<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:

    string getKey(map<char, int>& m) {
        string key;
        for (auto&[c, cnt]: m) {
            key += string(1, c) + to_string(cnt) + ",";
        }
        return key;
    }

    bool contains(map<char, int>& a, map<char, int> &b) {
        for (auto&[c, _]: b) {
            if (a[c] > 0)
                return true;
        }
        return false;
    }

    int visit(vector<map<char, int>>& stickers, map<char, int>& target, map<string, int>& memo) {
        if (target.empty()) return 0;
        
        string k = getKey(target);
        if (memo.contains(k)) return memo[k];

        int ret = INT_MAX;
        for (auto& stick: stickers) {
            if (!contains(stick, target)) {
                continue;
            }
            map<char, int> newTarget;
            for (auto&[c, cnt]: target) {
                int remain = cnt - stick[c];
                if (remain > 0) {
                    newTarget[c] = cnt - stick[c];
                }
            }
            ret = min(ret, 1 + visit(stickers, newTarget, memo));
        }
        memo[getKey(target)] = ret;
        return ret;
    }

    int minStickers(vector<string>& stickers, string target) {
        vector<bool> st(26, false);
        for (auto& s: stickers) {
            for (auto c: s) {
                st[c-'a'] = true;
            }
        }
        for (auto c: target) {
            if (!st[c-'a']) {
                return -1;
            }
        }

        map<char, int> t;
        for (auto& c:target) {
            t[c] ++;
        }

        vector<map<char, int>> sts;
        for (auto& s: stickers) {
            map<char, int> m;
            for (char& c: s) {
                if (t.contains(c)) {
                    m[c]++;
                }
            }
            sts.push_back(m);
        }


        map<string, int> memo;
        return visit(sts, t, memo);
    }
};
382618