leetcode-problemset/leetcode-cn/originData/count-number-of-special-subsequences.json

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        "question": {
            "questionId": "2086",
            "questionFrontendId": "1955",
            "categoryTitle": "Algorithms",
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            "title": "Count Number of Special Subsequences",
            "titleSlug": "count-number-of-special-subsequences",
            "content": "<p>A sequence is <strong>special</strong> if it consists of a <strong>positive</strong> number of <code>0</code>s, followed by a <strong>positive</strong> number of <code>1</code>s, then a <strong>positive</strong> number of <code>2</code>s.</p>\n\n<ul>\n\t<li>For example, <code>[0,1,2]</code> and <code>[0,0,1,1,1,2]</code> are special.</li>\n\t<li>In contrast, <code>[2,1,0]</code>, <code>[1]</code>, and <code>[0,1,2,0]</code> are not special.</li>\n</ul>\n\n<p>Given an array <code>nums</code> (consisting of <strong>only</strong> integers <code>0</code>, <code>1</code>, and <code>2</code>), return<em> the <strong>number of different subsequences</strong> that are special</em>. Since the answer may be very large, <strong>return it modulo </strong><code>10<sup>9</sup> + 7</code>.</p>\n\n<p>A <strong>subsequence</strong> of an array is a sequence that can be derived from the array by deleting some or no elements without changing the order of the remaining elements. Two subsequences are <strong>different</strong> if the <strong>set of indices</strong> chosen are different.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [0,1,2,2]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The special subsequences are bolded [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,2], [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,<strong><u>2</u></strong>], and [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,<strong><u>2</u></strong>].\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,2,0,0]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no special subsequences in [2,2,0,0].\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [0,1,2,0,1,2]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> The special subsequences are bolded:\n- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,0,1,2]\n- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,0,1,<strong><u>2</u></strong>]\n- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,0,1,<strong><u>2</u></strong>]\n- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,0,<strong><u>1</u></strong>,<strong><u>2</u></strong>]\n- [<strong><u>0</u></strong>,1,2,<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>]\n- [<strong><u>0</u></strong>,1,2,0,<strong><u>1</u></strong>,<strong><u>2</u></strong>]\n- [0,1,2,<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>]\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 2</code></li>\n</ul>\n",
            "translatedTitle": "统计特殊子序列的数目",
            "translatedContent": "<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>\n\n<ul>\n\t<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>\n\t<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>\n</ul>\n\n<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>\n\n<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>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [0,1,2,2]\n<b>输出：</b>3\n<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>] 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,2,0,0]\n<b>输出：</b>0\n<b>解释：</b>数组 [2,2,0,0] 中没有特殊子序列。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [0,1,2,0,1,2]\n<b>输出：</b>7\n<b>解释：</b>特殊子序列包括：\n- [<strong>0</strong>,<strong>1</strong>,<strong>2</strong>,0,1,2]\n- [<strong>0</strong>,<strong>1</strong>,2,0,1,<strong>2</strong>]\n- [<strong>0</strong>,<strong>1</strong>,<strong>2</strong>,0,1,<strong>2</strong>]\n- [<strong>0</strong>,<strong>1</strong>,2,0,<strong>1</strong>,<strong>2</strong>]\n- [<strong>0</strong>,1,2,<strong>0</strong>,<strong>1</strong>,<strong>2</strong>]\n- [<strong>0</strong>,1,2,0,<strong>1</strong>,<strong>2</strong>]\n- [0,1,2,<strong>0</strong>,<strong>1</strong>,<strong>2</strong>]\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 2</code></li>\n</ul>\n",
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