<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 = stickers.size();

        vector<vector<int>> stickerCounts(n, vector<int>(26, 0));
        for (int i = 0; i < n; ++i) {
            string sticker = stickers[i];

            for (int cIdx = 0; cIdx < sticker.length(); ++cIdx) {
                ++stickerCounts[i][sticker[cIdx] - 'a'];
            }
        }

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

        return minStickersDfs(stickerCounts, target, cache);
    }

private:
    int minStickersDfs(vector<vector<int>>& stickerCounts, string& target, unordered_map<string, int>& cache) {
        if (cache.find(target) != cache.end()) {
            return cache[target];
        }

        vector<int> targetCount(26, 0);
        for (int i = 0; i < target.length(); ++i) {
            ++targetCount[target[i] - 'a'];
        }

        int result = INT_MAX;
        for (int i = 0; i < stickerCounts.size(); ++i) {
            vector<int> stickerCount = stickerCounts[i];

            if (stickerCount[target[0] - 'a'] == 0) {
                continue;
            }

            string newTarget;
            for (int cIdx = 0; cIdx < 26; ++cIdx) {
                if (targetCount[cIdx] > 0) {
                    int remain = targetCount[cIdx] - stickerCount[cIdx];

                    for (int k = 0; k < std::max(remain, 0); ++k) {
                        newTarget.push_back('a' + cIdx);
                    }
                }
            }

            int tempRes = minStickersDfs(stickerCounts, newTarget, cache);
            if (tempRes != -1) {
                result = std::min(result, tempRes + 1);
            }
        }

        if (result < INT_MAX) {
            cache[target] = result;
            return result;
        } else {
            cache[target] = -1;
            return -1;
        }
    }
};
68976