<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 valid(double a, double b) {
        return fabs(a + b - 24.0) < 0.0001 or fabs(a - b - 24.0) < 0.0001 or
               fabs(a * b - 24.0) < 0.0001 or (b != 0 and fabs(a / b - 24.0) < 0.0001);
    }
    
    bool valid(double a, double b, double c) {
        return valid(a + b, c) or valid(a, b + c) or valid(a - b, c) or
               valid(a, b - c) or valid(a * b, c) or valid(a, b * c) or
               valid(a / b, c) or valid(a, b / c);
    }
    
    bool get_perm(int idx, vector<double>& cards) {
        if (idx == 4) {
            return valid(cards[0] + cards[1], cards[2], cards[3]) or
                   valid(cards[0], cards[1] + cards[2], cards[3]) or
                   valid(cards[0], cards[1], cards[2] + cards[3]) or
                   valid(cards[0] - cards[1], cards[2], cards[3]) or
                   valid(cards[0], cards[1] - cards[2], cards[3]) or
                   valid(cards[0], cards[1], cards[2] - cards[3]) or
                   valid(cards[0] * cards[1], cards[2], cards[3]) or
                   valid(cards[0], cards[1] * cards[2], cards[3]) or
                   valid(cards[0], cards[1], cards[2] * cards[3]) or
                   valid(cards[0] / cards[1], cards[2], cards[3]) or
                   valid(cards[0], cards[1] / cards[2], cards[3]) or
                   valid(cards[0], cards[1], cards[2] / cards[3]);
        }
        
        bool res = false;
        unordered_set<int> s;
        for (int i = idx; i < 4 and !res; i++) {
            if (s.count(cards[i]))
                continue;
            s.insert(cards[i]);
            swap(cards[idx], cards[i]);
            res |= get_perm(idx + 1, cards);
            swap(cards[idx], cards[i]);
        }
        return res;
    }
    
    bool judgePoint24(vector<int>& nums) {
        vector<double> cards;
        for (auto& x : nums)
            cards.push_back((double)x);
        return get_perm(0, cards);
    }
};
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