<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 {
private:
    vector<double> allPossibleCombination(double &a, double &b)
    {
        vector<double>combination={a+b,a-b,b-a,a*b};
        if(b){
            combination.push_back(a/b);
        }
        if(a){
            combination.push_back(b/a);
        }
        return combination;
    }
    bool checkResult(vector<double> &list)
    {
        if(list.size()==1)
        {
            return abs(list[0]-24)<=0.01;
                
        }
 
        int i,j;
        for(i=0;i<list.size();i++)
        {
            for(j=i+1;j<list.size();j++)
            {
                vector<double>newList;
                int k;
                for(k=0;k<list.size();k++)
                {
                    if(k!=i && k!=j)
                    {
                        newList.push_back(list[k]);
                    }
                }
                for(double &res :allPossibleCombination(list[i],list[j]))
                {
                    newList.push_back(res);
                    if(checkResult(newList))
                    {
                        return true;
                    }
                    newList.pop_back();
                }
            }
        }
        return false;
    
    }
public:
    bool judgePoint24(vector<int>& cards) {
        vector<double>list(cards.begin(),cards.end());
        return checkResult(list);
    }
};
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