Shortest Path Problems (42)

The Shortest Path problem is one of the most fundamental concepts in graph algorithms. It focuses on finding the minimum distance, cost, or number of steps required to travel from one node to another in a graph. These problems appear in many real-world systems such as GPS navigation, network routing, airline scheduling, and social network analysis.

In coding interviews, shortest path questions test your understanding of Graph traversal, optimization strategies, and algorithmic efficiency. Many top tech companies expect candidates to recognize when a graph can be modeled with weighted or unweighted edges and to choose the correct algorithm accordingly. Classic algorithms like Dijkstra's Algorithm, Bellman-Ford, Floyd–Warshall, and BFS-based shortest path approaches frequently appear in interviews.

Several important patterns emerge when solving shortest path problems:

• Using Breadth-First Search to compute shortest paths in unweighted graphs.
• Applying priority queues with Heap (Priority Queue) for efficient weighted shortest path algorithms like Dijkstra.
• Handling negative weights using dynamic relaxation techniques similar to Dynamic Programming.
• Optimizing paths in DAGs using Topological Sort.

Recognizing these patterns allows you to quickly decide which approach to apply based on graph properties such as edge weights, cycles, or constraints on the number of edges. Interview questions often combine shortest path logic with other concepts like grids, state transitions, or multi-source searches.

FleetCode provides 31 carefully selected Shortest Path problems designed to build your intuition step by step. By practicing these problems, you will learn how to model problems as graphs, choose the correct algorithm, analyze time complexity, and implement optimized solutions confidently in interviews.