<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 dp[102][102];
    
    int solve(string s, int l, int r){
        if(l>r) return 0;
        if(l==r) return 1;
        
        if(dp[l][r]!=-1) return dp[l][r];
        
        int ans = 1+solve(s, l+1, r);
        
        for(int i = l+1; i <= r; i++){
            if(s[l]==s[i]){
                ans = min(ans, solve(s, l+1, i-1)+solve(s, i, r));
            }
        }
        
        return dp[l][r] = ans;
    }
    
    int strangePrinter(string s) {
        string str = "";
        str += s[0];
        
        for(int i = 1; i < s.size(); i++){
            if(s[i]==s[i-1]) continue;
            str += s[i];
        }
        
        memset(dp, -1, sizeof(dp));
        return solve(str, 0, str.size()-1);
    }
};
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