Breadth-First Search Questions at Zenefits: What to Expect

Breadth-First Search (BFS) is a core algorithm for navigating graphs and trees level by level. At Zenefits, which builds HR, payroll, and benefits software, this skill is directly relevant. Their platform manages complex, interconnected data: employee reporting hierarchies, organizational charts, workflow dependencies, and permission networks. Traversing these structures efficiently to find shortest paths, calculate degrees of separation, or validate configurations is a daily engineering task. With 3 out of their 21 tagged interview questions focusing on BFS, it's clear they test for practical, clean implementations that handle real-world data relationships.

What to Expect — Types of Problems

Zenefits’ BFS problems typically model real organizational or system relationships. You won't see abstract puzzles; expect problems grounded in business logic.

1. Shortest Path in an Unweighted Graph: This is the most classic use. Given a network (like employees in a company org chart), find the minimum number of "steps" or connections between two nodes. This models finding the reporting distance between two employees or the steps in an approval chain.
2. Level-Order Traversal & Aggregation: Problems that require processing all nodes at the same depth before moving deeper. For example, calculating the average salary at each management level in a company hierarchy or returning a list of employees by department tier.
3. Connected Components & State Propagation: Determining how many isolated groups exist in a network (like separate teams in an org) or simulating the spread of a change (like a policy update) through a connected graph from a source node.

The common thread is translating a business scenario into a graph—identifying what constitutes a node (an employee, a document, a state) and an edge (a reporting line, a dependency, a transition).

How to Prepare — Study Tips with One Code Example

Master the standard iterative BFS template using a queue. Your mental checklist should be: Queue, Visited Set, Level Tracking.

• Queue: Manages the exploration frontier.
• Visited Set: Prevents cycles and redundant processing—critical in graphs, not just trees.
• Level Tracking: Essential for problems requiring shortest path length or level-wise operations. You can track this by recording the queue size at the start of each level.

Practice implementing this pattern until it's automatic. Here is the core template for finding the shortest path length from a start node to a target node in an unweighted graph:

from collections import deque

def bfs_shortest_path(graph, start, target):
    if start == target:
        return 0
    queue = deque([start])
    visited = set([start])
    distance = 0

    while queue:
        # Process all nodes at the current level
        for _ in range(len(queue)):
            node = queue.popleft()
            # Check neighbors
            for neighbor in graph[node]:
                if neighbor == target:
                    return distance + 1
                if neighbor not in visited:
                    visited.add(neighbor)
                    queue.append(neighbor)
        distance += 1
    return -1  # Target not reachable

Recommended Practice Order

Build competency progressively. Start with pure traversal on trees, then introduce graphs and level-tracking, and finally solve integrated problems.

1. Fundamentals: Binary Tree Level Order Traversal. This cements the queue and level-size pattern without a visited set.
2. Core Graph Search: Find if a path exists between two nodes in a graph. This adds the visited set to handle cycles.
3. Shortest Path Application: Word Ladder or a similar problem. This applies the full template to find a minimum transformation sequence.
4. Zenefits-Specific Practice: Finally, tackle the problems tagged for Zenefits to acclimate to their problem framing and constraints.

Practice Breadth-First Search at Zenefits