<p>You are given an integer array <code>cards</code> of length <code>4</code>. You have four cards, each containing a number in the range <code>[1, 9]</code>. You should arrange the numbers on these cards in a mathematical expression using the operators <code>[&#39;+&#39;, &#39;-&#39;, &#39;*&#39;, &#39;/&#39;]</code> and the parentheses <code>&#39;(&#39;</code> and <code>&#39;)&#39;</code> to get the value 24.</p>

<p>You are restricted with the following rules:</p>

<ul>
	<li>The division operator <code>&#39;/&#39;</code> represents real division, not integer division.

	<ul>
		<li>For example, <code>4 / (1 - 2 / 3) = 4 / (1 / 3) = 12</code>.</li>
	</ul>
	</li>
	<li>Every operation done is between two numbers. In particular, we cannot use <code>&#39;-&#39;</code> as a unary operator.
	<ul>
		<li>For example, if <code>cards = [1, 1, 1, 1]</code>, the expression <code>&quot;-1 - 1 - 1 - 1&quot;</code> is <strong>not allowed</strong>.</li>
	</ul>
	</li>
	<li>You cannot concatenate numbers together
	<ul>
		<li>For example, if <code>cards = [1, 2, 1, 2]</code>, the expression <code>&quot;12 + 12&quot;</code> is not valid.</li>
	</ul>
	</li>
</ul>

<p>Return <code>true</code> if you can get such expression that evaluates to <code>24</code>, and <code>false</code> otherwise.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> cards = [4,1,8,7]
<strong>Output:</strong> true
<strong>Explanation:</strong> (8-4) * (7-1) = 24
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> cards = [1,2,1,2]
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>cards.length == 4</code></li>
	<li><code>1 &lt;= cards[i] &lt;= 9</code></li>
</ul>

class Solution {
public:

    bool check(vector<double>&A){
        int n = A.size();
        unordered_set<double> t[n][n];
        for(int i =0; i < n; i++) t[i][i].insert(A[i]);
        for(int l = 2; l <=n; l++)
            for(int i =0; i + l -1 < n; i++){
                int j = i+l-1;
                for(int k = i; k < j; k++){
                    auto A = t[i][k];
                    auto B = t[k+1][j];
                    for(auto a:A)
                        for(auto b : B){
                            t[i][j].insert(a+b);
                            t[i][j].insert(a-b);
                            t[i][j].insert(a*b);
                            if(abs(b) > pow(10,-3))t[i][j].insert(a/b);
                        }
                    
                }
            }
        
        for(auto x: t[0][n-1])
        {
            if(abs(x-24) <= pow(10,-2))return 1;
        }
        return 0;
    }

    bool judgePoint24(vector<int>& A) {
        sort(A.begin(), A.end());
        vector<double> B;
        for(auto x: A){
            B.push_back(x);
        }
        do{
            if(check(B)) return 1;
        }while(next_permutation(B.begin(), B.end()));
        return 0;
    }
};
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