<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:
    unordered_map<string , int> dp;
    int traverse(vector<unordered_map<char , int>> &stickers , unordered_map<char , int> &tar){
        bool isempty = true;
        string target;
        for(auto &i: tar){
            target += string( i.second , i.first);
            if(i.second > 0){
                isempty = false;
            }
        }
        if(isempty){
            return 0;
        }
        if(dp.find(target) != dp.end()){
            return dp[target];
        }
        int result = INT32_MAX;

        for(auto &sticker : stickers){
            if(sticker.find(target[0]) == sticker.end()){
                continue;
            }
            unordered_map<char , int> temp = tar;
            for(auto &i : sticker){
                temp[i.first] -= i.second;
                if(temp[i.first]<0)     temp[i.first] = 0;
            }
            int tempResult = traverse(stickers , temp);
            if(tempResult != -1){
                result = min(result , 1 + tempResult);
            }
        }
        if(result == INT32_MAX){
            result = -1;
        }
        return dp[target] = result;
    }
    int minStickers(vector<string>& stickers, string target) {
        vector<unordered_map<char , int>> sticker;
        for(auto i : stickers){
            unordered_map<char , int> mp;
            for(auto j : i){
                mp[j]++;
            }
            sticker.push_back(mp);
        }
        unordered_map<char , int> tar;
        for(auto i : target){
            tar[i]++;
        }
        return traverse(sticker , tar);
    }
};
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