<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 n, m;
    vector<int> dp;
    vector<vector<int>> stateMap;
    string target;
    vector<string> strs;
    const int INF = 1e9;

    int minStickers(vector<string>& stickers, string _target) {
        strs = stickers, target = _target;
        n = target.size(), m = strs.size();
        dp = vector<int>(1 << n, -1);
        stateMap = vector<vector<int>>(1 << n, vector<int>(26, -1));
        int res = dfs(0);
        if (res == INF) res = -1;
        return res;
    }

    int fill(int state, char c) {
        if (stateMap[state][c - 'a'] != -1) return stateMap[state][c - 'a'];
        stateMap[state][c - 'a'] = state;
        for (int i = 0; i < n; i ++) {
            if (!((state >> i) & 1) && target[i] == c) {
                stateMap[state][c - 'a'] = state + (1 << i);
                break;
            }
        }
        return stateMap[state][c - 'a'];
    }

    int dfs(int state) {
        if (dp[state] != -1) return dp[state];
        if (state == (1 << n) - 1) {
            dp[state] = 0;
            return 0;
        }
        dp[state] = INF;
        for (auto& s: strs) {
            int newState = state;
            for (char c: s) {
                newState = fill(newState, c);
            }
            if (newState != state) {
                dp[state] = min(dp[state], dfs(newState) + 1);
            }
        }
        return dp[state];
    }
};
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