<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>

class Solution:
    def partition(self, s: str) -> List[List[str]]:
        # def isPalindrome(s, left, right):
        #     while left < right:
        #         if s[left] != s[right]:
        #             return False
        #         left += 1
        #         right -= 1
        #     return True
        
        # def backtrack(s, start, current_partition, result):
        #     if start == len(s):
        #         result.append(list(current_partition))
        #         return
        #     for end in range(start, len(s)):

        #         if isPalindrome(s, start, end):
        #             current_partition.append(s[start:end+1])

        #             backtrack(s, end+1, current_partition, result)

        #             current_partition.pop()
        # res = []
        # backtrack(s, 0, [], res)
        # return res

        def dfs(start):
            if start == len(s):
                return [[]]
            if start in memo:
                return memo[start]

            res = []
            for end in range(start + 1, len(s) + 1):
                tmp_word = s[start:end]
                if tmp_word == tmp_word[::-1]:
                    for rest in dfs(end):
                        res.append([tmp_word] + rest)
            memo[start] = res
            return res

        memo = {}
        return dfs(0)
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