What is the optimal time complexity of solving Partition Problem?

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 Problem?

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 Problem?

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 Problem?

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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Competitive ProgrammingEasy

Partition Problem

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

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Problem Statement

Easy

Write a function can_partition_equal_sum(arr) that returns True if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal, and False otherwise.

Constraints

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

Examples

Example 1

Input

can_partition_equal_sum([1, 5, 11, 5])

Output

True

Explanation

The array can be partitioned as {1, 5, 5} and {11}, which both sum to 11.

Example 2

Input

can_partition_equal_sum([1, 5, 3])

Output

False

Explanation

No equal sum partition is possible.

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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