# 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:
[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`
* `-109 <= nums[i] <= 109`

问数组的所有子数组内(最大值-最小值）的和。相当于求所有子数组内最大值的和-所有子数组内最小值的和。sum(arr(i) \* cnt(i)), cnt(i) 是以arr\[i]为最小值的子数组个数。设\[l, i, r]是以arr\[i]为最小值的最长子数组，那cnt\[i]即（左边选个长度 \* 右边选个长度）的所有可能性: (i - l) \* (r - i). 为了对每个arr\[i]找到对应的l和r，用monotonic stack存当前最小值所在index，当arr\[i]比s\[-1]还小时，抛出s\[-1]且res += (i - s\[-1]) \* (s\[-1] \* s\[-2]), 再s.append(i)。

```python
class Solution:
    def subArrayRanges(self, nums: List[int]) -> int:
        A, s, res = [-inf] + nums + [-inf], [], 0
        for i, num in enumerate(A):
            while s and num < A[s[-1]]:
                j = s.pop()
                res -= (i - j) * (j - s[-1]) * A[j]
            s.append(i)
        A, s = [inf] + nums + [inf], []
        for i, num in enumerate(A):
            while s and num > A[s[-1]]:
                j = s.pop()
                res += (i - j) * (j - s[-1]) * A[j]
            s.append(i)
        return res pytho
```