032. Normalized Palindrome

Why this mechanism works

Opposite ends can be compared after irrelevant characters are skipped independently. A mismatch at the next meaningful pair disproves a palindrome immediately. The skip loops need bounds checks because the entire remaining region may be punctuation.

State and boundaries

left and right delimit unexamined characters. All meaningful pairs outside them have already matched.

Protocol

1. Start at both ends.
2. Skip non-alphanumeric characters on the left.
3. Skip them on the right.
4. Compare lowercase meaningful characters.
5. Reject a mismatch or move both pointers inward.

Visualization

A man, a plan, a canal: Panama
A <-----------------------> a
next meaningful pair: m <-> m

Python implementation

def normalized_palindrome(text):
    left, right = 0, len(text) - 1
    while left < right:
        while left < right and not text[left].isalnum():
            left += 1
        while left < right and not text[right].isalnum():
            right -= 1
        if text[left].lower() != text[right].lower():
            return False
        left += 1
        right -= 1
    return True

Worked execution

Recorded state changes after statements; L numbers refer to the solution file. Long traces are explicitly condensed.

L2 normalized_palindrome: left, right = 0, len(text) - 1
text='A man, a plan, a canal: Panama'; left=0; right=29

L10 normalized_palindrome: left += 1
text='A man, a plan, a canal: Panama'; left=1; right=29

L11 normalized_palindrome: right -= 1
text='A man, a plan, a canal: Panama'; left=1; right=28

L5 normalized_palindrome: left += 1
text='A man, a plan, a canal: Panama'; left=2; right=28

L10 normalized_palindrome: left += 1
text='A man, a plan, a canal: Panama'; left=3; right=28

L11 normalized_palindrome: right -= 1
text='A man, a plan, a canal: Panama'; left=3; right=27

L10 normalized_palindrome: left += 1
text='A man, a plan, a canal: Panama'; left=4; right=27

L11 normalized_palindrome: right -= 1
text='A man, a plan, a canal: Panama'; left=4; right=26

... 20 intermediate state changes omitted ...

L11 normalized_palindrome: right -= 1
text='A man, a plan, a canal: Panama'; left=16; right=17

L5 normalized_palindrome: left += 1
text='A man, a plan, a canal: Panama'; left=17; right=17

L10 normalized_palindrome: left += 1
text='A man, a plan, a canal: Panama'; left=18; right=17

L11 normalized_palindrome: right -= 1
text='A man, a plan, a canal: Panama'; left=18; right=16

L2 normalized_palindrome: left, right = 0, len(text) - 1
text='!!!'; left=0; right=2

L5 normalized_palindrome: left += 1
text='!!!'; left=1; right=2

L5 normalized_palindrome: left += 1
text='!!!'; left=2; right=2

L10 normalized_palindrome: left += 1
text='!!!'; left=3; right=2

L11 normalized_palindrome: right -= 1
text='!!!'; left=3; right=1

Why the solution is correct

Skipping removes only characters the contract ignores. Matching the next meaningful endpoints is necessary for any palindrome, and after a match the interior is the remaining subproblem. Exhausting it proves all required pairs matched.

Time and space

O(n) time and O(1) auxiliary space for ASCII input.

Common mistakes

Skipping with if instead of while fails on several punctuation marks. Unbounded skipping can move a pointer outside the string.

Reasoning card

Transfer exercise

Permit deletion of at most one meaningful character. At the first mismatch, which two subproblems must be considered?