<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) {
        string str; str.reserve(s.size());
        str.push_back(s[0]);
        for (int i = 1; i < s.size(); ++i) {
            if (s[i] != s[i - 1]) {
                str.push_back(s[i]);
            }
        }
        cout << str << endl;

        int n = str.size();
        dp = vector<vector<int>>(n, vector<int>(n, 10000));
        for (int i = 0; i < n; ++i) {
            dp[i][i] = 1;
        }

        for (int i = n - 2; i >= 0; --i) {
            for (int j = i + 1; j < n; ++j) {
                vector<pair<int, int>> g;
                int first = -1;
                for (int k = i + 1; k <= j; ++k) {
                    if (first == -1 && str[k] != str[i]) {
                        first = k;
                    }

                    if (first != -1 && str[k] == str[i]) {
                        g.emplace_back(first, k - 1);
                        first = -1;
                    }
                }
                if (first != -1) {
                    g.emplace_back(first, j);
                }
                int min_val = 1000;
                TraverseGroupings(g, 0, 0, min_val);
                dp[i][j] = 1 + min_val;
            }
        }
        return dp[0][n - 1];
    }

    void TraverseGroupings(const vector<pair<int, int>>& g, int start, int val, int& min_val) {
        if (start == g.size()) {
            min_val = min(min_val, val);
            return;
        }

        for (int finish = start; finish < g.size(); ++finish) {
            TraverseGroupings(g, finish + 1, val + dp[g[start].first][g[finish].second], min_val);
        }
    }

    vector<vector<int>> dp;
};
28432