sum-of-subarray-ranges

Sum of Subarray Ranges

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subArrayRanges

You are given an integer array <code>nums</code>. The range of a subarray of <code>nums</code> is the difference between the largest and smallest element in the subarray.

Return the sum of all subarray ranges of <code>nums</code>.

A subarray is a contiguous non-empty sequence of elements within an array.

&nbsp;
Example 1:

<pre>
Input: nums = [1,2,3]
Output: 4
Explanation: The 6 subarrays of nums are the following:
[1], range = largest - smallest = 1 - 1 = 0 
[2], range = 2 - 2 = 0
[3], range = 3 - 3 = 0
[1,2], range = 2 - 1 = 1
[2,3], range = 3 - 2 = 1
[1,2,3], range = 3 - 1 = 2
So the sum of all ranges is 0 + 0 + 0 + 1 + 1 + 2 = 4.</pre>

Example 2:

<pre>
Input: nums = [1,3,3]
Output: 4
Explanation: The 6 subarrays of nums are the following:
[1], range = largest - smallest = 1 - 1 = 0
[3], range = 3 - 3 = 0
[3], range = 3 - 3 = 0
[1,3], range = 3 - 1 = 2
[3,3], range = 3 - 3 = 0
[1,3,3], range = 3 - 1 = 2
So the sum of all ranges is 0 + 0 + 0 + 2 + 0 + 2 = 4.
</pre>

Example 3:

<pre>
Input: nums = [4,-2,-3,4,1]
Output: 59
Explanation: The sum of all subarray ranges of nums is 59.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>-109 &lt;= nums[i] &lt;= 109</code></li>
</ul>

&nbsp;
Follow-up: Could you find a solution with <code>O(n)</code> time complexity?

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