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
• 1
• 1

Hint:

1. Compute all sums and save it in array.
2. Then just go from LEFT to RIGHT index and calculate answer modulo 1e9 + 7.

Solution:

To solve this problem, we can follow these steps:

1. Generate all possible sums of non-empty continuous subarrays.
2. Sort the resulting array of sums.
3. Calculate the sum of the elements from the left index to the right index (1-based).
4. Return the result modulo 10⁹ + 7.

Let's implement this solution in PHP: 1508. Range Sum of Sorted Subarray Sums

<?php // Example usage
$nums = array(1, 2, 3, 4);
$n = 4;
$left = 1;
$right = 5;

echo rangeSum($nums, $n, $left, $right); // Output: 13

$left = 3;
$right = 4;
echo rangeSum($nums, $n, $left, $right); // Output: 6

$left = 1;
$right = 10;
echo rangeSum($nums, $n, $left, $right); // Output: 50

?>

Explanation:

1. 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.

2. Sorting the Sums:

   • Use PHP's sort() function to sort the $sums array in non-decreasing order.

3. 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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