<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) {
        vector<float> current;
       
        vector<bool> used(cards.size(), false);
        
        return permutation(cards, current, used);
    }

    bool permutation(const vector<int>& cards, vector<float> current, vector<bool>& used) {
        if (current.size() == 4) {
            if(checkPair(current)) {
                return true;
            }
            return false;
        }

        for (int i = 0; i < cards.size(); i++) {
            if (used[i]) {
                continue;
            }
            used[i]  = true;
            current.push_back(cards[i]);
            if (permutation(cards, current, used)) {
                return true;
            }
            current.pop_back();
            used[i] = false;
        }
        return false;
    }

    bool checkPair(vector<float> current) {
        vector<float> as = getPossible(current[0], current[1]);
        for (float a: as) {
            vector<float> bs = getPossible(current[3], current[2]);
            for (float b: bs) {
                auto res = getPossible(a, b);
                for (float r: res) {
                    if (abs(r-24.0) <= 0.1) {
                        // cout << "r "<< r-24  << " " << endl;
                        return true;
                    }
                }
            }

            vector<float> cs = getPossible(a, current[2]);
            for (float c: cs) {
                auto res = getPossible(c, current[3]);
                for (float r: res) {
                    if (abs(r-24.0) <= 0.1) {
                        // cout << "r "<< r-24  << " " << endl;
                        return true;
                    }
                }
            }
        }

        
        return false;
    }

    vector<float> getPossible(float a, float b){
        return {a-b, a+b, b-a, a*b, a/b, b/a};
    }
};
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