131. Palindrome Partitioning

131. Palindrome Partitioning

Difficulty: Medium

Topics: String, Dynamic Programming, Backtracking

Given a string s, partition s such that every substring¹ of the partition is a palindrome². Return all possible palindrome partitioning of s.

Example 1:

• Input: s = "aab"
• Output: [["a","a","b"],["aa","b"]]

Example 2:

• Input: s = "a"
• Output: [["a"]]

Constraints:

• 1 <= s.length <= 16
• s contains only lowercase English letters.

Solution:

We can use a combination of backtracking and dynamic programming. The goal is to explore all possible partitions and check if each partition is a palindrome.

Steps to Solve:

1. Backtracking:

   • We'll explore every possible partitioning of the string. For each possible starting index, we try to partition the string at every possible end index.
   • If a substring is a palindrome, we recursively partition the remaining string.

2. Palindrome Check:

   • We need a helper function to check if a given substring is a palindrome. This can be done by comparing the substring with its reverse.

3. Collect Results:

   • When we reach the end of the string, we've found a valid partitioning, so we add it to the result list.

Let's implement this solution in PHP: 131. Palindrome Partitioning

<?php
// Example usage:
$s1 = "aab";
$s2 = "a";
print_r(partition($s1)); // Output: [["a","a","b"],["aa","b"]]
print_r(partition($s2)); // Output: [["a"]]
?>

Explanation:

1. partition($s): This function initializes the backtracking process.
2. backtrack($s, $start, &$current, &$result):
   • It explores each substring starting at index start.
   • If a palindrome is found, it's added to the current partition ($current), and the function is called recursively for the next part of the string.
   • Once all partitions from the current start point are explored, the last substring is removed from $current to backtrack and try other possibilities.
3. isPalindrome($s): This helper function checks if a string is a palindrome by comparing characters from the start and end.

Time Complexity:

• The time complexity is exponential in the worst case, as we explore all possible partitions (backtracking).
• The palindrome check is (O(n)) for each substring.

This solution works efficiently for the given constraint where the maximum length of the string is 16.

Contact Links

If you found this series helpful, please consider giving the repository a star on GitHub or sharing the post on your favorite social networks 😍. Your support would mean a lot to me!

If you want more helpful content like this, feel free to follow me:

• LinkedIn
• GitHub

1. Substring A substring is a contiguous non-empty sequence of characters within a string. ↩

2. Palindrome A palindrome is a string that reads the same forward and backward. ↩