leetcode-problemset/leetcode-cn/problem (Chinese)/统计特殊子序列的数目 [count-number-of-special-subsequences].html

<p><strong>特殊序列</strong> 是由&nbsp;<strong>正整数</strong>&nbsp;个 <code>0</code>&nbsp;，紧接着&nbsp;<strong>正整数</strong>&nbsp;个 <code>1</code>&nbsp;，最后 <strong>正整数</strong>&nbsp;个 <code>2</code>&nbsp;组成的序列。</p>

<ul>
	<li>比方说，<code>[0,1,2]</code> 和&nbsp;<code>[0,0,1,1,1,2]</code>&nbsp;是特殊序列。</li>
	<li>相反，<code>[2,1,0]</code>&nbsp;，<code>[1]</code>&nbsp;和&nbsp;<code>[0,1,2,0]</code>&nbsp;就不是特殊序列。</li>
</ul>

<p>给你一个数组&nbsp;<code>nums</code>&nbsp;（<strong>仅</strong>&nbsp;包含整数&nbsp;<code>0</code>，<code>1</code>&nbsp;和&nbsp;<code>2</code>），请你返回 <b>不同特殊子序列的数目</b>&nbsp;。由于答案可能很大，请你将它对&nbsp;<code>10<sup>9</sup> + 7</code> <strong>取余</strong> 后返回。</p>

<p>一个数组的 <strong>子序列</strong>&nbsp;是从原数组中删除零个或者若干个元素后，剩下元素不改变顺序得到的序列。如果两个子序列的 <strong>下标集合</strong>&nbsp;不同，那么这两个子序列是 <strong>不同的</strong>&nbsp;。</p>

<p>&nbsp;</p>

<p><strong>示例 1：</strong></p>

<pre>
<b>输入：</b>nums = [0,1,2,2]
<b>输出：</b>3
<b>解释：</b>特殊子序列为 [<strong>0</strong>,<strong>1</strong>,<strong>2</strong>,2]，[<strong>0</strong>,<strong>1</strong>,2,<strong>2</strong>] 和 [<strong>0</strong>,<strong>1</strong>,<strong>2</strong>,<strong>2</strong>] 。
</pre>

<p><strong>示例 2：</strong></p>

<pre>
<b>输入：</b>nums = [2,2,0,0]
<b>输出：</b>0
<b>解释：</b>数组 [2,2,0,0] 中没有特殊子序列。
</pre>

<p><strong>示例 3：</strong></p>

<pre>
<b>输入：</b>nums = [0,1,2,0,1,2]
<b>输出：</b>7
<b>解释：</b>特殊子序列包括：
- [<strong>0</strong>,<strong>1</strong>,<strong>2</strong>,0,1,2]
- [<strong>0</strong>,<strong>1</strong>,2,0,1,<strong>2</strong>]
- [<strong>0</strong>,<strong>1</strong>,<strong>2</strong>,0,1,<strong>2</strong>]
- [<strong>0</strong>,<strong>1</strong>,2,0,<strong>1</strong>,<strong>2</strong>]
- [<strong>0</strong>,1,2,<strong>0</strong>,<strong>1</strong>,<strong>2</strong>]
- [<strong>0</strong>,1,2,0,<strong>1</strong>,<strong>2</strong>]
- [0,1,2,<strong>0</strong>,<strong>1</strong>,<strong>2</strong>]
</pre>

<p>&nbsp;</p>

<p><strong>提示：</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 2</code></li>
</ul>