<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 dfs(vector<vector<int>>& freq, string target, unordered_map<string, int>& memo) {
        if (memo.count(target)) {
            return memo[target];
        }
        vector<int> cnt(26, 0);
        for (auto ch : target) {
            cnt[ch - 'a']++;
        }
        int ans = INT_MAX;
        for (auto bucket : freq) {
            bool check = false;
            for (int i = 0; i < 26; i++) {
                if (cnt[i] > 0 && bucket[i] > 0) {
                    check = true;
                    break;
                }
            }
            if (!check) {
                continue;
            }
            string t = "";
            for (int i = 0; i < 26; i++) {
                if (bucket[i] < cnt[i]) {
                    t += string(cnt[i] - bucket[i], i + 'a');
                }
            }
            auto res = dfs(freq, t, memo);
            if (res != -1) {
                ans = min(ans, res+1);
            }
        }
        if (ans == INT_MAX) {
            memo[target] = -1;
        } else {
            memo[target] = ans;
        }
        return memo[target];
    }

    int minStickers(vector<string>& stickers, string target) {
        vector<vector<int>> freq;
        for (auto word : stickers) {
            vector<int> bucket(26, 0);
            for (auto ch : word) {
                bucket[ch-'a']++;
            }
            freq.push_back(bucket);
        }

        unordered_map<string, int> memo;
        memo[""] = 0;

        return dfs(freq, target, memo);
    }
};
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