891. Sum of Subsequence Widths

Description

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

Solution: Math

• Time complexity: O(nlogn)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
const sumSubseqWidths = function (nums) {
  const MODULO = 10 ** 9 + 7;
  const n = nums.length;
  let result = 0;
  let count = 1;

  nums.sort((a, b) => a - b);

  for (let index = 0; index < n; index++) {
    const num1 = nums[index];
    const num2 = nums[n - 1 - index];

    result += (num1 - num2) * count;
    result %= MODULO;
    count = (count * 2) % MODULO;
  }
  return result;
};