Design a Scalable, Fault-Tolerant Distributed Order System
Company: Amazon
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Onsite
##### Scenario
Round covering distributed-system design and algorithm implementation.
##### Question
Design a highly available, low-latency distributed order-processing system. Explain architecture, scalability levers, and fault-tolerance mechanisms. Implement LeetCode 987 ‘Vertical Order Traversal of a Binary Tree’ and analyze its time–space complexity.
##### Hints
Explain component interactions clearly; for LC987 discuss traversal strategy and sorting keys.
Overview: This question evaluates system-design and algorithmic competencies, combining distributed-systems concepts — high availability, low-latency architecture, scalability levers, and fault-tolerance mechanisms — with practical binary-tree traversal and time–space complexity analysis.
Given a binary tree represented by a level-order list where null denotes a missing child, return its vertical order traversal. Assign coordinates so the root is at row 0, column 0; the left child of a node at (r, c) is at (r+1, c-1) and the right child is at (r+1, c+1). The output should list columns from left to right. Within each column, nodes are ordered by row ascending; if multiple nodes share the same row and column, order them by value ascending.
Constraints
- 0 <= n <= 10^4 where n is the number of list entries
- Node values are integers in the range [-10^9, 10^9]
- Input is a level-order (breadth-first) representation using null for missing nodes
- Duplicates are allowed
- Return an empty list if the input is empty or the root is null
Hints
- Assign each node (row, col) coordinates via BFS or DFS starting with (0,0) at the root.
- Collect triples (col, row, value), sort by (col asc, row asc, value asc), then group by column.
- Building the tree from the level-order list can be done with a queue.
- Be careful with tie-breaking: same column and row must be ordered by value.