Breadth-First Search Questions at Nutanix: What to Expect

Breadth-First Search (BFS) is a core algorithm for navigating graphs and trees level by level. At Nutanix, a company specializing in cloud infrastructure and hyper-converged systems, BFS appears in approximately 18% of their technical interview questions (12 out of 68 total). This high frequency reflects its direct application to real-world infrastructure problems. Distributed systems, network topologies, and data center management often involve modeling nodes and connections—whether you're finding the shortest path between servers, calculating propagation delays, or traversing a state space for a configuration. Mastering BFS demonstrates you can think systematically about connectivity and layered exploration, which is crucial for engineering at Nutanix.

What to Expect — Types of Problems

Nutanix BFS questions typically extend beyond simple tree traversal. Expect problems that model real-world scenarios using graphs.

• Shortest Path in Unweighted Graphs: The most direct application. Given a network of servers or a grid representing a data center layout, find the minimum steps or hops between two points.
• Level-Order Traversal & Related Calculations: Problems may involve processing all nodes at a given distance (level), useful for simulating broadcast messages or analyzing concentric network zones.
• Connected Components & State Reachability: Given a system with interdependent components (like VMs or storage nodes), determine if all are reachable or group them into isolated clusters. You might also use BFS to explore possible states from a starting configuration.
• Modified Grid Traversals: Many problems are framed on a 2D grid, representing a layout or map. You'll use BFS to find the shortest path around obstacles, spread something (like a signal or update) across adjacent cells, or find the nearest target.

How to Prepare — Study Tips with One Code Example

Focus on the pattern, not just memorization. The core BFS pattern uses a queue to explore neighbors before moving deeper.

1. Internalize the Template: Be able to write the standard BFS skeleton from memory—initializing a queue, a "visited" set, and the level-by-level loop.
2. Identify the "Graph": Practice mapping the problem's elements (grid cells, tree nodes, system states) to graph vertices and defining what constitutes an "edge" or a valid move.
3. Handle Variations: Prepare for twists like multiple starting points, obstacles, or tracking additional data per node (e.g., distance, path).
4. Complexity Analysis: Always state the time and space complexity, typically O(N) for nodes visited.

Here is the essential BFS template for a graph, adaptable to most problems:

from collections import deque

def bfs(graph, start):
    visited = set([start])
    queue = deque([start])

    while queue:
        node = queue.popleft()
        # Process node here (e.g., check if it's a target)
        print(node)

        for neighbor in graph[node]:
            if neighbor not in visited:
                visited.add(neighbor)
                queue.append(neighbor)
    # Return result if needed

Recommended Practice Order

Build competency progressively:

1. Fundamentals: Start with basic level-order tree traversal and BFS on a simple adjacency list graph.
2. Grid Basics: Solve classic shortest path in a binary matrix or "number of islands" (connected components) on a grid.
3. Multiple Sources: Practice problems where BFS starts from several points simultaneously, like "rotting oranges" or "walls and gates."
4. Shortest Path Guarantee: Tackle problems where BFS guarantees the shortest path in an unweighted context, such as "word ladder" or "open the lock."
5. Complex State: Finally, attempt problems where the graph node is a custom state (e.g., a combination of positions or data), requiring you to encode/decode states for the visited set.

Practice Breadth-First Search at Nutanix