Sort Array Using Prefix Reversals - Solution & Explanation

Problem Overview: You need to sort an array using only prefix reversals. A prefix reversal flips the first k elements of the array. The challenge is finding a sequence of flips that produces a sorted array efficiently.

Approach 1: Brute Force Simulation (O(n³) time, O(1) space)

The brute force idea tries multiple prefix reversals at each position until the array becomes sorted. You repeatedly scan the array, identify misplaced elements, and test flips that move values closer to their target positions. This works for small inputs but wastes time because every flip may require another full scan to validate ordering. Use this approach only to understand how prefix reversals affect array state.

Approach 2: Greedy Pancake Sort (O(n²) time, O(1) space)

This is the standard and expected solution. Iterate from the end of the array toward the beginning. For each index, locate the maximum element in the unsorted portion, reverse its prefix to bring it to the front, then reverse the larger prefix to move it into its final sorted position. Each iteration fixes exactly one element, which keeps the logic simple and deterministic. This approach is commonly categorized under greedy and array problems because every operation greedily places the next largest value.

Approach 3: Optimized Greedy with Early Skip (O(n²) time, O(1) space)

You can reduce unnecessary reversals by skipping elements already positioned correctly. Before performing any flip, check whether the current maximum already sits at its target index. If it does, continue immediately to the next iteration. This does not improve worst-case complexity, but it reduces operations significantly on partially sorted arrays. Interviewers often appreciate this refinement because it shows attention to practical optimization instead of only asymptotic analysis.

Recommended for interviews: Interviewers expect the greedy pancake sort solution because it directly matches the constraints of prefix reversals. Showing the brute force idea first demonstrates problem exploration, but the greedy method proves you can identify the invariant: after every two reversals, one element reaches its final position. Understanding prefix operations and in-place manipulation also overlaps with sorting interview patterns.