Amazon·Software Engineer·Online Assessment (OA)·Intermediate

Intermediate

Jul 2026

Summary

Amazon SWE coding round with a dynamic programming problem on partitioning arrays. The problem was dressed up in server/expense language but once you strip that away it's a pretty classic min/max partition cost question.

Questions Asked (1)

Given a list of servers with associated costs and an integer p, partition the list into exactly p contiguous segments. The cost of each segment is the sum of its first and last element. Return both the minimum and maximum total cost achievable across all valid partitions.

Algorithms & Data Structures

Author's notes

Took me a minute to realize the segment cost formula means the endpoints are what matter, not the whole interior.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Recognize that the total cost is the sum of the first element of the first segment, the last element of the last segment, and the last element of each of the first p-1 segments (which are also the first elements of the subsequent segments). Thus, the problem reduces to selecting p-1 cut points from the n-1 possible positions between elements, where the cost contribution of a cut after index i is arr[i] + arr[i+1]. To minimize or maximize the total cost, sort these cut costs and pick the smallest or largest p-1 cuts, respectively.

Pro tip: Clarify edge cases upfront: if p=1, the total cost is simply the sum of the first and last elements; if p=n, each segment is a single element, so the total cost is twice the sum of all elements minus the first and last. Also, confirm whether the list can be partitioned into exactly p segments (requires n >= p).

1. Understand the cost structure

Derive that the total cost equals arr[0] + arr[n-1] + sum of arr[i] + arr[i+1] for each cut after index i. This simplifies the problem to choosing p-1 cuts.

2. Identify candidate cuts

For each possible cut position i from 0 to n-2, compute the cost contribution c_i = arr[i] + arr[i+1]. There are n-1 such values.

3. Select cuts for min and max

To minimize total cost, pick the p-1 smallest c_i; to maximize, pick the p-1 largest c_i. Use sorting or selection algorithms.

4. Compute final totals

Add arr[0] + arr[n-1] to the sum of selected cuts to get the minimum and maximum total costs.

5. Handle edge cases

Check if p=1 (no cuts) or p=n (all cuts), and ensure n >= p. Also consider if the list is empty or p is invalid.

Key Points to Mention

The total cost can be expressed as arr[0] + arr[n-1] + sum of selected cut costs.
Each cut after index i contributes arr[i] + arr[i+1] to the total cost.
The problem reduces to selecting p-1 cuts from n-1 possible positions.
Sorting the cut costs allows easy selection of the smallest or largest p-1 values.
Time complexity: O(n log n) due to sorting, or O(n) with selection algorithms like quickselect.
Edge cases: p=1, p=n, and invalid p (p > n or p < 1).

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