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:
    def judgePoint24(self, cards: List[int]) -> bool:
        def dfs(nums: List[float]):
            n = len(nums)
            if n == 1:
                if abs(nums[0] - 24) < 1e-6:
                    return True
                return False
            ok = False
            for i in range(n):
                for j in range(n):
                    if i != j:
                        nxt = [nums[k] for k in range(n) if k != i and k != j]
                        for op in ops:
                            match op:
                                case "/":
                                    if nums[j] == 0:
                                        continue
                                    ok |= dfs(nxt + [nums[i] / nums[j]])
                                case "*":
                                    ok |= dfs(nxt + [nums[i] * nums[j]])
                                case "+":
                                    ok |= dfs(nxt + [nums[i] + nums[j]])
                                case "-":
                                    ok |= dfs(nxt + [nums[i] - nums[j]])
                            if ok:
                                return True
            return ok

        ops = ("+", "-", "*", "/")
        nums = [float(x) for x in cards]
        return dfs(nums)
