← IBM Interview Insights

IBM·Data Scientist·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

IBM Data Scientist interview that was basically one algorithmic problem the whole time. The problem looked deceptively clean on the surface but the efficient solution took a while to see.

Questions Asked (1)

Q1

Given an integer array, you repeatedly take the first element, append it to the end, then bubble it leftward past any larger neighbors until it finds its sorted position. What is the minimum number of such operations to make the array non-decreasing, or return -1 if it's impossible?

Algorithms & Data Structures
Author's notes

I spent the first few minutes just simulating it on paper to convince myself I understood the operation correctly, which was probably the right call.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First, clarify the operation: it's a rotation of the first element to the end followed by a leftward bubble sort pass. Then, recognize that the minimum number of operations is the minimum number of elements that need to be moved to achieve a sorted array, which can be found by identifying the longest non-decreasing subsequence that can remain in place. Finally, check if the remaining elements can be moved to their correct positions via the operation, and return the count or -1 if impossible.

Pro tip: Don't jump into coding; first walk through a small example to ensure you understand the operation, and discuss edge cases like already sorted arrays or duplicates. This shows structured problem-solving and communication skills valued at IBM.

1. Understand the operation

Restate the operation in your own words: take the first element, move it to the end, then bubble it left past larger elements until it's in sorted position. Confirm with the interviewer if needed.

2. Identify the goal

The goal is to make the array non-decreasing with minimum operations. Each operation moves one element to its correct position relative to the sorted order, but may disrupt others.

3. Find the longest non-decreasing subsequence

The elements that are already in non-decreasing order and can remain in place form a subsequence. The minimum operations is the number of elements not in this subsequence, provided the remaining elements can be moved to the end in the correct order.

4. Check feasibility

After removing the subsequence, the remaining elements must be able to be moved to the end in non-decreasing order. This is possible if the remaining elements are already in non-decreasing order when considered in the order they appear. If not, return -1.

5. Compute and return

If feasible, return the number of operations (size of remaining elements). Otherwise, return -1.

Key Points to Mention

  • The operation is equivalent to a rotation followed by a bubble pass, which effectively moves the first element to its correct sorted position.
  • The minimum number of operations equals the number of elements that are not part of the longest non-decreasing subsequence that can remain in place.
  • Feasibility requires that the elements to be moved are already in non-decreasing order relative to each other.
  • Edge cases: already sorted array (0 operations), array with all equal elements (0 operations), array that cannot be sorted (return -1).
  • Time complexity: O(n log n) for finding the longest non-decreasing subsequence, or O(n) with a greedy approach for this specific problem.
  • Space complexity: O(n) for storing the subsequence or O(1) with careful implementation.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.