Amazon·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026

Summary

Got a pretty gnarly algorithmic problem at Amazon for a SWE role. The problem looked deceptively simple at first but the optimal solution has some real depth to it, and I left feeling like I only partially cracked it.

Questions Asked (1)

Given an array of integers, find the minimum number of bulk replacement operations (each operation replaces every occurrence of one value with another) to make all occurrences of every distinct value contiguous in the array.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This wrecked me a little.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First, clarify the problem constraints and define what 'contiguous' means for each value. Then, model the problem as finding the minimum number of merges of value groups, possibly using a graph or interval-based approach. Finally, discuss algorithmic strategies, complexity, and trade-offs, and consider edge cases.

Pro tip: Demonstrate structured thinking by breaking down the problem into subproblems and discussing potential solutions with their complexities before coding. Mention that you would verify with examples and edge cases.

1. Clarify the problem

Ask questions to ensure you understand the operation: replacing all occurrences of one value with another, and the goal: each distinct value's occurrences form a contiguous block. Confirm constraints like array size, value range, and whether the operation can be applied to any value.

2. Identify key observations

Note that the final array will have each distinct value appearing in a single contiguous segment. The order of segments can be arbitrary. The operation effectively merges two values into one, reducing the number of distinct values.

3. Model the problem

Represent the array as a sequence of value groups (maximal contiguous runs of the same value). The problem reduces to merging groups of the same value by replacing other values, minimizing the number of replacements.

4. Devise an algorithm

Consider approaches like dynamic programming, graph coloring, or interval merging. For example, treat each distinct value as a node and compute the minimum number of merges needed to make each value's occurrences contiguous. Discuss time and space complexity.

5. Discuss trade-offs and edge cases

Compare brute-force, greedy, and optimal solutions. Mention edge cases: array already contiguous, all elements same, all distinct, large arrays. Explain why the chosen approach is efficient and correct.

Key Points to Mention

Definition of 'contiguous' for each value: all occurrences of a value must be in one continuous block.
The operation replaces all occurrences of one value with another, effectively merging two values.
The problem can be modeled as merging groups of identical values to minimize replacements.
Potential algorithms: dynamic programming over value groups, graph-based merging, or interval covering.
Time and space complexity analysis of the proposed solution.
Edge cases: already contiguous array, all elements distinct, all elements same, and large input sizes.

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