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Sum of Subarray Minimums (medium)
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Problem Statement

Given an array of integers arr, return the sum of the minimum values from all possible contiguous subarrays within arr. Since the result can be very large, return the final sum modulo (10<sup>9</sup> + 7).

Examples

Example 1:

  • Input: arr = [3, 1, 2, 4, 5]
  • Expected Output: 30
  • Explanation:
    • The subarrays are: [3], [1], [2], [4], [5], [3,1], [1,2], [2,4], [4,5], [3,1,2], [1,2,4], [2,4,5], [3,1,2,4], [1, 2, 4, 5], [3, 1, 2, 4, 5].
    • The minimum values of these subarrays are: 3, 1, 2, 4, 5, 1, 1, 2, 4, 1, 1, 2, 1, 1, 1.
    • Summing these minimums: 3 + 1 + 2 + 4 + 5 + 1 + 1 + 2 + 4 + 1 + 1 + 2 + 1 + 1 + 1 = 30.

Example 2:

  • Input: arr = [2, 6, 5, 4]
  • Expected Output: 36
  • Explanation:
    • The subarrays are: [2], [6], [5], [4], [2,6], [6,5], [5,4], [2,6,5], [6,5,4], [2,6,5,4].
    • The minimum values of these subarrays are: 2, 6, 5, 4, 2, 5, 4, 2, 4, 2.
    • Summing these minimums: 2 + 6 + 5 + 4 + 2 + 5 + 4 + 2 + 4 + 2 = 36.

Example 3:

  • Input: arr = [7, 3, 8]
  • Expected Output: 35
  • Explanation:
    • The subarrays are: [7], [3], [8], [7,3], [3,8], [7,3,8].
    • The minimum values of these subarrays are: 7, 3, 8, 3, 3, 3.
    • Summing these minimums: 7 + 3 + 8 + 3 + 3 + 3 = 27.

Constraints:

  • 1 <= arr.length <= 3 * 10<sup>4</sup>
  • 1 <= arr[i] <= 3 * 10<sup>4</sup>

Try it yourself

Try solving this question here:

Python3
Python3
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