Reversal and palindrome checks

Understand the idea

Palindrome checking compares symmetric positions. A reversed copy checks the same property but uses extra memory. Normalize only according to an explicit specification.

Work through an example

For 'level', compare l/l then e/e; center v needs no partner. 'lever' fails at the outer l/r pair.

Time and space complexity

O(n) time/O(1) auxiliary state for exact code-point checking; reversed copy O(n) space.

Why it works

Every position outside [left,right] already matches its mirror.

Common mistakes

• Do not discard punctuation without permission from the contract.
• Reversing code points can separate combining marks from bases.

Chapter lab · Python implementation

These examples operate on Python Unicode code points. A user-visible character can span several code points; normalization and grapheme segmentation need separate policies. The lab compares mirror positions without allocating a reversed copy. For every text problem, state whether case, punctuation, and whitespace matter.

This shared lab connects the chapter's topics. Follow the current lesson's worked example first, then trace the complete implementation. Additional algorithms described in topic exercises are variations you can implement independently.

def palindrome(text):
    left, right = 0, len(text)-1
    while left < right:
        if text[left] != text[right]:
            return False
        left += 1
        right -= 1
    return True

def frequencies(text):
    counts = {}
    for char in text:
        counts[char] = counts.get(char,0)+1
    return counts

Run and test the lab

Copy the implementation and these assertions into a Python 3 file and run it. An assertion failure means the actual result differs from the expectation. Add the current topic's exercise and boundary tests to deepen your understanding.

assert palindrome('level') and palindrome('')
assert not palindrome('lever')
assert frequencies('abaca')=={'a':3,'b':1,'c':1}