<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:
    def strangePrinter(self, s: str) -> int:
        memo = {}
        def helper(i,j):
            if (i,j) in memo:
                return memo[(i,j)]

            if i==j: #single char
                return 1
            
            elif i==j-1: #two chars, could be same
                    return 1 if s[i] == s[j] else 2
            
            # case 1: reuse starting character for the end too if both same (a in aba)
            turns = float('inf') #cuz wont be calculated if start end diff
            if s[i] == s[j]:
                turns = helper(i,j-1)
            
            #case 2: dont resuse, split string at every index and get minimum turns needed to form it entirely
            for k in range(i,j):
                turns = min(turns, helper(i,k) + helper(k+1,j))

            memo[(i,j)] = turns
            return turns
        
        return helper(0,len(s)-1)
20500