<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 isPalindrome(string &s, int i, int j){
        while(i < j){
            if(s[i] != s[j]){
                return false;
            }
            i++;
            j--;
        }
        return true;
    }

int solve(string s, int i, int j, vector<vector<int>>&dp){
    if(i>=j || isPalindrome(s,i,j)){
        return 0;
    }
    if(dp[i][j]!=-1){
        return dp[i][j];
    }
  int ans=INT_MAX;
    for(int k=i; k<j; k++){
      if(isPalindrome(s, i, k)) {
        int right=0;
        if(dp[k+1][j]!=-1){
          right=dp[k+1][j];
        }
        else{
            right=solve(s,k+1,j,dp);
        }
         int temp= 1+right ;
          ans=min(ans,temp);
      }
    //   int temp= 1+ solve(s, i , k, dp)+solve(s,k+1,j,dp);
    //    ans=min(ans,temp);
    }
    return dp[i][j]=ans;
}
    int minCut(string s) {
        int N =s.size();
        
        vector<vector<int>>dp(N, vector<int>(N ,-1));  
        return solve(s, 0 , N-1, dp);
    }
};
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