2104 - Sum of Subarray Ranges.

Medium

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

Return the sum of all subarray ranges of nums.

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

Example 1:

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.

Example 2:

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.

Example 3:

Input: nums = 4,-2,-3,4,1

Output: 59

Explanation: The sum of all subarray ranges of nums is 59.

Constraints:

• 1 <= nums.length <= 1000

• <code>-10⁹<= numsi<= 10⁹</code>

Follow-up: Could you find a solution with O(n) time complexity?