an integer is a palindrome without string conversion.
+    Determines if an integer is a palindrome without using string conversion.
 
     Logic:
-    1. Filter out negative numbers and multiples of 10.
-    2. Reverse the second half of the number.
-    3. Compare the two halves.
+    1. Negative numbers are not palindromes.
+    2. Numbers ending in 0 (except 0 itself) are not palindromes.
+    3. Reverse half of the number and compare.
+
+    Examples:
+    >>> is_palindrome(121)
+    True
+    >>> is_palindrome(12321)
+    True
+    >>> is_palindrome(10)
+    False
+    >>> is_palindrome(-121)
+    False
+    >>> is_palindrome(0)
+    True
     """
     if number < 0 or (number % 10 == 0 and number != 0):
         return False