<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:
        palindrome_endings: Dict[int, Set[int]] = defaultdict(set)
        for idx in range(len(s)):
            start, end = idx, idx
            while start >= 0 and end < len(s) and s[start] == s[end]:
                palindrome_endings[start].add(end)
                start -= 1
                end += 1
            start, end = idx, idx + 1
            while start >= 0 and end < len(s) and s[start] == s[end]:
                palindrome_endings[start].add(end)
                start -= 1
                end += 1
        if len(s) - 1 in palindrome_endings[0]:
            return 0
        dp = {len(s) - 1: 0, len(s): -1}
        for i in range(len(s) - 2, -1, -1):
            dp[i] = min([1 + dp[end+1] for end in palindrome_endings[i]])
        return dp[0]
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