<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 solve(int i, int j, string s, vector<vector<int>> &dp)
    {
        if(dp[i][j]!=-1)
        return dp[i][j];
        if(i==j)
        return dp[i][j]=1;
        else if(i>j)
        return dp[i][j]=0;
        else if(s[i]==s[j])
        return dp[i][j]=solve(i+1,j,s,dp);
        else{
            int ans=INT_MAX;
            ans=min(ans,1+solve(i+1,j,s,dp));
            for(int k=i+1;k<j;k++)
            {
                if(s[i]==s[k])
                {
                    int xx,yy;
                    if(dp[i][k]!=-1)
                    xx=dp[i][k];
                    else xx=solve(i,k,s,dp);
                    if(dp[k+1][j]!=-1)
                    yy=dp[k+1][j];
                    else yy=solve(k+1,j,s,dp);
                    ans=min(ans,xx+yy);
                }
            }
            return dp[i][j]=ans;
        }
    }

    int strangePrinter(string s) {
        string ss="";
        int n=s.length();
        ss+=s[0];
        for(int i=1;i<n;i++)
        {
            if(s[i]!=s[i-1])
            {
                ss+=s[i];
            }
        }
        n=ss.length();
        vector<vector<int>> dp(n,vector<int>(n,-1));
        return solve(0,n-1,ss,dp);
        return 0;
    }
};
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