Dijkstra’s Shortest Path Algorithm and A* Algorithm A-Level Resources

A Level Computer Science: Dijkstra’s Shortest Path Algorithm and A* Algorithm

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Frequently Asked Questions

What is the primary goal of Dijkstra's Shortest Path Algorithm?

Dijkstra's algorithm aims to find the shortest paths from a specified source node to all other nodes in a weighted graph, ensuring the most efficient route is determined.

In what scenarios is Dijkstra's algorithm particularly effective, and what are its limitations?

Dijkstra's algorithm is effective for finding shortest paths in graphs with non-negative edge weights. Its limitations include inefficiency when dealing with graphs with negative edge weights and the need for additional modifications to handle such cases.

How does A* Algorithm incorporate a heuristic, and what is the purpose of this heuristic?

A* uses a heuristic function to estimate the remaining cost to reach the goal from a given node. This heuristic guides the algorithm's exploration, combining informed decisions with the efficiency of algorithms like Dijkstra's to find the shortest path more quickly.

What conditions must be satisfied for A* Algorithm to guarantee finding the shortest path?

A* guarantees finding the shortest path if the heuristic is admissible (never overestimates the cost) and consistent (satisfies the triangle inequality). If these conditions are met, A* will always find the optimal solution.

How do Dijkstra's algorithm and A* algorithm differ in terms of their use of heuristics and optimality guarantees?

Dijkstra's algorithm does not use heuristics and guarantees optimality in finding the shortest path, but it may be less efficient. A* combines heuristics with the benefits of algorithms like Dijkstra's and also guarantees optimality under certain conditions, making it more efficient in many practical scenarios.