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907. Sum of Subarray Minimums

Difficulty Topics

Description

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

Solution

sum-of-subarray-minimums.py
class Solution:
    def sumSubarrayMins(self, arr: List[int]) -> int:
        arr.append(0)
        res = 0
        M = 10 ** 9 + 7
        stack = [-1]

        for i, x in enumerate(arr):
            while stack and x < arr[stack[-1]]:
                mid = stack.pop()
                res += (mid - stack[-1]) * (i - mid) * arr[mid]
            stack.append(i)

        return res % M