Depth-First Search Questions at Nutanix: What to Expect

Depth-First Search (DFS) is a core algorithm for navigating graphs and trees, making it essential for solving problems involving hierarchical data, connected components, and pathfinding. At Nutanix, a company specializing in cloud infrastructure and hyper-converged systems, 13 of their 68 coding questions are tagged with DFS. This high frequency reflects the nature of their engineering challenges. Systems software, distributed file systems, and network management often involve traversing directory trees, analyzing network node connectivity, or exploring state spaces in resource management—all domains where DFS is a fundamental tool. Mastering it demonstrates you can think recursively and handle complex, nested data structures, a key skill for building and optimizing their core platforms.

What to Expect — Types of Problems

Nutanix's DFS questions typically fall into a few practical categories. You won't see abstract algorithm theory; you'll solve applied problems.

• Tree and N-ary Tree Traversal: This is the most common type. Expect to manipulate file system paths, serialize/deserialize directory structures, or compute properties like maximum depth or subtree sums. Questions often involve binary trees or trees where nodes can have multiple children.
• Graph Traversal and Connectivity: Problems may involve finding connected components in a network of servers or storage nodes, checking if a graph is bipartite (useful for resource allocation), or detecting cycles in dependencies.
• Pathfinding and Backtracking: Some questions require finding specific paths, such as a path that sums to a target value within a tree, or generating all possible configurations. This tests your ability to implement DFS with state management and pruning.
• Matrix Traversal (Flood Fill): While less frequent, you might encounter problems where you need to explore a grid, like identifying isolated storage blocks or regions in a system map.

The problems are medium difficulty, focusing on correct implementation and clean handling of edge cases over clever optimization.

How to Prepare — Study Tips with One Code Example

Focus on internalizing the recursive pattern and its iterative stack-based alternative. Practice writing DFS from scratch until it's automatic. Always clarify input/output formats and edge cases (empty tree, null graph) first.

The most critical pattern is the standard recursive traversal for a binary tree. You must be able to modify this skeleton to accumulate results, check conditions, or traverse in different orders (pre-order, in-order, post-order).

def dfs(node):
    if not node:
        return
    # Pre-order processing here (visit root first)
    print(node.val)
    dfs(node.left)
    # In-order processing here (for BST)
    dfs(node.right)
    # Post-order processing here (visit root last)

# Example: Collect all node values in a list (pre-order)
def collect_values(node, result):
    if not node:
        return
    result.append(node.val)
    collect_values(node.left, result)
    collect_values(node.right, result)

Recommended Practice Order

Build competence progressively. Start with basic tree traversals to cement the pattern. Move to problems where you modify the tree or compute a single value (like max depth). Then tackle path-based problems and collection of multiple results (like finding all paths). Finally, practice graph-specific problems (adjacency list representation, cycle detection, connected components). Time yourself to simulate interview conditions.

Practice Depth-First Search at Nutanix