feat: add solution 1955. Count Number of Special Subsequences

Author: tzuyi0817

solutions/1955. Count Number of Special Subsequences/README.md

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+# [1955. Count Number of Special Subsequences](https://leetcode.com/problems/count-number-of-special-subsequences)
+
+## Description
+
+<div class="elfjS" data-track-load="description_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>
+
+<ul>
+	<li>For example, <code>[0,1,2]</code> and <code>[0,0,1,1,1,2]</code> are special.</li>
+	<li>In contrast, <code>[2,1,0]</code>, <code>[1]</code>, and <code>[0,1,2,0]</code> are not special.</li>
+</ul>
+
+<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>
+
+<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>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre><strong>Input:</strong> nums = [0,1,2,2]
+<strong>Output:</strong> 3
+<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>].
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre><strong>Input:</strong> nums = [2,2,0,0]
+<strong>Output:</strong> 0
+<strong>Explanation:</strong> There are no special subsequences in [2,2,0,0].
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre><strong>Input:</strong> nums = [0,1,2,0,1,2]
+<strong>Output:</strong> 7
+<strong>Explanation:</strong> The special subsequences are bolded:
+- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,0,1,2]
+- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,0,1,<strong><u>2</u></strong>]
+- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,0,1,<strong><u>2</u></strong>]
+- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,0,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
+- [<strong><u>0</u></strong>,1,2,<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
+- [<strong><u>0</u></strong>,1,2,0,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
+- [0,1,2,<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</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>
+</div>
+
+<p>&nbsp;</p>
+
+## Solutions
+
+**Solution: `Dynamic Programming`**
+
+- Time complexity: <em>O(n)</em>
+- Space complexity: <em>O(1)</em>
+
+<p>&nbsp;</p>
+
+### **JavaScript**
+
+```js
+/**
+ * @param {number[]} nums
+ * @return {number}
+ */
+const countSpecialSubsequences = function (nums) {
+  const MODULO = 10 ** 9 + 7;
+  const dp = [1, 0, 0, 0];
+
+  for (const num of nums) {
+    dp[num + 1] = (dp[num + 1] * 2 + dp[num]) % MODULO;
+  }
+
+  return dp[3];
+};
+```

solutions/1955. Count Number of Special Subsequences/solution.js

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+/**
+ * @param {number[]} nums
+ * @return {number}
+ */
+const countSpecialSubsequences = function (nums) {
+  const MODULO = 10 ** 9 + 7;
+  const dp = [1, 0, 0, 0];
+
+  for (const num of nums) {
+    dp[num + 1] = (dp[num + 1] * 2 + dp[num]) % MODULO;
+  }
+
+  return dp[3];
+};