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1589. Maximum Sum Obtained of Any Permutation

We have an array of integers, nums, and an array of requests where requests[i] = [starti, endi]. The ith request asks for the sum of nums[starti] + nums[starti + 1] + ... + nums[endi - 1] + nums[endi]. Both starti and endi are 0-indexed.

Return the maximum total sum of all requests among all permutations of nums.

Since the answer may be too large, return it modulo 109 + 7.

Example 1:

Input: nums = [1,2,3,4,5], requests = [[1,3],[0,1]]
Output: 19
Explanation: One permutation of nums is [2,1,3,4,5] with the following result:
requests[0] -> nums[1] + nums[2] + nums[3] = 1 + 3 + 4 = 8
requests[1] -> nums[0] + nums[1] = 2 + 1 = 3
Total sum: 8 + 3 = 11.
A permutation with a higher total sum is [3,5,4,2,1] with the following result:
requests[0] -> nums[1] + nums[2] + nums[3] = 5 + 4 + 2 = 11
requests[1] -> nums[0] + nums[1] = 3 + 5  = 8
Total sum: 11 + 8 = 19, which is the best that you can do.

Example 2:

Input: nums = [1,2,3,4,5,6], requests = [[0,1]]
Output: 11
Explanation: A permutation with the max total sum is [6,5,4,3,2,1] with request sums [11].

Example 3:

Input: nums = [1,2,3,4,5,10], requests = [[0,2],[1,3],[1,1]]
Output: 47
Explanation: A permutation with the max total sum is [4,10,5,3,2,1] with request sums [19,18,10].

Constraints:

• n == nums.length
• 1 <= n <= 105
• 0 <= nums[i] <= 105
• 1 <= requests.length <= 105
• requests[i].length == 2
• 0 <= starti <= endi < n

Solutions (Rust)

1. Solution

impl Solution {
    pub fn max_sum_range_query(nums: Vec<i32>, requests: Vec<Vec<i32>>) -> i32 {
        let mut nums = nums;
        let mut suffix_sum = vec![0; nums.len()];

        for request in &requests {
            if request[0] > 0 {
                suffix_sum[request[0] as usize - 1] -= 1;
            }
            suffix_sum[request[1] as usize] += 1;
        }

        for i in (0..suffix_sum.len() - 1).rev() {
            suffix_sum[i] += suffix_sum[i + 1];
        }

        nums.sort_unstable();
        suffix_sum.sort_unstable();

        (nums
            .iter()
            .zip(suffix_sum.iter())
            .map(|(x, y)| *x as i64 * *y as i64)
            .sum::<i64>()
            % 1_000_000_007) as i32
    }
}