<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][256], n;
    string str;

    int rec(int i, int j, char b) {
        if (i > j) return 0;
        if (i == j) return 1;
        if (dp[i][j][b] != 0) return dp[i][j][b];
        int ans = j-i+1;

        // no base.
        if (str[i] == str[j]) {
            ans = min(ans, 1 + rec(i+1, j-1, str[i]));
        } else {
            ans = min(ans, 1 + min(rec(i+1, j, str[i]), rec(i, j-1, str[j])));
        }
        for (int k = i; k <= j; k++) {
            if (str[k] == b) {
                ans = min(ans, rec(i, k-1, b) + rec(k+1, j, b));
            }
            if (k != j)
            ans = min(ans, rec(i, k, '0') + rec(k+1, j, '0'));
        }
        return dp[i][j][b] = ans;
    }
    
    int strangePrinter(string s) {
        string condensed;
        condensed.push_back(s[0]);
        for (auto c : s) {
            if (condensed.back() == c) continue;
            else condensed.push_back(c);
        }
        str = condensed;
        n = condensed.size();
        return rec(0, n-1, '0');   
    }
};
19482