sum-of-good-subsequences

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Algorithms

You are given an integer array <code>nums</code>. A good subsequence is defined as a subsequence of <code>nums</code> where the absolute difference between any two consecutive elements in the subsequence is exactly 1.

Return the sum of all possible good subsequences of <code>nums</code>.

Since the answer may be very large, return it modulo <code>109 + 7</code>.

Note that a subsequence of size 1 is considered good by definition.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [1,2,1]

Output: 14

Explanation:

<ul>
	<li>Good subsequences are: <code>[1]</code>, <code>[2]</code>, <code>[1]</code>, <code>[1,2]</code>, <code>[2,1]</code>, <code>[1,2,1]</code>.</li>
	<li>The sum of elements in these subsequences is 14.</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: nums = [3,4,5]

Output: 40

Explanation:

<ul>
	<li>Good subsequences are: <code>[3]</code>, <code>[4]</code>, <code>[5]</code>, <code>[3,4]</code>, <code>[4,5]</code>, <code>[3,4,5]</code>.</li>
	<li>The sum of elements in these subsequences is 40.</li>
</ul>
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 105</code></li>
</ul>