<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 {
public:
    vector<vector<string>> partition(string s) {
        unordered_map<string, vector<vector<string>>> memo;
        dfs(s, memo);
        return memo[s];
    }

    vector<vector<string>> dfs(string s, unordered_map<string, vector<vector<string>>>& memo)
    {
        if (s.empty())
        {
            return {{}};
        }

        if (memo.find(s) != memo.end())
        {
            return memo[s];
        }

        vector<vector<string>> result;
        for (int len = 1; len <= s.size(); len++)
        {
            if (isvalid(s.substr(0, len)))
            {
                vector<vector<string>> subResult = dfs(s.substr(len), memo);

                for (auto list : subResult)
                {
                    list.insert(list.begin(), s.substr(0, len));
                    result.push_back(list);
                }
            }
        }
        memo[s] = result;

        return result;
    }

    bool isvalid(string s)
    {
        int left = 0, right = s.size() - 1;
        while (left <= right)
        {
            if (s[left] == s[right])
            {
                left++;
                right--;
            }
            else
            {
                return false;
            }
        }
        return true;
    }
};
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