Circle·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Coding round at Circle for a software engineer role. One meaty graph/shortest-path problem that also required me to explain the algorithm, complexity, and a few tricky constraints out loud. Left feeling like I handled the core logic okay but stumbled a bit on the cycle-avoidance explanation.

Questions Asked (1)

Given a list of flights (each with an ID, source, destination, departure time, arrival time, and price), implement a function that finds the cheapest itinerary from an origin to a destination. Only consider itineraries where the first flight departs within a given date range. Return the minimum total price and the ordered list of flight IDs, or -1 if no valid itinerary exists. You also need to explain your algorithm, its time and space complexity, and how you handle connection ordering and cycle prevention.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The core pathfinding part I got to pretty quickly.

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AI HintsAI Generated

Suggested Approach

Model the flights as a weighted directed graph where edge weight is price, then use a modified Dijkstra's algorithm to find the cheapest itinerary from origin to destination while enforcing the departure date range and preventing cycles. Clearly explain the algorithm, its time and space complexity, and how you handle connection ordering and cycle prevention.

Pro tip: Mention that you can optimize by only considering flights departing within the date range and using a priority queue to explore paths in increasing cost order, ensuring the first valid itinerary found is optimal.

1. Clarify requirements and edge cases

Ask about input format, date range inclusivity, whether multiple flights can have the same source/destination, and if itineraries can have multiple stops. Confirm that cycles are not allowed and that the first flight must depart within the given date range.

2. Model as a graph problem

Represent each flight as a directed edge from source to destination with weight equal to price. The graph is a directed weighted graph. The goal is to find the minimum cost path from origin to destination that starts with a flight departing within the date range.

3. Choose and adapt an algorithm

Use Dijkstra's algorithm with a priority queue to explore paths in increasing total cost. Modify it to only consider initial flights departing within the date range and to prevent cycles by tracking visited airports in the current path.

4. Analyze complexity and trade-offs

Time complexity: O(E log V) where E is number of flights and V is number of airports, but with cycle prevention it may be higher. Space complexity: O(V + E) for graph and priority queue. Discuss trade-offs between Dijkstra and BFS/DFS with pruning.

5. Handle connection ordering and cycle prevention

Ensure that connecting flights have departure time after arrival time of previous flight. Prevent cycles by not revisiting airports already in the current path, or by using a visited set per path.

Key Points to Mention

Graph representation: flights as edges, airports as nodes, price as weight.
Dijkstra's algorithm for minimum cost path, with priority queue.
Filtering initial flights by departure date range.
Cycle prevention by tracking visited airports in the current path.
Time complexity: O(E log V) or O(E + V log V) with optimizations.
Space complexity: O(V + E) for graph and auxiliary data structures.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.