<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 {
    void permutations(int i, vector<int> cards, vector<vector<int>>& perm) {
        if (i == cards.size()) {
            perm.push_back(cards);
            return;
        }
        for (int j = i; j < cards.size(); j++) {
            swap(cards[i], cards[j]);
            permutations(i + 1, cards, perm);
            swap(cards[i], cards[j]);
        }
    }
    vector<double> combine(int k, double val, vector<double>& nums) {
        vector<double> temp;
        for(int i = 0; i < nums.size(); i++) {
            if(i == k) {
                temp.push_back(val);
                i++;
            } else {
                temp.push_back(nums[i]);
            }
        }
        return temp;
    }
    bool isPossible(vector<double> nums) {
        if (nums.size() == 1) {
            return abs(nums[0] - 24) < 1e-5;
        }
        for (int i = 0; i < nums.size() - 1; i++) {
            if(isPossible(combine(i, nums[i] + nums[i+1], nums))) return true;
            if(isPossible(combine(i, nums[i] - nums[i+1], nums))) return true;
            if(isPossible(combine(i, nums[i] * nums[i+1], nums))) return true;
            if(nums[i+1] && isPossible(combine(i, nums[i] / nums[i+1], nums))) return true;
        }
        return false;
    }

public:
    bool judgePoint24(vector<int>& cards) {
        vector<vector<int>> perm;
        permutations(0, cards, perm);
        for (vector<int>& p : perm) {
            vector<double> temp(p.begin(), p.end());
            if (isPossible(temp))
                return true;
        }
        return false;
    }
};
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