Sum Of Subsequence Widths - Leetcode Solution

Sum of Subsequence Widths is a problem on LeetCode that asks you to find the sum of the difference between the maximum and minimum values of all non-empty subsequences of an array. Here's a detailed solution to the problem:

1. Sort the given array in non-decreasing order. This will help us in calculating the maximum and minimum values of each subsequence efficiently.

2. For each element in the sorted array, calculate the number of subsequences it appears in as the product of the number of subsequences that occur before it and the number of subsequences that occur after it. Let's call this number 'count'.

3. For each value of 'count', calculate its corresponding contribution to the final answer as (2^(count-1) * element). This formula is derived from the simple observation that each subsequence can either include or exclude the given element, and there are 2^(count-1) subsequences that include it.

4. Add up the contributions of all the elements to get the final answer.

Here's the Python code for the solution:

def sumSubseqWidths(A): A.sort() n = len(A) ans = 0 mod = 10**9 + 7 for i in range(n): count = (1 << i) - (1 << (n - i - 1)) ans = (ans + count * A[i]) % mod return ans

The time complexity of this solution is O(nlogn) due to the sorting operation, and the space complexity is O(1) since we're only using a constant amount of extra space for variables.

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