Range Sum of Sorted Subarray Sums
1508. Range Sum of Sorted Subarray Sums
Medium
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 109 + 7.
Example 1:
- Input: nums = [1,2,3,4], n = 4, left = 1, right = 5
- Output: 13
- Explanation: All subarray sums are 1, 3, 6, 10, 2, 5, 9, 3, 7, 4. After sorting them in non-decreasing order we have the new array [1, 2, 3, 3, 4, 5, 6, 7, 9, 10]. The sum of the numbers from index le = 1 to ri = 5 is 1 + 2 + 3 + 3 + 4 = 13.
Example 2:
- Input: nums = [1,2,3,4], n = 4, left = 3, right = 4
- Output: 6
- Explanation: The given array is the same as example 1. We have the new array [1, 2, 3, 3, 4, 5, 6, 7, 9, 10]. The sum of the numbers from index le = 3 to ri = 4 is 3 + 3 = 6.
Example 3:
- Input: nums = [1,2,3,4], n = 4, left = 1, right = 10
- Output: 50
Constraints:
- n == nums.length
- 1 <= nums.length <= 1000
- 1 <= nums[i] <= 100
- 1 <= left <= right <= n * (n + 1) / 2
Hint:
- Compute all sums and save it in array.
- Then just go from LEFT to RIGHT index and calculate answer modulo 1e9 + 7.
Solution:
To solve this problem, we can follow these steps:
- Generate all possible sums of non-empty continuous subarrays.
- Sort the resulting array of sums.
- Calculate the sum of the elements from the left index to the right index (1-based).
- Return the result modulo 109 + 7.
Let's implement this solution in PHP: 1508. Range Sum of Sorted Subarray Sums
Explanation:
Generating Subarray Sums:
- Iterate through each starting index i of the subarray.
- For each starting index i, compute the sum of subarrays ending at index j (where j >= i).
- Append each computed subarray sum to the $sums array.
Sorting the Sums:
- Use PHP's sort() function to sort the $sums array in non-decreasing order.
Summing the Required Range:
- Iterate from the left-1 index to the right-1 index (since the problem uses 1-based indexing).
- Accumulate the sum of the elements in this range, taking care to use modulo 109 + 7 to avoid overflow.
This solution efficiently generates all subarray sums, sorts them, and computes the required range sum as specified.
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