<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:
    //int ispalli(int i, int j, string s){
     ////   while(j>i ){
      //      if(s[i]==s[j]){
       //         i++;
       //         j--;
       //     }
       //     else{
       //         return false;
        //    }
        //}
       // return true;
    //}
    bool ispalli(string& str, int s, int e, vector<vector<int>>& Paldp) {
        if (s >= e) return true; // Correct base case for palindrome check

        if (Paldp[s][e] != -1) return Paldp[s][e];

        if (str[s] == str[e]) {
            return Paldp[s][e] = ispalli(str, s + 1, e - 1, Paldp);
        } else {
            return Paldp[s][e] = false;
        }
    }
    /*int f(int i,string s,vector<int>& dp){
        if(i==s.length() || ispalli(i,s.length()-1,s)){
            return 0;
        }
       
        if(dp[i]!=-1){
            return dp[i];
        }
        int mini=1e9;
        for(int j=i;j<s.length();j++){
            if(ispalli(i,j,s)){
                int cost=1+f(j+1,s,dp);
                mini=min(mini, cost);
            }
        }
        return dp[i]=mini;
    }*/
    int minCut(string s) {
        int n=s.length();
        //vector<int>dp(n,-1);
        //return f(0,s,dp)-1;
        vector<int>dp(n+1,0);
        vector<vector<int>>Paldp(n,vector<int>(n,-1));
        for(int i=0;i<n;i++){
            for(int j=i;j<n;j++){
                ispalli(s,i,j,Paldp);
                
                
            }
        }
        
        for(int i=n-1;i>=0;i--){
              int mini=1e9;
            for(int j=i;j<s.length();j++){
              if(Paldp[i][j]){
                int cost=1+dp[j+1];
                mini=min(mini, cost);
             }
          }
          dp[i]=mini;

        }
        return dp[0]-1;
        
    }
};
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