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Solution 8: Maximum Specular Span (Longest Palindromic Substring)

Approach Explanation

We iterate through each character (and each gap between characters) and "expand around center" to find the longest palindrome centered there.

Step-by-Step Logic

  1. Initialize start = 0, end = 0.
  2. For i from 0 to len(s) - 1:
    • len1 = expand(i, i) (odd length).
    • len2 = expand(i, i + 1) (even length).
    • max_len = max(len1, len2).
    • If max_len > end - start:
      • Update start = i - (max_len - 1) // 2.
      • Update end = i + max_len // 2.
  3. Return s[start : end + 1].

Complexity

  • Time Complexity: O(N^2).
  • Space Complexity: O(1).

Code

def longest_palindrome(s):
    if not s: return ""
    
    def expand(l, r):
        while l >= 0 and r < len(s) and s[l] == s[r]:
            l -= 1
            r += 1
        # Length is (r-1) - (l+1) + 1 = r - l - 1
        return r - l - 1
        
    res_start = res_end = 0
    for i in range(len(s)):
        l1 = expand(i, i)
        l2 = expand(i, i + 1)
        mx = max(l1, l2)
        if mx > res_end - res_start:
            res_start = i - (mx - 1) // 2
            res_end = i + mx // 2
            
    return s[res_start : res_end + 1]