<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
{   //https://www.youtube.com/watch?v=uKdv5osHud8
    vector<double> getValidOperations(double a, double b)
    {
        vector<double> validOperations;
        validOperations.push_back(a + b);
        validOperations.push_back(a * b);
        validOperations.push_back(a - b);
        validOperations.push_back(b - a);
        if (abs(b) > FLT_EPSILON)
            validOperations.push_back(a / b);
        if (abs(a) > FLT_EPSILON)
            validOperations.push_back(b / a);
        return validOperations;
    }

    bool isPossible(vector<double> &arr)
    {
        int n = (int)arr.size();
        if (n == 1)
        {
            return abs(24.0 - arr[0]) <= FLT_EPSILON;
        }

        for (int fn = 0; fn < n; fn++)
        {
            for (int sn = fn+1; sn < n; sn++)
            {
                //if (sn == fn) continue;
                double firstNumber = arr[fn];
                double secondNumber = arr[sn];
                vector<double> validOperations = getValidOperations(firstNumber, secondNumber);
                vector<double> nextArr;
                for (double validOperation : validOperations)
                {
                    nextArr.clear();
                    nextArr.push_back(validOperation);

                    for (int i = 0; i < n; i++)
                    {
                        if (i == fn or i == sn)
                            continue;
                        nextArr.push_back(arr[i]);
                    }
                    if (isPossible(nextArr))
                        return true;
                }
            }
        }
        return false;
    }

public:
    bool judgePoint24(vector<int> &cards)
    {
        vector<double> arr(cards.begin(), cards.end());

        return isPossible(arr);
    }
};
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