What is the optimal time complexity of solving Partition Equal Subset Sum?

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 Partition Equal Subset Sum?

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 Partition Equal Subset Sum?

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 Partition Equal Subset Sum?

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.

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Partition Equal Subset Sum

Learn how to solve the 'Partition Equal Subset Sum' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Given an integer array nums, return True if you can partition the array into two subsets such that the sum of the elements in both subsets is equal, or False otherwise.

Write a function canPartition(nums: List[int]) -> bool.

Constraints

•1 <= len(nums) <= 200
•1 <= nums[i] <= 100

Examples

Example 1

Input

nums = [1,5,11,5]

Output

True

Explanation

The array can be partitioned as [1, 5, 5] and [11].

Example 2

Input

nums = [1,2,3,5]

Output

False

Explanation

The array cannot be partitioned into equal sum subsets.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

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

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