Sum of Subsequence Widths

arraymathsorting

Problem Statement

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 10 ^9 + 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] .

Examples

Example 1

Input: nums = [2,1,3]
Output: 6
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 <= 10 ^5

1 <= nums[i] <= 10 ^5

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMath