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Algorithms

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.

You are restricted with the following rules:

<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 not allowed.</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>

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

&nbsp;
Example 1:

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

Example 2:

<pre>
Input: cards = [1,2,1,2]
Output: false
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>cards.length == 4</code></li>
	<li><code>1 &lt;= cards[i] &lt;= 9</code></li>
</ul>

judgePoint24

24 Game

Array

Math

Backtracking

给定一个长度为4的整数数组&nbsp;<code>cards</code>&nbsp;。你有 <code>4</code> 张卡片，每张卡片上都包含一个范围在 <code>[1,9]</code> 的数字。您应该使用运算符&nbsp;<code>['+', '-', '*', '/']</code>&nbsp;和括号&nbsp;<code>'('</code>&nbsp;和&nbsp;<code>')'</code>&nbsp;将这些卡片上的数字排列成数学表达式，以获得值24。

你须遵守以下规则:

<ul>
	<li>除法运算符 <code>'/'</code> 表示实数除法，而不是整数除法。

	<ul>
		<li>例如，&nbsp;<code>4 /(1 - 2 / 3)= 4 /(1 / 3)= 12</code>&nbsp;。</li>
	</ul>
	</li>
	<li>每个运算都在两个数字之间。特别是，不能使用 <code>“-”</code> 作为一元运算符。
	<ul>
		<li>例如，如果 <code>cards =[1,1,1,1]</code> ，则表达式 <code>“-1 -1 -1 -1”</code> 是 不允许 的。</li>
	</ul>
	</li>
	<li>你不能把数字串在一起
	<ul>
		<li>例如，如果 <code>cards =[1,2,1,2]</code> ，则表达式 <code>“12 + 12”</code> 无效。</li>
	</ul>
	</li>
</ul>

如果可以得到这样的表达式，其计算结果为 <code>24</code> ，则返回 <code>true </code>，否则返回 <code>false</code>&nbsp;。

&nbsp;

示例 1:

<pre>
输入: cards = [4, 1, 8, 7]
输出: true
解释: (8-4) * (7-1) = 24
</pre>

示例 2:

<pre>
输入: cards = [1, 2, 1, 2]
输出: false
</pre>

&nbsp;

提示:

<ul>
	<li><code>cards.length == 4</code></li>
	<li><code>1 &lt;= cards[i] &lt;= 9</code></li>
</ul>