Sum of Subsequence Widths

HardMathmath

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Problem

The **width** of a sequence is its largest element minus its smallest element. Given an integer array nums, consider every non-empty subsequence (any subset of positions, keeping their order). Return the sum of the widths of all of them. Subsequences taken from different position sets count separately even if they contain the same values. There are 2^n - 1 subsequences, so enumerate nothing: find each element's total contribution. Return the sum modulo 1_000_000_007.

Examples

Input: nums = [2,1,3]
Output: 6
Subsequences: [2],[1],[3] have width 0; [2,1] width 1, [2,3] width 1, [1,3] width 2, [2,1,3] width 2. Total 6.
Input: nums = [2]
Output: 0
The only subsequence has width 0.

Constraints

  • 1 <= nums.length <= 10^5
  • 1 <= nums[i] <= 10^5

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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