# 2104 Sum of Subarray Ranges

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:
, range = largest - smallest = 1 - 1 = 0
, range = 2 - 2 = 0
, 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:
, range = largest - smallest = 1 - 1 = 0
, range = 3 - 3 = 0
, 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`
• `-109 <= nums[i] <= 109`

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

 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 `````` ``````''' O(n^2) ''' class Solution: def subArrayRanges(self, nums: List[int]) -> int: res = 0 for i in range(len(nums)): min_val = max_val = nums[i] for j in range(i, len(nums)): min_val = min(min_val, nums[j]) max_val = max(max_val, nums[j]) res += (max_val - min_val) return res ''' O(n) ''' class Solution: def subArrayRanges(self, nums: List[int]) -> int: def get_sum(op): total = 0 stack = [] for i in range(len(nums) + 1): # Between left boundary and right boundary # nums[x] is the largest/smallest element while stack and (i == len(nums) or op(nums[i], nums[stack[-1]])): mid = stack.pop() right_boundary = i left_boundary = stack[-1] if stack else -1 total += nums[mid] * (right_boundary - mid) * (mid - left_boundary) stack.append(i) return total max_sum = get_sum(lambda x, y: x > y) min_sum = get_sum(lambda x, y: x < y) return max_sum - min_sum``````