<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 dp[101][101];

    string removeDuplicates(string s){
        int n = s.length();
        char prev = '*';
        string ans;
        for(int i=0;i<n;i++){
            if(s[i] == prev){
            }
            else{
               ans += s[i];
               prev = s[i];
            }
        }
        return ans;
    }

    int helper(int i, int j, string s){
    if(i>j){
        return 0;
    }
    if(i==j){
        return 1;
    }
    if(dp[i][j] != -1){
        return dp[i][j];
    }

    int ans = 1 + helper(i+1,j,s);
    for(int k=i+1;k<=j;k++){
        if(s[k]==s[i]){
            ans = min(ans,helper(i,k-1,s) + helper(k+1,j,s));
        }
    }
    return dp[i][j] = ans;
    }

    int strangePrinter(string s) {
        s = removeDuplicates(s);
        cout<<s;
        int n = s.length();
        memset(dp,-1,sizeof(dp));
        return helper(0,n-1,s);
    }
};
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