<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 judgePoint24(vector<int>& cards) {
        // Convert to double
        vector<double> newCards;
        for (int i : cards)
            newCards.push_back((double)i);

        // Depth First Search
        return judgeHelper(newCards);

    }

    bool judgeHelper(vector<double>& cards) {
        // Base Case
        if (cards.size() == 1) {
            if (cards[0] >= 24 - 0.0000001 && cards[0] <= 24 + 0.0000001) {
                return true;
            }
            else
                return false;
        }
        
        // Recursive Case
        int size = cards.size();
        for (int i = 0; i < size - 1; i++) {
            for (int j = i + 1; j < size; j++) {
                double first = cards[i];
                double second = cards[j];

                vector<double> newCards(cards);
                newCards.erase(newCards.begin() + j);
                newCards.erase(newCards.begin() + i);

                for (int l = 1; l <= 4; l++) {
                    // Edge Caes
                    if (l == 4 && second == 0.0)
                        continue;
                    
                    double newDouble = calNextDouble(first, second, l);
                    newCards.push_back(newDouble);

                    if (judgeHelper(newCards) == true)
                        return true;
                    newCards.pop_back();

                    // One more time for divide
                    if (l == 4) {
                        newDouble = 1.0 / newDouble;
                        newCards.push_back(newDouble);

                        if (judgeHelper(newCards) == true)
                            return true;
                        newCards.pop_back();
                    }
                }
            }
        }

        return false;
    }

    double calNextDouble(double first, double second, int index) {
        double result;

        switch (index) {
            case 1:
                result = first + second;
                break;
            case 2:
                result = first - second;
                break;
            case 3:
                result = first * second;
                break;
            case 4:
                result = first / second;
                break;
        }

        if (result < 0)
            result *= -1;
        return result;
    }
};
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