0679: 24 Game

Problem Statement

You are given an integer array cards of length 4. You have four cards, each containing a number in the range [1, 9]. You should arrange the numbers on these cards in a mathematical expression using the operators ['+', '-', '*', '/'] and the parentheses '(' and ')' to get the value 24.

You are restricted with the following rules:

  • The division operator '/' 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>

Return true if you can get such expression that evaluates to 24, and false otherwise.

Example 1:

Input: cards = [4,1,8,7]
Output: true
Explanation: (8-4) * (7-1) = 24

Example 2:

Input: cards = [1,2,1,2]
Output: false

Constraints:

  • cards.length == 4
  • 1 <= cards[i] <= 9

Code Solution