<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>

def combines(n1, n2):
    result = [
        n1 + n2,
        n1 - n2,
        n2 - n1,
        n1 * n2,
    ]

    # Handle divide-by-zero
    if n1 != 0:
        result.append(n2 / n1)
    if n2 != 0:
        result.append(n1 / n2)

    return result


def is_near_24(num):
    # Handle floating point math issues
    return abs(num - 24) < 1e-5


class Solution:
    def judgePoint24(self, cards: List[int]) -> bool:
        # Base case: only 2 "cards" left. See if any ops work out.
        if len(cards) == 2:
            return any(is_near_24(n) for n in combines(*cards))

        # Combine two "cards" into one with an op, keeping the remaining cards
        for i_c1 in range(len(cards) - 1):  # Pick 1st card
            for i_c2 in range(i_c1, len(cards)):  # Pick 2nd card
                if i_c1 == i_c2:
                    continue  # Can't pick the same card twice
                remaining_cards = [c for i, c in enumerate(cards) if i not in (i_c1, i_c2)]
                for combined in combines(cards[i_c1], cards[i_c2]):
                    if self.judgePoint24(remaining_cards + [combined]):
                        return True
        return False

16900