<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(object): # iteration, real dp
  def partition(self, s):
    """
    :type s: str
    :rtype: List[List[str]]
    """
    pal = [[False for i in range(0, len(s))] for j in range(0, len(s))]
    ans = [[[]]] + [[] for _ in range(len(s))] # length is n+1

    for i in range(0, len(s)):
      for j in range(0, i + 1):
        if (s[j] == s[i]) and ((j + 1 > i - 1) or (pal[j + 1][i - 1])):
          pal[j][i] = True
          for res in ans[j]:
            a = res + [s[j:i + 1]]
            ans[i + 1].append(a)


    return ans[-1]
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