<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 recf(int i, int j, string s, vector<vector<int>> &memo){
        if (i > j) return 0;           
        if (i == j) return 1;            
        if (memo[i][j] != -1) return memo[i][j]; 
        
        int result = recf(i + 1, j,s,memo) + 1;   

        for (int k = i + 1; k <= j; ++k) {
            if (s[k] == s[i]) {
                result = min(result, recf(i, k - 1,s,memo) + recf(k + 1, j,s,memo));
            }
        }
        return memo[i][j] = result;
    };
    int strangePrinter(string &s) {
        if (s.empty()) return 0;
        std::string filtered_s;
        for (char c : s) {
            if (filtered_s.empty() || c != filtered_s.back()) {
                filtered_s.push_back(c);
            }
        }
        int n = filtered_s.size();
        vector<vector<int>> memo(n, vector<int>(n, -1));
        return recf(0, n - 1,filtered_s,memo);
    }
};

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