<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 s1 = s[0];
        // s1.push_back(s[0]);
        for (int i = 1; i < s.size(); i++) {
            if (s[i] != s[i-1]) {
                s1.push_back(s[i]);
            }
        }
        // cout << "orig:" << s << endl;
        // cout << s1 << endl;
        n = s1.size();
        dp.resize(n*n*as, -1);
        // cout << "size: " << n*n*as << endl;
        return 1 + rec(0, n, s[0]);
    }

    int rec(int start, int end, char c) {
        if (start >= end) {
            return 0;
            // if (s1[start] == c) {
            //     return 0;
            // } else {
            //     return 1;
            // }
        }
        // if (start > end) {
        //     return 0;
        // }
        int id = get_id(start, end, c);
        if (dp[id] != -1) {
            // cout << "!" << endl;
            return dp[id];
        }
        if (s1[start] == c) {
            // cout << "!!" << endl;
            return dp[id] = rec(start+1,end,c);
        }
        int res = INT_MAX;
        char curr = s1[start];
        // res = min(res,)
        for (int i = start; i < end; i++) {
            if (s1[i] == curr) {
                int v = rec(start, i+1, curr) + 1 + rec(i+1, end, c);
                res = min(res, v);
            }
            // int v = rec()
        }
        return dp[id] = res;
    }

    int get_id(int start, int end, char c) {
        // cout << start << " : " << end << " : " << c << " : " << n*as*start + as*end + int(c-'a') << endl;
        return n*as*start + as*(end-1) + int(c-'a');
    }

    const int as = 26;
    int n;
    vector<int> dp;
    string s1;
};
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