<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:
    int memo[50][1 << 15];
    Solution () {
        memset(memo, -1, sizeof (memo));
    }
    int minStickers(vector<string>& stickers, string target) {
        vector<vector<int>> freq(stickers.size(), vector<int> (26, 0));
        for (int i = 0; i < stickers.size(); ++i) {
            for (int j = 0; j < stickers[i].length(); ++j) {
                freq[i][stickers[i][j] - 'a']++;
            }
        }
        int res = dp(0, 0, freq, target);
        if (res > 15) {
            res = -1;
        }
        return res;
    }

    int dp(int id, int mask, vector<vector<int>> &freq, string &target) {
        if (mask == ((1 << target.length()) - 1)) {
            return 0;
        }
        if (id == freq.size()) {
            return 20;
        }
        if (memo[id][mask] != -1) {
            return memo[id][mask];
        }
        int res1 = dp(id + 1, mask, freq, target);
        int newMask = mask;
        vector<pair<int, int>> changedFreq;
        for (int i = 0; i < target.length(); ++i) {
            if ((newMask & (1 << i)) == 0) {
                if (freq[id][target[i] - 'a']) {
                    --freq[id][target[i] - 'a'];
                    changedFreq.emplace_back(id, target[i] - 'a');
                    newMask = newMask | (1 << i);
                }
            }
        }
        int res2 = 20;
        for (auto element: changedFreq) {
            ++freq[element.first][element.second];
        }
        if (mask != newMask)
            res2 = 1 + dp(id, newMask, freq, target);
        return memo[id][mask] = min(res1, res2);
    }
};
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