<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 strangePrinterImpl(
        const std::string& s,
        std::unordered_map<std::string, int>& cache)
    {
        auto cached = cache.find(s);
        if (cached != cache.end()) {
            return cached->second;
        }

        std::vector<int> results = {0};
        for (size_t i = 0; i < s.size(); ++i) {
            int currentResult = results.back() + 1;
            for (size_t previous = 0; previous < i; ++previous) {
                if (s[previous] == s[i]) {
                    currentResult = std::min(
                        currentResult,
                        results[previous + 1] + strangePrinterImpl(s.substr(previous + 1, i - previous - 1), cache)
                    );
                }
            }

            results.push_back(currentResult);
        }

        cache[s] = results.back();
        return results.back();
    }

    int strangePrinter(string s) {
        std::unordered_map<std::string, int> cache;

        return strangePrinterImpl(s, cache);
    }
};
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