Minimum Reverse Operations

Minimum Reverse Operations

What is this problem about?

The Minimum Reverse Operations problem gives you an array of length n, a starting index p, and a list of banned positions. In each operation, you can reverse any contiguous subarray of a fixed length k. Starting from position p, find the minimum number of such reversal operations to reach each index in the array, or report -1 if unreachable. This Minimum Reverse Operations coding problem is a sophisticated BFS on reachable positions with non-trivial neighbor computation.

Why is this asked in interviews?

Infosys includes this hard problem to evaluate BFS mastery combined with mathematical reasoning about reachable positions after a fixed-length reversal. The key insight — figuring out which indices are reachable from a given position in one step — requires number theory reasoning (parity constraints). The array, BFS, and ordered set interview pattern is central, and the use of sets to efficiently skip visited/banned positions makes this a strong test of data structure selection.

Algorithmic pattern used

The approach is BFS with sorted set (ordered set) optimization. From any position i, a reversal of length k can move to positions within a computable range. Due to parity constraints, reachable positions from i in one step form a set of even or odd indices in a range. Use two sorted sets (one for even indices, one for odd indices) tracking unvisited positions. During BFS, extract all reachable positions from current index, mark them visited, and remove them from the sets. This avoids O(n) per-node scanning.

Example explanation

Array length n=5, k=3, banned=[1], starting at p=0. From 0, reachable in one step (k=3 reversal): position 2. From 2: reachable positions in range. BFS level 0: [0], level 1: [2], level 2: [4]. Position 1 is banned, position 3 might take 2 steps. Result array: [0, -1, 1, 2, 2].

Common mistakes candidates make

• Attempting to recompute reachable neighbors by brute force for each BFS node (O(nk) total, too slow).
• Ignoring the parity constraint that limits reachable positions to same-parity indices.
• Not correctly banning positions before BFS starts.
• Confusing the sorted set removal step with the BFS level tracking.

Interview preparation tip

This problem teaches a critical BFS optimization: when the set of unvisited nodes is large but you process them in bulk per BFS level, using sorted sets lets you extract ranges efficiently. Practice BFS problems where neighbors aren't direct adjacencies but mathematically defined ranges — they require combining graph traversal with arithmetic insight. Implementing ordered sets (like SortedList in Python or TreeSet in Java) fluently is a useful skill for hard interview questions.