<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> m;
        return helper(0, s.length() - 1, s, m);        
    }

private:
    int helper(int i, int j, const std::string& s, std::unordered_map<std::string, int>& m) {
        if (i > j) {
            return 0;
        }
        
        std::string k = std::to_string(i) + "-" + std::to_string(j);
        if (m.count(k)) {
            return m[k];
        }
        
        int r = helper(i, j - 1, s, m) + 1;

        for (int p = i; p < j; p++) {
            if (s[p] == s[j]) {
                r = std::min(r, helper(i, p, s, m) + helper(p + 1, j - 1, s, m));
            }
        }
        
        m[k] = r;
        return r;
    }    
};

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