Split and Merge Array Transformation - Solution & Explanation

Problem Overview: You are given an array and a set of allowed operations that split elements or merge adjacent elements. The goal is to determine whether one configuration can be transformed into another using these operations. Each transformation creates a new array state, so the task becomes exploring valid states efficiently without revisiting duplicates.

Approach 1: Brute Force State Simulation (Exponential Time, High Space)

The most direct idea is to simulate every possible sequence of split and merge operations. At each step, iterate through the array, attempt all valid splits and merges, and generate new arrays. This quickly explodes because each operation creates multiple branches. Without tracking visited states, the same configuration appears repeatedly. Time complexity grows exponentially with the number of operations, and space complexity is also exponential due to storing intermediate states.

Approach 2: Breadth-First Search with Hash Set (Optimal BFS Traversal)

Treat each array configuration as a node in a graph. An edge exists between two nodes if one can be obtained from the other via a single split or merge operation. Use Breadth-First Search to explore states level by level starting from the initial array. Each generated configuration is encoded (for example as a string or tuple) and stored in a visited hash table to prevent reprocessing duplicates.

During BFS, generate neighbors by iterating through the array and applying valid split or merge operations. Push unseen states into a queue. If the target configuration appears, the transformation is possible. BFS guarantees the shortest sequence of operations if the problem asks for minimum steps. Time complexity depends on the number of reachable states but is typically expressed as O(S * N), where S is the number of unique states explored and N is the array length. Space complexity is O(S) for the queue and visited set.

This approach works well because each state is processed once and duplicate configurations are eliminated using hashing. Arrays are naturally modeled as nodes in a state graph, making BFS the most natural traversal strategy when exploring transformation sequences involving arrays.

Recommended for interviews: Start by explaining the brute force simulation to demonstrate understanding of the operations and the search space. Then transition to the BFS state‑graph model with a visited hash set. Interviewers usually expect the BFS approach because it systematically explores transformations while avoiding repeated work.