<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 util(string s, vector<vector<int>> &memo, int start, int end)
{
    if (memo[start][end] != -1)
    {
        return memo[start][end];
    }
    if (start == end)
    {
        memo[start][end] = 1;
        return 1;
    }

    int size = end - start + 1;

    memo[start][start] = 1;
    for (int i = 1; i < size; i++)
    {
        int index = start + i;
        if (s[index] == s[index - 1])
        {
            memo[start][i + start] = memo[start][i - 1 + start];
        }
        else
        {

            memo[start][i + start] = memo[start][i - 1 + start] + 1;
            int left = index - 1;
            while (left >= start)
            {
                if (s[left] == s[index])
                {
                    memo[start][i + start] = min(memo[start][left] + util(s, memo, left + 1, index - 1), memo[start][i + start]);
                }
                left--;
            }
        }
    }

    return memo[start][end];
}

int strangePrinter(string s)
{
    int len = s.length();

    vector<vector<int>> memo(len, vector<int>(len, -1));

    return util(s, memo, 0, len - 1);
}
};
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