<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:
        palindromes = set()

        def palindrome(i,j) :
            while i>=0 and j<len(s) and s[i]==s[j] :
                palindromes.add((i,j)) 
                i-=1
                j+=1

        n = len(s)
        for i in range(n) :
            palindrome(i,i)
            palindrome(i,i+1) 
        dp = [1e6]*(n+1) 
        dp[-1] = 0
        for i in range(n-1,-1,-1) :
            ans = 1e6
            for j in range(i, n) :
                if (i,j) in palindromes :
                    ans = min(ans, 1+dp[j+1])
            dp[i] = ans
        return dp[0]-1
               



        
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