907 Sum of Subarray Minimums

Given an array of integers arr, find the sum of min(b), where b ranges over every (contiguous) subarray of arr. Since the answer may be large, return the answer modulo 109 + 7.

Example 1:

Input: arr = [3,1,2,4]
Output: 17
Explanation: 
Subarrays are [3], [1], [2], [4], [3,1], [1,2], [2,4], [3,1,2], [1,2,4], [3,1,2,4]. 
Minimums are 3, 1, 2, 4, 1, 1, 2, 1, 1, 1.
Sum is 17.

Example 2:

Input: arr = [11,81,94,43,3]
Output: 444

Constraints:

• 1 <= arr.length <= 3 * 104
• 1 <= arr[i] <= 3 * 104

For each element, find how many subarrays containing this element with this element as the minimum.

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class Solution:
    def sumSubarrayMins(self, arr: List[int]) -> int:
        MIN_VAL = float('-inf')
        MOD = 10**9 + 7
        res = 0
        stack = []  #  non-decreasing 
        arr = [MIN_VAL] + arr + [MIN_VAL]
        for i, n in enumerate(arr):
            while stack and arr[stack[-1]] > n:
                cur = stack.pop()
                # arr[cur] is the min between arr[stack[-1]] and arr[i] (exclusive)
                res += arr[cur] * (cur - stack[-1]) * (i - cur) 
            stack.append(i)
        return res % MOD