<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 {
public:
    bool isvalid(string &s,int i,int j,vector<vector<int>> &dp2)
    {
        if(dp2[i][j]!=-1)return dp2[i][j];
        int ci = i, cj = j;
        while (i < j  &&  i < s.size()  &&  i >= 0  &&  j < s.size()  &&  j >= 0) {
            if (dp2[i][j] != -1) return dp2[ci][cj] = dp2[i][j];
            if (s[i] != s[j]) return dp2[ci][cj] = false;
            i++;
            j--;
        }
        return dp2[ci][cj]=true;
    }


    int rec(int ind,string &s,vector<long long int> &dp1,vector<vector<int>> &dp2)
    {
        if(isvalid(s, ind, s.size() - 1,dp2))return 0;
        int cuts=INT_MAX;
        if(dp1[ind]!=-1)return dp1[ind];
        for(int i=ind;i<s.size();i++)
        {
            if(isvalid(s,ind,i,dp2))
            {
                cuts=min(cuts,rec(i+1,s,dp1,dp2));
            }
        }
        if(cuts!=INT_MAX)return dp1[ind]=cuts+1;
        return dp1[ind]=cuts;
    }

    int minCut(string s) {
        int n=s.size();
        vector<long long int> dp1(n,-1);
        vector<vector<int>> dp2(n,vector<int>(n,-1));
        return rec(0,s,dp1,dp2);
    }
};
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