Question

Write a program that uses a stack object to determine if a string is a palindrome (i.e., the string is spelled identically backward and forward). The program should ignore spaces and punctuation.

Short answer

Use a stack to reverse and compare characters of a cleaned string to check for palindrome properties.

Step-by-step solution

Understand the Palindrome

A palindrome is a string that reads the same forwards and backwards. In this task, the provided string must be checked for palindrome properties by ignoring spaces and punctuation. For example, 'A man, a plan, a canal, Panama' is a palindrome.

Initialize the Stack and Preprocess the String

Create a stack data structure to help in checking the palindrome. Preprocess the string by removing all non-alphanumeric characters and converting it to lowercase or uppercase uniformly.

Push Characters onto the Stack

Iterate through the processed string and push all characters onto the stack. This stack will hold the characters in reverse order compared to their original sequence in the string.

Pop from the Stack and Compare

Iterate through the processed string again. For each character, pop the top character from the stack and compare it to the current character in the iteration. If any character does not match, the string is not a palindrome.

Complete the Check

If all characters match after completely iterating through the string and checking the stack, then the input string is a palindrome.

Implement the Solution

Here is a simple Python implementation: ``` import string def is_palindrome(s): stack = [] cleaned_string = ''.join(ch for ch in s if ch.isalnum()).lower() for char in cleaned_string: stack.append(char) for char in cleaned_string: if char != stack.pop(): return False return True # Example usage: string = 'A man, a plan, a canal, Panama' print(is_palindrome(string)) # Output: True ```

Key concepts

Stack Data Structure

A stack is a simple yet powerful data structure that follows the Last In, First Out (LIFO) principle. This means that the last element added to the stack is the first one to be removed. Imagine a stack of plates; you add new plates to the top and also remove the top plate first.

In the context of palindrome checking, a stack helps reverse the order of characters. As you iterate through the string, you place each character onto the stack. When you retrieve these characters (or "pop" them off the stack), they come off in reverse order. This is critical for palindrome checking since comparing the string with its reverse is key.

Using a stack for palindrome checking offers an elegant solution due to its intrinsic ability to reverse data using simple operations:

• **Push:** Add a character to the top of the stack.
• **Pop:** Remove the character from the top of the stack.
• **Peek:** Look at the top character without removing it (though not necessary for our palindrome algorithm).

By leveraging this data structure, we ensure an effective and memory-efficient palindrome checker.

String Processing

String processing is an essential step in our palindrome algorithm. The core idea is to prepare the string so that only relevant characters are compared. Ignoring spaces and punctuation is crucial, as these do not affect palindrome properties.

Here are the steps involved in processing the string:

• **Cleaning the String:** Use functions like `isalnum()` in Python to filter out non-alphanumeric characters. This leaves us with only letters and numbers.
• **Uniform Case Conversion:** To avoid mismatches due to letter casing (e.g., 'A' vs. 'a'), convert all characters to the same case using `.lower()` or `.upper()`.

For example, the string `'A man, a plan, a canal, Panama'` becomes `amanaplanacanalpanama` after string processing. This streamlined version is perfect for stack operations and checking against a palindrome property.

Algorithm Implementation

Implementing the algorithm entails turning our plan into code. The goal is to accurately determine whether a given string is a palindrome using a stack. Here’s how the process unfolds:

• **Initialize a Stack:** Begin by creating an empty stack where characters will be stored.
• **Preprocess the String:** Clean and prepare the string as explained earlier, ensuring only relevant data is considered.
• **Push Characters to Stack:** Iterate over the cleaned string and push each character onto the stack. This reverses the order by default.
• **Compare Characters:** Iterate again through the cleaned string. For each character, pop the top of the stack and compare it with the current string character. For a perfect palindrome, all comparisons should match.

Here's a brief illustration of the implementation in Python: ```python import string def is_palindrome(s): stack = [] cleaned_string = ''.join(ch for ch in s if ch.isalnum()).lower() for char in cleaned_string: stack.append(char) for char in cleaned_string: if char != stack.pop(): return False return True ``` This code efficiently checks for palindromes, considering only the necessary characters and using the stack's LIFO nature to compare the original and reversed character sequences.