<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 {
private:
    int strangePrinterHelper(unordered_map<string, int>& cachedResults, string s) {
        if(s == "") { return 0; }
        if(cachedResults.contains(s)) { return cachedResults[s]; }

        int minOperations = strangePrinterHelper(cachedResults, s.substr(1)) + 1;
        for(int i = 1; i < s.length(); i++) {
            if(s[0] == s[i]) {
                minOperations = min(minOperations, strangePrinterHelper(cachedResults, s.substr(0, i)) + strangePrinterHelper(cachedResults, s.substr(i + 1)));
            }
        }
        cachedResults[s] = minOperations;
        return minOperations;
    }

public:
    int strangePrinter(string s) {
        unordered_map<string, int> cachedResults;
        return strangePrinterHelper(cachedResults, s);
    }
};
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