Range Sum of Sorted Subarray Sums

Problem Description

You are given the array nums consisting of n positive integers. You computed the sum of all non-empty continuous subarrays from the array and then sorted them in non-decreasing order, creating a new array of n * (n + 1) / 2 numbers. Return the sum of the numbers from index left to index right (indexed from 1), inclusive, in the new array. Since the answer can be a huge number return it modulo 10^9 + 7.

Key Insights

• The number of subarrays in an array of size n is n * (n + 1) / 2.
• We can generate all subarray sums using a nested loop.
• Sorting the subarray sums allows us to easily access the required indices.
• The indices left and right are 1-based, so we need to adjust them when accessing the sorted array.
• The result must be computed modulo 10^9 + 7 to handle large numbers.

Space and Time Complexity

Time Complexity: O(n^2 log(n^2)) for generating and sorting subarray sums, where n is the length of nums.
Space Complexity: O(n^2) for storing the subarray sums.

Solution

To solve this problem, we will:

1. Use a nested loop to compute all possible subarray sums.
2. Store these sums in a list.
3. Sort the list of subarray sums.
4. Sum the elements from the sorted list between the indices left and right, adjusting for 1-based indexing.

Code Solutions