891. Sum of Subsequence Widths

Problem Link

Description

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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

Solution

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Python3

class Solution:
    def sumSubseqWidths(self, nums: List[int]) -> int:
        N = len(nums)
        nums.sort()
        res = 0
        M = 10 ** 9 + 7
 
        P = []
        k = 1
        for _ in range(N):
            P.append(k)
            k *= 2
            k %= M
 
        for i, x in enumerate(nums):
            res += x * P[i]
            res -= x * P[N - i - 1]
            res %= M
        
        return res