Is Split and Merge Array Transformation easy or hard?

Split and Merge Array Transformation is typically classified as a Medium difficulty problem. The operations themselves are straightforward, but recognizing the state-space search and implementing BFS with proper state encoding and deduplication adds complexity.

Split and Merge Array Transformation Python/Java solution

Implement the BFS approach by storing the starting array in a queue and generating new arrays through valid split and merge operations. Encode each array state as a tuple (Python) or string (Java) to store in a hash set for fast duplicate detection. Continue exploring until the target configuration is found or all states are exhausted.

How to solve Split and Merge Array Transformation in O(n)?

A strict O(n) solution generally does not exist because the problem requires exploring multiple transformation states. The closest practical approach is BFS with hashing, which avoids revisiting duplicate arrays. By pruning repeated states and invalid transitions, the search becomes manageable for typical constraints.

What is the best approach for Split and Merge Array Transformation?

The most effective approach models the problem as a state graph and uses Breadth-First Search (BFS). Each array configuration is treated as a node, and split or merge operations generate neighboring states. A hash set stores visited configurations to avoid duplicates. This ensures every reachable configuration is processed at most once.

Is Split and Merge Array Transformation asked at Google/Amazon/Meta?

Array transformation problems combined with BFS state exploration frequently appear in interviews at companies like Google, Amazon, and Meta. Variants involve transforming strings, arrays, or graphs using minimal operations. The key skill being tested is recognizing the state-space search pattern and applying BFS efficiently.

What data structure is used in Split and Merge Array Transformation?

The core data structures are a queue for BFS traversal and a hash set for tracking visited states. Arrays represent the state itself, often encoded as tuples or strings for hashing. This combination ensures fast lookup and systematic exploration of transformation steps.

What is the time complexity of Split and Merge Array Transformation?

The BFS solution runs in O(S * N) time, where S is the number of unique array states explored and N is the array length. Each state requires generating possible split and merge operations across the array. Space complexity is O(S) because the queue and visited set store explored configurations.

3690. Split and Merge Array Transformation - Practice Online

You are given two integer arrays nums1 and nums2, each of length n. You may perform the following split-and-merge operation on nums1 any number of times:

Choose a subarray nums1[L..R].
Remove that subarray, leaving the prefix nums1[0..L-1] (empty if L = 0) and the suffix nums1[R+1..n-1] (empty if R = n - 1).
Re-insert the removed subarray (in its original order) at any position in the remaining array (i.e., between any two elements, at the very start, or at the very end).

Return the minimum number of split-and-merge operations needed to transform nums1 into nums2.

Example 1:

Input: nums1 = [3,1,2], nums2 = [1,2,3]

Output: 1

Explanation:

Split out the subarray [3] (L = 0, R = 0); the remaining array is [1,2].
Insert [3] at the end; the array becomes [1,2,3].

Example 2:

Input: nums1 = [1,1,2,3,4,5], nums2 = [5,4,3,2,1,1]

Output: 3

Explanation:

Remove [1,1,2] at indices 0 - 2; remaining is [3,4,5]; insert [1,1,2] at position 2, resulting in [3,4,1,1,2,5].
Remove [4,1,1] at indices 1 - 3; remaining is [3,2,5]; insert [4,1,1] at position 3, resulting in [3,2,5,4,1,1].
Remove [3,2] at indices 0 - 1; remaining is [5,4,1,1]; insert [3,2] at position 2, resulting in [5,4,3,2,1,1].

Constraints:

2 <= n == nums1.length == nums2.length <= 6
-10⁵ <= nums1[i], nums2[i] <= 10⁵
nums2 is a permutation of nums1.