Matrix Questions at Nutanix: What to Expect

Matrix questions are a significant part of Nutanix's technical interview process, making up 11 of their 68 total coding problems. This focus reflects the company's core engineering challenges. Nutanix software creates a seamless, scalable computing fabric that abstracts and pools resources across servers—a system fundamentally built on distributed data structures and state management that often map conceptually to 2D grids. Proficiency with matrix traversal, transformation, and analysis is not just an algorithmic exercise here; it's directly relevant to problems involving cluster management, data placement, and network simulation. Doing well on these questions demonstrates you can think about systems-level problems with the spatial and computational efficiency they require.

What to Expect — Types of Problems

The matrix problems at Nutanix typically fall into a few key categories. Expect traversal patterns like spiral order, diagonal traversal, or zigzag (snake) order. These test your ability to manipulate indices and loop boundaries precisely. Search and pathfinding problems are also common, such as searching a row-and-column-sorted matrix, or finding the shortest path in a grid (a classic BFS application). Another frequent type involves modification in-place, like rotating an image (matrix) by 90 degrees or setting matrix cells to zero based on certain conditions without using extra space. These problems evaluate your understanding of space complexity and your ability to work within constraints, mirroring real-world system limitations.

How to Prepare — Study Tips with One Code Example

Start by mastering the fundamental techniques: navigating a matrix using nested loops, understanding row-major vs. column-major order, and using direction arrays for BFS/DFS. Practice writing these patterns from scratch until they are automatic. Then, focus on the specific problem types mentioned. For each type, learn the core algorithm and its common variations.

A critical pattern is using BFS for shortest path in a grid. This involves a queue, a visited set (or a modified input matrix to track visits), and direction vectors for moving up, down, left, and right. Here is a template for finding the shortest path from the top-left to bottom-right cell, where 0 is a passable cell and 1 is an obstacle:

from collections import deque

def shortestPathBinaryMatrix(grid):
    if not grid or grid[0][0] == 1:
        return -1
    n = len(grid)
    directions = [(0,1),(0,-1),(1,0),(-1,0),(1,1),(1,-1),(-1,1),(-1,-1)]
    queue = deque([(0, 0, 1)])  # (row, col, distance)
    grid[0][0] = 1  # Mark as visited

    while queue:
        r, c, dist = queue.popleft()
        if r == n-1 and c == n-1:
            return dist
        for dr, dc in directions:
            nr, nc = r + dr, c + dc
            if 0 <= nr < n and 0 <= nc < n and grid[nr][nc] == 0:
                queue.append((nr, nc, dist + 1))
                grid[nr][nc] = 1  # Mark visited
    return -1

Recommended Practice Order

1. Basics: Practice simple traversals (row-wise, column-wise) and operations like transposition.
2. Core Patterns: Solve standard problems: spiral traversal, matrix rotation, set matrix zeroes, and search in a sorted matrix.
3. Graph-based Grid Problems: Move to BFS/DFS on grids—number of islands, shortest path, and surrounded regions.
4. Nutanix-Specific: Finally, tackle the 11 Matrix problems in the Nutanix company tag. This order builds from foundational skills to the specific application you'll need.

Practice Matrix at Nutanix