<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:

    string removeDuplicate(string s) {
        char p = s[0];
        string s1;
        s1 += p;

        for (int i=1; i<s.length(); i++) {
            if (s[i]==p) continue;
            s1 += s[i];
            p = s[i];
        }
        return s1;
    }

    int minTurns(int start, int end, string s, int** memo) {
        if (start > end) return 0;

        if (memo[start][end]!=-1) return memo[start][end];

        int min2 = 1 + minTurns(start+1, end, s, memo);
        //std::cout<<start<<" : " << end << " " << min2 << endl;
        for (int k=start+1; k<=end; k++) {
            if (s[start]==s[k]) {
                int m1 = minTurns(start, k-1, s, memo) + minTurns(k+1, end, s, memo);
                min2 =  min2>m1 ? m1 : min2;
            }
        }
        //std::cout<<start<<" :: " << end << " " << min2 << endl;
        memo[start][end] = min2;
        return min2;
    }

    int strangePrinter(string s) {
        string s1 = removeDuplicate(s);
        int n = s1.length();
        int **memo = new int*[n];
        for (int i=0; i<n; i++) {
            memo[i] = new int[n];
            for (int j=0; j<n; j++) {
                memo[i][j] = -1;
            }
        }
    
        return minTurns(0, n-1, s1, memo);
    }
};
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