Special Array II

Special Array II

What is this problem about?

Building on the concept of parity, the Special Array II interview question asks you to handle multiple queries on a single array. For each query, which consists of a range [start, end], you must determine if the subarray from start to end is "special" (meaning all adjacent elements have different parity). This version of the problem elevates the difficulty by requiring an efficient way to answer many queries without re-scanning the array every time.

Why is this asked in interviews?

This Special Array II coding problem is a classic example of moving from a brute-force approach to an optimized one using pre-computation. Companies like Meta and Google ask this to see if you can apply the Prefix Sum interview pattern or Binary Search to range-based queries. It tests your ability to recognize that if you have many queries on the same static data, spending time upfront to build a helper structure will save significant time later.

Algorithmic pattern used

The most efficient approach uses the Prefix Sum or Difference Array technique. You can create an auxiliary array that tracks "violations"—indices where the parity of an element is the same as the one before it. By calculating a prefix sum of these violations, you can determine if any violation exists between start and end in $O(1)$ time by checking if prefixSum[end] - prefixSum[start] is zero. Alternatively, you could store the indices of all violations in a list and use Binary Search to see if any violation falls within the query range.

Example explanation

Array: [1, 4, 3, 2, 6, 8, 7] Violations occur at index 4 (2 and 6 are both even) and index 5 (6 and 8 are both even). Violation count array: [0, 0, 0, 0, 1, 1, 0] (where 1 means a violation with the previous element). Prefix Sum of violations: [0, 0, 0, 0, 1, 2, 2]

Query 1: Range [0, 2] (Subarray [1, 4, 3]). prefixSum[2] - prefixSum[0] = 0 - 0 = 0. No violations. Result: True.

Query 2: Range [2, 5] (Subarray [3, 2, 6, 8]). prefixSum[5] - prefixSum[2] = 2 - 0 = 2. There are violations. Result: False.

Common mistakes candidates make

• Brute Force per Query: Re-iterating through the subarray for every query, leading to $O(Q \times N)$ time, which will time out for large inputs.
• Prefix Sum Offset: Getting the index off by one when calculating the sum of violations within a range.
• Memory Management: Not realizing they need an extra array for pre-computation and trying to solve it with constant space for multiple queries.
• Misinterpreting the Condition: Only checking the parity of the start and end elements instead of every adjacent pair within the range.

Interview preparation tip

Whenever you encounter "multiple queries" on a "static range," immediately think of Prefix Sums, Segment Trees, or Binary Search on pre-processed data. These are the standard tools for reducing query time from linear to constant or logarithmic. Practice converting raw array properties into cumulative counts to master this pattern.