<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 {

    vector<vector<int>> v;
    map<vector<int>, unordered_map<int, int>> c;

    vector<int> count(string &s) {
        vector<int> m('z' - 'a' + 1, 0);
        for (char c : s) {
            m[c - 'a']++;
        }
        return m;
    }

    int dp(int pos, vector<int> &target) {
        if (pos == v.size()) {
            bool allZeroes = true;
            for (int i : target) {
                if (i != 0) {
                    allZeroes = false;
                    break;
                }
            }
            return allZeroes ? 0 : INT_MAX;
        }

        if (c.count(target) && c[target].count(pos)) {
            return c[target][pos];
        }

        c[target][pos] = INT_MAX;
        int &res = c[target][pos];
        // do not take
        res = min(res, dp(pos + 1, target));

        // take
        bool take = false;
        auto t = target;
        for (int i = 0; i < target.size(); i++) {
            if (v[pos][i] > 0 && target[i] > 0) {
                t[i] -= min(target[i], v[pos][i]);
                take = true;
            }
        }

        if (take) {
            int subRes = dp(pos, t);
            if (subRes != INT_MAX) {
                res = min(res, 1 + subRes);
            }
        }

        return res;
    }

public:
    int minStickers(vector<string>& stickers, string target) {
        for (auto &s : stickers) {
            v.push_back(count(s));
        }

        auto t = count(target);
        int res = dp(0, t);
        return res == INT_MAX ? -1 : res;
    }
};
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