What is the optimal time complexity of solving Sum of all subsets?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Sum of all subsets?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Sum of all subsets?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Sum of all subsets?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

Back to Practice Dashboard

Python BasicsEasy

Sum of all subsets

Learn how to solve the 'Sum of all subsets' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Easy

Write a function sum_of_all_subsets(arr) that takes an array of integers and returns the total sum of all elements across all possible subsets. For an array of n elements, each element appears in exactly 2^(n-1) subsets. So the total sum equals sum(arr) * 2^(n-1). Use recursion to compute this.

Constraints

•1 <= len(arr) <= 20
•-100 <= arr[i] <= 100

Examples

Example 1

Input

arr = [1, 2, 3]

Output

Explanation

Subsets: [], [1], [2], [3], [1,2], [1,3], [2,3], [1,2,3]. Sums: 0+1+2+3+3+4+5+6 = 24. Or: (1+2+3)*2^(3-1) = 6*4 = 24.

Example 2

Input

arr = [5, 10]

Output

Explanation

Subsets: [], [5], [10], [5,10]. Sums: 0+5+10+15 = 30. Or: (5+10)*2^1 = 15*2 = 30.

Example 3

Input

arr = [4]

Output

Explanation

Subsets: [], [4]. Sums: 0 + 4 = 4. Or: 4 * 2^0 = 4.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor