<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 {
    bool check(string &s, int i, int j, vector<vector<int>> &x){
        int a=i,b=j;
        if(x[a][b]!=-1) return x[a][b];
        while(i<=j){
            if(s[i]!=s[j]) return x[a][b]= 0;
            i++; j--;
        }

        return x[a][b]= 1;
    }

    int fun(string &s, int i, vector<int> &lol, vector<vector<int>> &x){
        if(i>=s.size()) return 0;
        if(i==s.size()-1) return 1;
        // cout<<i<<" ";
        if(lol[i]!=-1) return lol[i];

        int a=INT_MAX;
        for(int j=i; j<s.size(); j++)
        if(check(s,i,j,x)) a=min(a,1+fun(s,j+1,lol,x));

        return lol[i]= a;
    }
public:
    int minCut(string s) {
        vector<vector<int>> x(s.size()+1,vector<int>(s.size()+1,-1));
        vector<int> lol(s.size(),-1);
        return fun(s,0,lol,x)-1;
    }
};
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