<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:
        dp = [[-1]*(len(s)+1) for _ in range(len(s)+1)]
        def isPalindrome(l, r , s):
            if l > r:
                return True
            if dp[l][r] != -1:
                return dp[l][r]
            res = False
            if s[l] == s[r]:
                res = isPalindrome(l+1, r-1, s)
            dp[l][r] = res
            return res
        helper_dp = [0]*(len(s)+1)

        for i in range(len(s)-1, -1, -1):
            min_cuts = float('inf')
            for j in range(i, len(s)):
                if isPalindrome(i, j, s):
                    min_cuts = min(min_cuts, helper_dp[j+1]+1)
            helper_dp[i] = min_cuts
        return helper_dp[0]-1


        # def helper(i):
        #     if i == len(s):
        #         return 0
        #     if helper_dp[i] != -1:
        #         return helper_dp[i]
        #     min_cuts = float('inf')
        #     for j in range(i, len(s)):
        #         isPali = isPalindrome(i, j, s)
        #         if isPali:
        #             min_cuts = min(min_cuts, 1 + helper(j+1))
        #     helper_dp[i] = min_cuts
        #     return min_cuts
        # return helper(0)-1

      
        
        
    

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