README.md

891. Sum of Subsequence Widths

The width of a sequence is the difference between the maximum and minimum elements in the sequence.

Given an array of integers nums, return the sum of the widths of all the non-empty subsequences of nums. Since the answer may be very large, return it modulo 109 + 7.

A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, [3,6,2,7] is a subsequence of the array [0,3,1,6,2,2,7].

Example 1:

Input: nums = [2,1,3]
Output: 6
Explanation: The subsequences are [1], [2], [3], [2,1], [2,3], [1,3], [2,1,3].
The corresponding widths are 0, 0, 0, 1, 1, 2, 2.
The sum of these widths is 6.

Example 2:

Input: nums = [2]
Output: 0

Constraints:

• 1 <= nums.length <= 105
• 1 <= nums[i] <= 105

Solutions (Rust)

1. Solution

impl Solution {
    pub fn sum_subseq_widths(mut nums: Vec<i32>) -> i32 {
        let mut x = 0;
        let mut pow2 = 1;
        let mut pow2_sum = 1;
        let mut ret = 0;

        nums.sort_unstable();

        for i in 1..nums.len() {
            x = (2 * x + (nums[i] - nums[i - 1]) as i64 * pow2_sum) % 1_000_000_007;
            pow2 = (2 * pow2) % 1_000_000_007;
            pow2_sum = (pow2_sum + pow2) % 1_000_000_007;
            ret = (ret + x) % 1_000_000_007;
        }

        ret as i32
    }
}