<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 rec(string& s, std::unordered_map<string, int>& memo){
        if (s.size() == 1)
            return 1;
        
        if (memo.count(s)>0)
            return memo[s];

        char a = s.back();
        s.pop_back();
        
        int val = rec(s, memo) + 1;
        for(int i=s.size()-1; i>=0; --i){
            if (s[i] != a)
                continue;
            auto part1 = s.substr(0, i+1);
            auto part2 = s.substr(i+1);
            val = std::min(val, rec(part1, memo) + rec(part2, memo));
        }
        s.push_back(a);
        memo[s] = val;
        return val;
    }

    int strangePrinter(string s) {
        string opts;
        opts.push_back(s[0]);
        for(int i=1; i<s.size(); ++i){
            if (s[i] == s[i-1])
                continue;
            opts.push_back(s[i]);
        }

        std::unordered_map<string, int> memo;

        return rec(opts, memo);
    }
};
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