<p>We are given <code>n</code> different types of <code>stickers</code>. Each sticker has a lowercase English word on it.</p>

<p>You would like to spell out the given string <code>target</code> by cutting individual letters from your collection of stickers and rearranging them. You can use each sticker more than once if you want, and you have infinite quantities of each sticker.</p>

<p>Return <em>the minimum number of stickers that you need to spell out </em><code>target</code>. If the task is impossible, return <code>-1</code>.</p>

<p><strong>Note:</strong> In all test cases, all words were chosen randomly from the <code>1000</code> most common US English words, and <code>target</code> was chosen as a concatenation of two random words.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> stickers = [&quot;with&quot;,&quot;example&quot;,&quot;science&quot;], target = &quot;thehat&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
We can use 2 &quot;with&quot; stickers, and 1 &quot;example&quot; sticker.
After cutting and rearrange the letters of those stickers, we can form the target &quot;thehat&quot;.
Also, this is the minimum number of stickers necessary to form the target string.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> stickers = [&quot;notice&quot;,&quot;possible&quot;], target = &quot;basicbasic&quot;
<strong>Output:</strong> -1
Explanation:
We cannot form the target &quot;basicbasic&quot; from cutting letters from the given stickers.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == stickers.length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>1 &lt;= stickers[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= target.length &lt;= 15</code></li>
	<li><code>stickers[i]</code> and <code>target</code> consist of lowercase English letters.</li>
</ul>

class Solution {
public:
    unordered_map<string, int> dp;
    vector<string> sticker_hist;
    int fillDp(const string& target) {
        if (dp.find(target) != dp.end()) return dp[target];
        int min_stickers = INT_MAX;
        for (string hist: sticker_hist) {
            // Apply sticker on target.
            string reduced;
            reduced.reserve(target.size());
            for (char c: target) {
                if (hist[c-'a']) {
                    hist[c-'a']--;
                } else {
                    reduced.push_back(c);                    
                }
            }
            if (reduced == target) {
                // No reduction.
                continue;
            }
            if (fillDp(reduced) != -1) {
                min_stickers = min(min_stickers, 1 + fillDp(reduced));
            }
        }
        dp[target] = min_stickers == INT_MAX ? -1 : min_stickers;
        return dp[target];
    }
    int minStickers(vector<string>& stickers, string target) {
        // dp[s] -> minimum stickers to build s where s is sorted.
        for (const string& sticker: stickers) {
            string hist(26, 0);
            for (char c: sticker) {
                hist[c-'a']++;
            }
            sticker_hist.push_back(hist);
        }
        sort(target.begin(), target.end());
        dp[""] = 0;
        return fillDp(target);
    }
};
129503