Is Split Array With Same Average easy or hard?

Split Array With Same Average is classified as a Hard problem on LeetCode. The challenge comes from recognizing the mathematical transformation from equal averages to a subset-sum condition and efficiently searching the subset space using dynamic programming or pruning.

Split Array With Same Average Python/Java solution

Python and Java solutions typically implement either recursive backtracking with pruning or dynamic programming using sets to track achievable sums. The DP version iterates through numbers and updates possible sums for subset sizes in reverse order to avoid reusing elements.

How to solve Split Array With Same Average in O(n)?

An O(n) solution is not known for this problem due to the combinatorial subset constraints. Practical solutions rely on subset-sum dynamic programming or meet-in-the-middle strategies, typically around O(n^2 * sum) or exponential with pruning for smaller inputs.

What is the best approach for Split Array With Same Average?

The most effective approach converts the equal-average condition into a subset sum problem. Using dynamic programming, track achievable sums for subsets of different sizes and check whether sum = (totalSum * k) / n exists. This avoids exploring every subset and significantly improves performance compared to brute-force recursion.

Is Split Array With Same Average asked at Google/Amazon/Meta?

Split Array With Same Average is a hard-level problem that appears in advanced algorithm interviews, especially where subset-sum transformations or mathematical reasoning are tested. Similar patterns are commonly asked at companies like Google, Amazon, and Meta when evaluating dynamic programming and combinatorial reasoning skills.

What data structure is used in Split Array With Same Average?

Common implementations use hash sets or bitsets to store reachable subset sums for each subset size. Dynamic programming arrays indexed by subset size and sum are also used to track state transitions efficiently.

What is the time complexity of Split Array With Same Average?

The recursive backtracking approach has exponential time complexity O(2^n) because it explores subset combinations. The optimized dynamic programming solution runs around O(n^2 * sum) time with O(n * sum) space by tracking achievable sums for subsets of each size.

Description Solution Video 12:43

805. Split Array With Same Average

Hard27.5% acceptance6 companies

You are given an integer array nums.

You should move each element of nums into one of the two arrays A and B such that A and B are non-empty, and average(A) == average(B).

Return true if it is possible to achieve that and false otherwise.

Note that for an array arr, average(arr) is the sum of all the elements of arr over the length of arr.

Example 1:

Input: nums = [1,2,3,4,5,6,7,8]
Output: true
Explanation: We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.

Example 2: