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Palindrome Partitioning

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C# program to implement the Partition(string s) function, which returns all possible palindrome partitioning of the input string.

Example 1
    

  • Input: s = "aab"
    • 

  • Output: [["a","a","b"],["aa","b"]]
    • 

  • Explanation:

      

    • Step 1: Generate all possible ways to partition the string.
      • 

    • Step 2: Check if each partition consists only of palindromes.

        

      • Partition ["a","a","b"]: "a" is a palindrome, "a" is a palindrome, "b" is a palindrome.
        • 

      • Partition ["aa","b"]: "aa" is a palindrome, "b" is a palindrome.
        • 

      • Partition ["a","ab"]: "a" is a palindrome, but "ab" is not a palindrome (rejected).
        • 

      • Partition ["aab"]: "aab" is not a palindrome (rejected).
        • 

      

      • 

    • Step 3: Collect all valid partitions where each substring is a palindrome.
      • 

    • Step 4: Return the list of valid palindrome partitions [["a","a","b"],["aa","b"]].
      • 

    •
Example 2
    

  • Input: s = "abba"
    • 

  • Output: [["a","b","b","a"],["a","bb","a"],["abba"]]
    • 

  • Explanation:

      

    • Step 1: Generate all possible ways to partition the string.
      • 

    • Step 2: Check if each partition consists only of palindromes.

        

      • Partition ["a","b","b","a"]: All individual characters are palindromes.
        • 

      • Partition ["a","bb","a"]: "a" is a palindrome, "bb" is a palindrome, "a" is a palindrome.
        • 

      • Partition ["abba"]: "abba" is a palindrome.
        • 

      • Other partitions like ["ab","ba"] are rejected because "ab" is not a palindrome.
        • 

      

      • 

    • Step 3: Collect all valid partitions where each substring is a palindrome.
      • 

    • Step 4: Return the list of valid palindrome partitions [["a","b","b","a"],["a","bb","a"],["abba"]].
      • 

    •
Constraints
    

  • 1 ≤ s.length ≤ 16
    • 

  • s consists of only lowercase English letters
    • 

  • Time Complexity: O(N * 2^N) where N is the length of the input string
    • 

  • Space Complexity: O(N * 2^N) for storing all possible palindrome partitions
    •
Backtracking PwCZomato
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Hint
Solution

Solution Hints

    
  
  • Use backtracking to explore all possible partitions
    • 
  
  • Precompute palindrome checks using dynamic programming for efficiency
    • 
  
  • For each position, decide whether to create a partition
    • 
  
  • Recursively solve the problem for the remaining substring
    •

Steps to solve by this approach:

 Step 1: Precompute whether each substring is a palindrome using dynamic programming.
 Step 2: Set up a backtracking algorithm to explore all possible partitions.
 Step 3: For each position in the string, check if the substring from the start to the current position is a palindrome.
 Step 4: If it is a palindrome, add it to the current partition and recursively solve for the remaining string.
 Step 5: When we reach the end of the string, add the current partition to the result.
 Step 6: Use backtracking to explore all possible combinations of partitions.
 Step 7: Return all valid palindrome partitions.

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