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Longest Palindromic Substring

Certification: Advanced Level Accuracy: 75% Submissions: 16 Points: 15

Write a Python function that finds the longest palindromic substring in a given string. A palindrome is a string that reads the same backward as forward.

Example 1
    

  • Input: "babad"
    • 

  • Output: "bab" (Note: "aba" is also a valid answer)
    • 

  • Explanation: 

      

    • Step 1: Take the input string "babad".
      • 

    • Step 2: Identify all palindromic substrings.
      • 

    • Step 3: Find the longest ones, which are "bab" and "aba".
      • 

    • Step 4: Return either "bab" or "aba" as they're the same length.
      • 

    

    •
Example 2
    

  • Input: "cbbd"
    • 

  • Output: "bb"
    • 

  • Explanation: 

      

    • Step 1: Take the input string "cbbd".
      • 

    • Step 2: Identify all palindromic substrings.
      • 

    • Step 3: Find the longest one, which is "bb".
      • 

    • Step 4: Return "bb" as the result.
      • 

    

    •
Constraints
    

  • 1 ≤ string length ≤ 1000
    • 

  • String contains only lowercase English letters
    • 

  • Time Complexity: O(n²), where n is the length of the string
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Expand around center approach: check palindromes by expanding from each position
    • 
  
  • Dynamic programming: build a table dp[i][j] indicating if s[i:j+1] is a palindrome
    • 
  
  • Manacher's algorithm for O(n) time complexity but more complex implementation
    • 
  
  • Handle even and odd length palindromes separately
    •

Steps to solve by this approach:

 Step 1: For each character in the string, consider it as a potential center of a palindrome.

 Step 2: Expand around the center for both odd and even length palindromes.

 Step 3: For odd length, expand around single character (i,i).

 Step 4: For even length, expand around adjacent characters (i,i+1).

 Step 5: Keep track of the start position and maximum length of palindromes found.

 Step 6: Return the substring from start to start+max_length.

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