<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">palindrome</span>.</p>

<p>Return <em>the <strong>minimum</strong> cuts needed for a palindrome partitioning of</em> <code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aab&quot;
<strong>Output:</strong> 1
<strong>Explanation:</strong> The palindrome partitioning [&quot;aa&quot;,&quot;b&quot;] could be produced using 1 cut.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;a&quot;
<strong>Output:</strong> 0
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;ab&quot;
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 2000</code></li>
	<li><code>s</code> consists of lowercase English letters only.</li>
</ul>

class Solution:
    def minCut(self, s: str) -> int:
        n = len(s)
        memo_c = [None]*n
        memo_p = [[None]*n for _ in range(n)]
        
        def helper(start, end):
            cut = end
            if start==end or is_p(start, end): return 0
            if memo_c[start] is not None: return memo_c[start]
            for i in range(start, end+1):
                if is_p(start, i):
                    cut = min(cut, 1+helper(i+1, end))
                    
            memo_c[start] = cut
            return cut
        
        def is_p(start, end):
            if start>=end: return True
            if memo_p[start][end] is not None: return memo_p[start][end]
            memo_p[start][end]= (s[start]==s[end] and is_p(start+1, end-1))
            return memo_p[start][end]
        
        return helper(0, n-1)
74301