<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 {
//[8,1,6,6]
//6÷(1-6÷8) 
public:
    bool judgePoint24(vector<int>& cards) {
        return judgePoint24Core(cards, 0);
    }
private:
    bool judgePoint24Core(vector<int>& cards, int index) {
        if(index == cards.size()) {
            unordered_set<double> res = getRes(cards, 0, index - 1);
            for(double num : res) {
                if(abs(num - 24) < 1e-8) {
                    return true;
                }
            }
            return false;
        }
        for(int i = index; i < cards.size(); ++i) {
            swap(cards[index], cards[i]);
            if(judgePoint24Core(cards, index + 1)) {
                return true;
            }
            swap(cards[index], cards[i]);
        }
        return false;        
    }
    unordered_set<double> getRes(const vector<int>& cards, int start, int end) {
        if(start == end) {
            return{double(cards[start])};
        }
        
        unordered_set<double> res;
        for(int i = start; i < end; ++i) {
            unordered_set<double> s1 = getRes(cards, start, i);
            unordered_set<double> s2 = getRes(cards, i + 1, end);
            for(double num1 : s1) {
                for(double num2 : s2) {
                    res.insert(num1 + num2);
                    res.insert(num1 - num2);
                    res.insert(num1 * num2);
                    if(num2 == 0) {
                        continue;
                    }
                    res.insert(num1 / num2);
                }
            }
        }
        return res;
    }
};
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