<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 strangePrinter(string s) {
        std::unordered_map<std::string, int> memo;
        return min_turns_to_print(0, s.length() - 1, s, memo);        
    }

private:
    int min_turns_to_print(int start, int end, const std::string& s, std::unordered_map<std::string, int>& memo) {
        if (start > end) {
            return 0;
        }
        
        std::string key = std::to_string(start) + "-" + std::to_string(end);
        if (memo.count(key)) {
            return memo[key];
        }
        
        int res = min_turns_to_print(start, end - 1, s, memo) + 1;

        for (int middle = start; middle < end; middle++) {
            if (s[middle] == s[end]) {
                res = std::min(res, min_turns_to_print(start, middle, s, memo) + min_turns_to_print(middle + 1, end - 1, s, memo));
            }
        }
        
        memo[key] = res;
        return res;
    }    
};
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