<p>There is a strange printer with the following two special properties:</p>

<ul>
	<li>The printer can only print a sequence of <strong>the same character</strong> each time.</li>
	<li>At each turn, the printer can print new characters starting from and ending at any place and will cover the original existing characters.</li>
</ul>

<p>Given a string <code>s</code>, return <em>the minimum number of turns the printer needed to print it</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aaabbb&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> Print &quot;aaa&quot; first and then print &quot;bbb&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aba&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> Print &quot;aaa&quot; first and then print &quot;b&quot; from the second place of the string, which will cover the existing character &#39;a&#39;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 100</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution {
public:
    int minturns(int i,string s,int n,vector<vector<int>>&memo){
        if(i==n){
            return 0;
        }
         if(memo[i][n]!=-1){
            return memo[i][n];
         }
        int miniturns=1+minturns(i+1,s,n,memo);
        //finding optimal possibilities
        for(int k=i+1;k<n;k++){
              if(s[i] == s[k]){
                int matchturns=minturns(i,s,k,memo)+minturns(k+1,s,n,memo);
                 miniturns=min(miniturns,matchturns);
              }
             
        }
        return memo[i][n]=miniturns;
    }
    string removeduplicates(string s){
        string r="";int i=0;
        while(i<s.length()){
            r+=s[i];
            char curr=s[i];
            while(i<s.length() && s[i]==curr){
                i++;
            }
            
        }
        return r;
    }
    int strangePrinter(string s) {
        s = removeduplicates(s);
        int n=s.length();
        vector<vector<int>>memo(n+1,vector<int>(n+1,-1));
        return minturns(0,s,n,memo);
         
    }
  
};
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