<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) 
    {
        std::memset(dp_, 0x3f, sizeof(dp_));
        int n = target.size();

        dp_[0] = 0;
        for (int state = 0; state < (1 << n); ++state)
        {
            for (auto&& sticker : stickers)
            {
                int nextState = findNextState(sticker, target, state);
                dp_[nextState] = std::min(dp_[nextState], dp_[state] + 1);
            }
        }

        if (dp_[(1 << n) - 1] >= 0x3f3f3f3f)
            return -1;
        return dp_[(1 << n) - 1];
    }

private:
    int findNextState(const std::string& sticker, const std::string& target, int state)
    {
        int n = target.size();
        int newState = state;
        for (auto ch : sticker)
        {
            for (int i = 0; i < n; ++i)
            {
                if (((newState >> i) & 0b01) == 0 && ch == target[i])
                {
                    newState |= (1 << i);
                    break;
                }
            }
        }

        return newState;
    }

private:
    int dp_[(1 << 15) + 1];
};
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