Count Number of Special Subsequences
<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>
Array; Dynamic Programming
class Solution {
    public int countSpecialSubsequences(int[] nums) {
        final int mod = (int) 1e9 + 7;
        int n = nums.length;
        int[][] f = new int[n][3];
        f[0][0] = nums[0] == 0 ? 1 : 0;
        for (int i = 1; i < n; ++i) {
            if (nums[i] == 0) {
                f[i][0] = (2 * f[i - 1][0] % mod + 1) % mod;
                f[i][1] = f[i - 1][1];
                f[i][2] = f[i - 1][2];
            } else if (nums[i] == 1) {
                f[i][0] = f[i - 1][0];
                f[i][1] = (f[i - 1][0] + 2 * f[i - 1][1] % mod) % mod;
                f[i][2] = f[i - 1][2];
            } else {
                f[i][0] = f[i - 1][0];
                f[i][1] = f[i - 1][1];
                f[i][2] = (f[i - 1][1] + 2 * f[i - 1][2] % mod) % mod;
            }
        }
        return f[n - 1][2];
    }
}