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Zero Array Transformation II

Medium
12.5%
Updated 8/1/2025

Zero Array Transformation II

What is this problem about?

Zero Array Transformation II is a more complex variation of the transformation problem. In this version, you are often asked to find the minimum number of queries (from a given sequence) required to make the array zero, or to determine if the array can be zeroed out using only the first k queries. This introduces a search dimension to the problem, as you need to find the threshold k that makes the transformation possible. It combines range updates with searching for an optimal value.

Why is this asked in interviews?

Companies like Meta and Bloomberg ask the Zero Array Transformation II interview question to see if candidates can combine multiple algorithmic concepts. It’s not enough to know how to handle range updates; you also need to know how to search for the answer efficiently. Since the property "is it possible to zero the array with k queries" is usually monotonic (if it's possible with k, it's also possible with k+1), it is a perfect candidate for Binary Search. This tests a candidate's "Binary Search on Answer" intuition.

Algorithmic pattern used

The algorithmic pattern for Zero Array Transformation II coding problem is Binary Search on the Result combined with a Difference Array. You binary search for the number of queries k. For a fixed k, you use the Difference Array technique (from Zero Array Transformation I) to check in O(N) time if the first k queries are sufficient to reduce all array elements to zero. This results in a total time complexity of O((N + Q) * log Q), which is highly efficient even for very large inputs.

Example explanation

Imagine an array [3, 2] and four queries: 1: [0, 1] 2: [0, 0] 3: [1, 1] 4: [0, 1] We want to find the minimum k queries to zero the array.

  • Try k=2 (first two queries): [0, 1] and [0, 0]. Index 0 gets -2, Index 1 gets -1. Array becomes [1, 1]. Not zero.
  • Try k=3 (first three): Adds [1, 1]. Index 0 gets -2, Index 1 gets -2. Array becomes [1, 0]. Not zero.
  • Try k=4: Adds [0, 1]. Index 0 gets -3, Index 1 gets -3. Array becomes [0, -1]. Zero! (Possible). The Zero Array Transformation II coding problem finds the smallest such k.

Common mistakes candidates make

A common error in the Zero Array Transformation II interview question is forgetting that the query order is fixed; you must use the first k queries, not any k queries. Another mistake is not recognizing the monotonic property, leading to a linear search for k instead of binary search. Candidates also sometimes struggle with the implementation of the difference array inside the binary search loop, often re-initializing it incorrectly or causing memory issues.

Interview preparation tip

Master the "Binary Search on Answer" technique. This pattern appears whenever you are asked to find a "minimum X to satisfy a condition" or "maximum Y while staying within limits." Combine this with the Difference Array technique to handle range-based conditions. In interviews at Meta, being able to articulate why binary search is applicable (due to monotonicity) is just as important as the implementation itself.

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