<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 {
    static constexpr int MAX = 101;
    vector<vector<int>> dp_;

    int solve(const string& s, string& res, int start, int end) {
        while (start < end && res[start] == s[start]) {
            ++start;
        }
        if (start == end) return 0;
        auto& cached = dp_[start][end];
        if (cached != 0) return cached;

        int ans = MAX;
        string copy = res;
        for (int i = start; i < end; ++i) {
            for (int j = start; j < end; ++j) res[j] = copy[j];

            fill(res.begin() + start, res.begin() + i + 1, s[i]);
            auto p1 = solve(s, res, start, i);
            auto p2 = solve(s, res, i + 1, end);
            auto curAns = 1 + p1 + p2;
            ans = min(ans, curAns);
        }
        cached = ans;
        return ans;
    }

public:
    int strangePrinter(string s) {
        dp_.resize(MAX, vector<int>(MAX, 0));
        string res(s.size(), '-');
        return solve(s, res, 0, s.size());
    }
};
52597