<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>

#include <vector>
#include <string>
#include <unordered_map>
#include <algorithm>
#include <climits>

using namespace std;

class Solution {
public:
    int minStickers(vector<string>& stickers, string target) {
        vector<unordered_map<char, int>> stickCount;
        for (const auto& sticker : stickers) {
            unordered_map<char, int> countMap;
            for (char c : sticker) {
                countMap[c]++;
            }
            stickCount.push_back(countMap);
        }

        unordered_map<string, int> cache;
        cache[""] = 0; // Base case: empty string requires 0 stickers.

        function<int(string)> DFS;
        DFS = [&](string substr) -> int {
            if (cache.find(substr) != cache.end()) return cache[substr];

            int res = INT_MAX;
            for (const auto& sticker : stickCount) {
                if (sticker.find(substr[0]) == sticker.end()) continue;  // Skip if the sticker does not have the first character of the substring.

                string remainT;
                unordered_map<char, int> tempCount = sticker;
                for (char ch : substr) {
                    if (tempCount[ch] > 0) {
                        tempCount[ch]--;
                    } else {
                        remainT += ch;
                    }
                }

                if (remainT.size() != substr.size()) {  // Sticker made some progress.
                    int subRes = DFS(remainT);
                    if (subRes != INT_MAX) {
                        res = min(res, 1 + subRes);
                    }
                }
            }

            cache[substr] = res;
            return res;
        };

        int result = DFS(target);
        return result == INT_MAX ? -1 : result;
    }
};
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