Breadth-First Search Questions at Walmart Labs: What to Expect

Breadth-First Search (BFS) is a core algorithm for navigating graphs and trees level-by-level. At Walmart Labs, with 14 BFS questions in their problem bank, it's a non-negotiable skill. The company's massive scale—managing global supply chains, real-time inventory, fulfillment networks, and millions of customer interactions—relies heavily on graph-based data models. Whether optimizing delivery routes (a graph of locations), analyzing social connections between products, or traversing hierarchical data structures, BFS provides the fundamental tool for finding shortest paths and exploring connected systems in a systematic, efficient way. Mastering it demonstrates you can think in terms of scalable, level-order exploration, a common requirement for building distributed systems at their level.

What to Expect — Types of Problems

Walmart Labs' BFS problems typically fall into two practical categories:

1. Shortest Path in Unweighted Graphs: This is the most direct application. You'll be given a graph (often represented as an adjacency list or a matrix) and asked to find the minimum number of steps or edges between two points. Common scenarios include navigating a grid (like a warehouse map), the classic "word ladder" problem, or finding the degree of separation in a network.
2. Level-Order Traversal & Analysis: Here, BFS is used to process nodes in layers. Problems may involve calculating the minimum depth of a tree, finding the largest value in each tree level, or performing operations that require all nodes at the same "distance" or stage to be handled together before moving deeper. This pattern is crucial for hierarchical data processing.

The constraints will often push you to consider space complexity carefully, as BFS uses a queue that can grow significantly.

How to Prepare — Study Tips with One Code Example

Focus on the pattern, not just memorization. The core BFS template involves a queue, a visited set, and a loop that processes nodes level by level.

1. Internalize the Template: Write the BFS skeleton from memory until it's automatic. This includes initializing the queue with the start node, marking it as visited, and then using a while loop to expand.
2. Practice on Grids: Many problems use a 2D grid. Practice moving in four (up, down, left, right) or eight directions. The key is to generate neighbor coordinates and validate them before adding to the queue.
3. Track Distance: For shortest path problems, integrate distance tracking directly into your queue (e.g., storing (node, distance) tuples) or use a counter within your level-order loop.

Here is the essential BFS template for finding the shortest path in an unweighted graph, applied to a common grid problem ("Number of Islands" variant for shortest path from top-left to bottom-right).

from collections import deque

def shortest_path(grid):
    if not grid or grid[0][0] == 1:
        return -1

    rows, cols = len(grid), len(grid[0])
    # Directions: right, left, down, up, and 4 diagonals
    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)
    visited = set((0, 0))

    while queue:
        r, c, dist = queue.popleft()
        if r == rows - 1 and c == cols - 1:
            return dist

        for dr, dc in directions:
            nr, nc = r + dr, c + dc
            if (0 <= nr < rows and 0 <= nc < cols and
                grid[nr][nc] == 0 and (nr, nc) not in visited):
                visited.add((nr, nc))
                queue.append((nr, nc, dist + 1))
    return -1

Recommended Practice Order

Build competence progressively. Start with pure BFS on trees (level-order traversal). Then move to standard graph shortest path problems on explicit adjacency lists. Next, tackle matrix/grid problems, which add the complexity of neighbor generation. Finally, practice the "word ladder" style problems, which often require you to implicitly build the graph during the BFS. This sequence solidifies the pattern before adding layers of complexity.

Practice Breadth-First Search at Walmart Labs