sum-of-variable-length-subarrays

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Algorithms

You are given an integer array <code>nums</code> of size <code>n</code>. For each index <code>i</code> where <code>0 &lt;= i &lt; n</code>, define a subarray <code>nums[start ... i]</code> where <code>start = max(0, i - nums[i])</code>.

Return the total sum of all elements from the subarray defined for each index in the array.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [2,3,1]

Output: 11

Explanation:

<table style="border: 1px solid black;">
	<tbody>
		<tr>
			<th style="border: 1px solid black;">i</th>
			<th style="border: 1px solid black;">Subarray</th>
			<th style="border: 1px solid black;">Sum</th>
		</tr>
		<tr>
			<td style="border: 1px solid black;">0</td>
			<td style="border: 1px solid black;"><code>nums[0] = [2]</code></td>
			<td style="border: 1px solid black;">2</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;"><code>nums[0 ... 1] = [2, 3]</code></td>
			<td style="border: 1px solid black;">5</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;"><code>nums[1 ... 2] = [3, 1]</code></td>
			<td style="border: 1px solid black;">4</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">Total Sum</td>
			<td style="border: 1px solid black;">&nbsp;</td>
			<td style="border: 1px solid black;">11</td>
		</tr>
	</tbody>
</table>

The total sum is 11. Hence, 11 is the output.
</div>

Example 2:

<div class="example-block">
Input: nums = [3,1,1,2]

Output: 13

Explanation:

<table style="border: 1px solid black;">
	<tbody>
		<tr>
			<th style="border: 1px solid black;">i</th>
			<th style="border: 1px solid black;">Subarray</th>
			<th style="border: 1px solid black;">Sum</th>
		</tr>
		<tr>
			<td style="border: 1px solid black;">0</td>
			<td style="border: 1px solid black;"><code>nums[0] = [3]</code></td>
			<td style="border: 1px solid black;">3</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;"><code>nums[0 ... 1] = [3, 1]</code></td>
			<td style="border: 1px solid black;">4</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;"><code>nums[1 ... 2] = [1, 1]</code></td>
			<td style="border: 1px solid black;">2</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;"><code>nums[1 ... 3] = [1, 1, 2]</code></td>
			<td style="border: 1px solid black;">4</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">Total Sum</td>
			<td style="border: 1px solid black;">&nbsp;</td>
			<td style="border: 1px solid black;">13</td>
		</tr>
	</tbody>
</table>

The total sum is 13. Hence, 13 is the output.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n == nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
</ul>

i	Subarray	Sum
0	`nums[0] = [2]`	2
1	`nums[0 ... 1] = [2, 3]`	5
2	`nums[1 ... 2] = [3, 1]`	4
Total Sum		11

i	Subarray	Sum
0	`nums[0] = [3]`	3
1	`nums[0 ... 1] = [3, 1]`	4
2	`nums[1 ... 2] = [1, 1]`	2
3	`nums[1 ... 3] = [1, 1, 2]`	4
Total Sum		13