Breadth-First Search Questions at LinkedIn: What to Expect

Breadth-First Search (BFS) is a core algorithm for traversing graphs and trees level-by-level. At LinkedIn, it's a frequent topic in technical interviews, appearing in 22 of their 180 cataloged problems. This prevalence stems from LinkedIn's engineering focus on networked systems—social graphs, recommendation engines, and infrastructure that maps connections between users, jobs, and content. BFS is the natural tool for finding shortest paths in unweighted graphs, performing level-order traversals, or exploring states in problems involving minimum steps or degrees of separation. Mastering it is non-negotiable for roles that handle data at LinkedIn's scale.

What to Expect — Types of Problems

LinkedIn's BFS questions typically fall into three categories.

1. Classic Graph Traversal & Shortest Path: These are direct applications of BFS on graph representations. You might be asked to find the shortest path between two nodes in an undirected graph, count the number of connected components, or determine if a path exists. Problems often model real-world scenarios like finding the minimum degree of connection between two members.
2. Tree Level-Order Traversal: While often solved with BFS, these problems explicitly require processing a tree level by level. Variations include zigzag (alternating direction) traversal, finding the largest value on each level, or calculating the average of each level.
3. Matrix/Grid Traversal: Many problems frame a 2D grid as a graph where each cell is a node connected to its adjacent cells. BFS is used to find the shortest path from a starting point, propagate influence (like in "rotting oranges" or "walls and gates" problems), or explore an area. This pattern is crucial for problems related to data propagation or geographic search.

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 nodes in order of their distance from the start. Always mark a node as visited the moment you enqueue it to avoid cycles. Practice writing this template from scratch until it's automatic.

A key pattern is BFS for shortest path in an unweighted graph. Here is the standard implementation:

from collections import deque

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

    while queue:
        level_size = len(queue)
        for _ in range(level_size):
            node = queue.popleft()
            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  # No path found

Recommended Practice Order

Start with fundamentals and build complexity.

1. Basic Traversal: Implement BFS on a simple graph and binary tree. Solve "Binary Tree Level Order Traversal."
2. Shortest Path: Practice the classic unweighted shortest path problem on an adjacency list.
3. Grid Problems: Apply BFS to a 2D matrix. Solve "Number of Islands" (though DFS is common, BFS works) and "Rotting Oranges."
4. LinkedIn-Specific: Tackle problems from LinkedIn's question list, beginning with easier frequency questions to build confidence before attempting harder ones.

Practice Breadth-First Search at LinkedIn