<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:
    unordered_map<uint64_t, int> cache;
    uint64_t getRangeKey(int start, int end) {
        uint64_t ret = ((uint64_t)start) << 32;
        ret |= end;
        return ret;
    }

    int helper(const string & s, int start, int end) {
        if (start >= end) return 0;
        auto key = getRangeKey(start, end);
        if (cache.find(key) != cache.end()) {
            // std::cout << ">>> hit cache: " << s.substr(start, end - start) << std::endl;
            return cache[key];
        }
        int cost = helper(s, start, end - 1) + 1;
        int len = end - start;
        for (int i = start; i < end - 1; i++) {
            if (s[i] == s[end - 1]) {
                cost = min(cost, helper(s, start, i + 1) + helper(s, i + 1, end - 1));
            }
        }
        // std::cout << ">>> " << s.substr(start, end - start) << ", " << cost << std::endl;
        cache[key] = cost;
        return cost;
    }

    int strangePrinter(string s) {
        return helper(s, 0, s.length());
    }
};
25747