<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 dphelper(string s,int start,int end,vector<vector<int>>& dp){
        if(start>end)   return 0;
        if(dp[start][end]!=0)   return dp[start][end];

        dp[start][end]=dphelper(s,start, end - 1, dp) + 1;
        for(int i=start;i<end;i++){
            if(s[i]==s[end]){
                dp[start][end]=min(dp[start][end],/*dphelper(s, start, i, dp)*/dp[start][i] + dphelper(s, i + 1, end - 1, dp));
            }
        }

        return dp[start][end];
    }
    int strangePrinter(string s) {
        if(s.size()==0) return 0;

        string s2;
        s2+=s[0];
        for(int i=1;i<s.size();i++){
            if(s[i-1]!=s[i]){
                s2+=s[i];
            }
        }

        if(s2.size()==1) return 1;

        int n = s2.size();
        vector<vector<int>> dp(n, vector<int>(n, 0));

        return dphelper(s2,0,n-1,dp);
    }
};
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