動機

每個數字都會分別在每個是最大最小的seg中擔任最大最小 所以只要把組合數算出來就好

在你以為要列舉時，直接算組合數

Problem

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: 6Explanation: 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

Sol

class Solution:
    def sumSubseqWidths(self, nums: List[int]) -> int:
        ret = 0
        for i,n in enumerate(sorted(nums)):
            ret += n * (1 << i) # left
            ret -= n * (1 << (len(nums)-i-1)) # right
        return ret % (10**9 + 7)