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g0801_0900.s0891_sum_of_subsequence_widths.readme.md Maven / Gradle / Ivy

891\. Sum of Subsequence Widths

Hard

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