<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:
    vector<double> ranges(double aFirstNum, double aSecondNum) {
        vector<double> myOutput;
        myOutput.push_back(aFirstNum + aSecondNum);
        myOutput.push_back(aFirstNum - aSecondNum);
        myOutput.push_back(aSecondNum - aFirstNum);
        myOutput.push_back(aFirstNum * aSecondNum);
        if (aFirstNum != 0) {
            myOutput.push_back(aSecondNum / aFirstNum);
        }
        if (aSecondNum != 0) {
            myOutput.push_back(aFirstNum / aSecondNum);
        }

        return myOutput;
    }

    bool solve(vector<double> &aCards) {
        if (aCards.size() == 1) {
            return abs(24 - aCards[0]) < 0.1;
        }

        for (int x = 0; x < aCards.size() - 1; x++) {
            for (int y = x + 1; y < aCards.size(); y++) {
                vector<double> myRemainingCards;
                for (int z = 0; z < aCards.size(); z++) {
                    if (z != x && z != y) {
                        myRemainingCards.push_back(aCards[z]);
                    }
                }

                int myFirstNum = aCards[x];
                int mySecondNum = aCards[y];

                vector<double> myRanges1;
                myRanges1.push_back(myFirstNum + mySecondNum);
                myRanges1.push_back(myFirstNum - mySecondNum);
                myRanges1.push_back(mySecondNum - myFirstNum);
                myRanges1.push_back(myFirstNum * mySecondNum);
                if (myFirstNum != 0) {
                    myRanges1.push_back(mySecondNum / myFirstNum);
                }
                if (mySecondNum != 0) {
                    myRanges1.push_back(myFirstNum / mySecondNum);
                }

                vector<double> myRanges = ranges(aCards[x], aCards[y]);
                for (int a = 0; a < min(myRanges.size(), myRanges1.size()); a++) {
                    cout << myRanges[a] << " " << myRanges1[a] << "\n";
                }

                for (int z = 0; z < myRanges.size(); z++) {
                    myRemainingCards.push_back(myRanges[z]);
                    if (solve(myRemainingCards)) {
                        return true;
                    }
                    myRemainingCards.pop_back();
                }
            }
        }

        return false;
    }

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

        return solve(myConvertedCards);
    }
};
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