<p>Given a string <code>s</code>, partition <code>s</code> such that every <span data-keyword="substring-nonempty">substring</span> of the partition is a <span data-keyword="palindrome-string"><strong>palindrome</strong></span>. Return <em>all possible palindrome partitioning of </em><code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "aab"
<strong>Output:</strong> [["a","a","b"],["aa","b"]]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = "a"
<strong>Output:</strong> [["a"]]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 16</code></li>
	<li><code>s</code> contains only lowercase English letters.</li>
</ul>

def is_palindrome(s):
    # Remove non-alphanumeric characters and convert to lowercase
    s = ''.join(char.lower() for char in s if char.isalnum())
    
    # Compare the string with its reverse
    return s == s[::-1]

class Solution:
    def partition(self, s):
        self.s = s  # Store the input string as an instance variable
        return self.dfs(0, "", [])  # Start DFS from index 0 with empty current string and list

    def dfs(self, index, curr_string, curr_list):
        s = self.s  # Get the stored input string
        if index >= len(s):
            return []  # Base case: if index is out of bounds, return empty list

        char = s[index]  # Get the current character
        curr_string += char  # Add the current character to the current string

        ret_list = []  # Initialize the list to store results

        if is_palindrome(curr_string):
            new_list = curr_list.copy()  # Create a copy of the current list
            new_list.append(curr_string)  # Add the current palindrome to the new list

            if index == len(s) - 1:
                return [new_list]  # If we've reached the end, return the current partition
            
            # Recursively call DFS with the next index, empty current string, and updated list
            ret_list.extend(self.dfs(index + 1, "", new_list))

        # Recursively call DFS with the next index, current string, and current list
        ret_list.extend(self.dfs(index + 1, curr_string, curr_list))
        
        return ret_list  # Return the list of all valid partitions

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