<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) {
        this->s.push_back(s[0]);
        for (int i = 1; i < s.length(); ++i) {
            if (s[i] != s[i - 1]) {
                this->s.push_back(s[i]);
            }
        }
        return dfs(0, this->s.length() - 1);
    }

private:
    std::string s;
    std::unordered_map<std::string, int> dp;

    int dfs(int left, int right) {
        std::string key = to_string(left) + "," + to_string(right);
        if (dp.count(key)) return dp[key];
        if (left > right) return 0;
        int ret = dfs(left + 1, right) + 1;
        for (int i = left + 2; i <= right; ++i) {
            if (s[i] == s[left]) {
                ret = min(ret, dfs(left, i - 1) + dfs(i + 1, right));
            }
        }
        return dp[key] = ret;
    }
};
31117