<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 dp[2003];
    bool computePalindrome(int i, int j, string &s,vector<vector<int>> &palindrome  ){
           if(i>=j){
            return palindrome[i][j]=1;
           }
           if(palindrome[i][j]!=-1) return palindrome[i][j];
           bool x=0;
         if(s[i]==s[j]){
              x=computePalindrome(i+1,j-1,s,palindrome);
         }

         computePalindrome(i+1, j,s,palindrome);
         computePalindrome(i, j-1, s , palindrome);

         return palindrome[i][j]=x;


    }
    int solve(int i,string &s, vector<vector<int>> &palindrome ){
        int n=s.size();
        if(i==n)  return 0;
        if(dp[i]!=-1) return dp[i];
        int ans=1e9;
        for(int j=i;j<n;j++){
            if(palindrome[i][j]){
           if( j==n-1){
              ans=min(ans,solve(j+1, s  , palindrome));
           }else{
               ans=min(ans, 1+solve(j+1, s, palindrome));
           }
            }
        }
        return dp[i]=ans;
    }
    int minCut(string s) {
        int n=s.size();
        vector<vector<int>> palindrome(n, vector<int>(n,-1));
        memset(dp,-1, sizeof(dp));
         computePalindrome(0,n-1,s,palindrome);
        return solve(0, s, palindrome);
    }
};
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