<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:
    // ['+', '-', '*', '/']
    double op(double& lhs, double& rhs, int type) {
        if (type == 0)
            return lhs + rhs;
        if (type == 1)
            return lhs - rhs;
        if (type == 2)
            return double(lhs) * double(rhs);
        if (type == 3) {
            if (rhs == 0) {
                return std::numeric_limits<int>::min();
            } else {
                return double(lhs) / double(rhs);
            }
        }
        if (type == 4)
            return double(rhs) - double(lhs);
        if (type == 5) {
            if (lhs == 0) {
                return std::numeric_limits<int>::min();
            } else {
                return double(rhs) / double(lhs);
            }
        }
        return -1;
    }
    int recurse(vector<double> numbers) {
        if (numbers.size() == 1) {
            return abs(numbers[0] - 24) <= 0.1;
        }
        vector<double> original = numbers;
        for (int i = 0; i < numbers.size() - 1; i++) {
            for (int j = i + 1; j < numbers.size(); j++) {
                for (int k = 0; k < 6; k++) {
                    double result = op(numbers[i], numbers[j], k);
                    if (result == std::numeric_limits<int>::min()) {
                        numbers = original;
                        continue;
                    }
                    // replace the two with result
                    numbers.erase(numbers.begin() + j);
                    numbers[i] = result;
                    if (recurse(numbers))
                        return true;
                    numbers = original;
                }
            }
        }
        return false;
    }
    bool judgePoint24(vector<int>& cards) {
        vector<double> c(cards.begin(), cards.end());
        return recurse(c);
    }
};
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