<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]]:
        memo={}
        def palindromes(i):
            palis = []
            for word_i in range(i, len(s)):
                sub = s[i:word_i+1]
                if sub==sub[::-1]:
                    palis.append(sub)
            return palis
        def dfs(i,sub):
            if i>=len(s):
                res.append(sub[:])
                return
            if i in memo:
                partitions=memo[i]
            else:
                partitions=palindromes(i)
                memo[i]=partitions
            for pali in partitions:
                sub.append(pali)
                dfs(i+len(pali),sub)
                sub.pop(-1)
        res=[]
        dfs(0,[])
        return res
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