Algorithms Analysis Practice Test 2025 – All-in-One Mastery Guide to Exam Success

The shortest-path algorithm is designed specifically for finding the best sequence of connections between nodes in a graph while minimizing the total cost or distance, which in this case translates to minimizing total flight time. This algorithm is particularly effective in directed graphs where each edge has a weight that can represent the flight time between connections.

Using the shortest-path algorithm, such as Dijkstra’s Algorithm or the Bellman-Ford Algorithm, allows for the examination of all possible paths and the aggregation of their respective weights (flight times). Ultimately, it identifies the path that has the minimum cumulative time from the starting point to the destination, which is exactly what one would need to optimize flight connections.

Both breadth-first search and depth-first search are primarily used for exploring the nodes and edges of a graph but do not take edge weights into consideration for path optimization. They can discover whether a path exists, but they lack the capability to determine the optimal path concerning flight time. The cycle-finding algorithm is used to identify cycles within a graph and is not concerned with path optimization, making it unsuitable for this scenario. Thus, the shortest-path algorithm emerges as the most appropriate choice for this problem.