<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 minStickers(vector<string>& stickers, string target) {
        int n = target.size();
        int init_state = (1 << n) - 1;
        vector<int> memo(1 << n, -1);
        memo[0] = 0;

        // Precompute frequency counts of stickers
        vector<vector<int>> stickerCounts;
        for (const string& sticker : stickers) {
            vector<int> count(26, 0);
            for (char c : sticker) {
                count[c - 'a']++;
            }
            stickerCounts.push_back(count);
        }

        int res = gen(init_state, stickerCounts, target, memo);
        return (res == INT_MAX) ? -1 : res;
    }

    int gen(int state, vector<vector<int>>& stickerCounts, string& target, vector<int>& memo) {
        if (memo[state] != -1)
            return memo[state];
        int res = INT_MAX;

        int n = target.size();

        for (const vector<int>& f : stickerCounts) {
            bool useful = false;
            for (int i = 0; i < n; ++i) {
                if ((state >> i) & 1 && f[target[i] - 'a'] > 0) {
                    useful = true;
                    break;
                }
            }
            if (!useful)
                continue;

            int newState = state;
            vector<int> f_copy = f;
            for (int i = 0; i < n; ++i) {
                if (!((state >> i) & 1))
                    continue;
                char c = target[i];
                if (f_copy[c - 'a'] > 0) {
                    f_copy[c - 'a']--;
                    newState ^= (1 << i);
                }
            }

            int newRes = gen(newState, stickerCounts, target, memo);
            if (newRes != INT_MAX)
                res = min(res, newRes + 1);
        }
        memo[state] = res;
        return res;
    }
};

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