<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:
    vector<vector<int>> dp;
    int solver(int l , int r , string s1)
    {
      if(l == r)
        return 1;
      if(l > r)
        return 0;
      if(dp[l][r] != -1)
        return dp[l][r];  

      int c1 = 1 + solver(l+1,r,s1);
      int c2 = INT_MAX;
      for(int j=l+1;j<=r;j++)
      {
        if(s1[j] == s1[l])
        {
          int temp = solver(l+1,j-1,s1) + solver(j,r,s1);
          c2 = min(c2 , temp); 
        }
      }    
      return dp[l][r] = min(c1,c2);
    }

    int strangePrinter(string s) {
       int n = s.size();
       string s1 = "";
       s1 += s[0];
       char prev = s[0];
       for(int i=1;i<n;i++)
       {
         if(s[i] != prev)
         {
           s1 += s[i];
           prev = s[i];  
         }      
       } 
       int n1 = s1.size();
       dp.resize(n1+1,vector<int>(n1+1,-1));
       return solver(0 , n1-1 , s1);
    }
};
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