24 Game
<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>
Array; Math; Backtracking
class Solution {
public:
    bool judgePoint24(vector<int>& cards) {
        vector<double> nums;
        for (int num : cards) {
            nums.push_back(static_cast<double>(num));
        }
        return dfs(nums);
    }

private:
    const char ops[4] = {'+', '-', '*', '/'};

    bool dfs(vector<double>& nums) {
        int n = nums.size();
        if (n == 1) {
            return abs(nums[0] - 24) < 1e-6;
        }
        bool ok = false;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (i != j) {
                    vector<double> nxt;
                    for (int k = 0; k < n; ++k) {
                        if (k != i && k != j) {
                            nxt.push_back(nums[k]);
                        }
                    }
                    for (char op : ops) {
                        switch (op) {
                        case '/':
                            if (nums[j] == 0) {
                                continue;
                            }
                            nxt.push_back(nums[i] / nums[j]);
                            break;
                        case '*':
                            nxt.push_back(nums[i] * nums[j]);
                            break;
                        case '+':
                            nxt.push_back(nums[i] + nums[j]);
                            break;
                        case '-':
                            nxt.push_back(nums[i] - nums[j]);
                            break;
                        }
                        ok |= dfs(nxt);
                        if (ok) {
                            return true;
                        }
                        nxt.pop_back();
                    }
                }
            }
        }
        return ok;
    }
};