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Advanced Topic 37 of 51 Algorithms

A* Search

Heuristic-guided shortest path search.

How it works

A* is a best-first shortest-path search that expands the node with the lowest f = g + h, where g is the cost from the start and h is a heuristic estimate of the remaining cost to the goal. If the heuristic is admissible, never overestimating, A* finds an optimal path, and with a consistent heuristic no node is expanded twice. A good heuristic prunes much of the search space compared with Dijkstra.

Where it is used

Pathfinding in video games and robotics, route planning, puzzle solving such as the 8-puzzle and natural language parsing use A*. Grid maps often use Manhattan or Euclidean distance.

Common pitfall

An overestimating heuristic can return suboptimal paths, and a weak one makes A* behave like Dijkstra. Memory use can be large because the open set holds many nodes. Tie-breaking, diagonal costs and updating nodes in the open set are common sources of bugs. Consider IDA* for memory limits.

Where it fits in the course

A* Search is topic 37 of 51 in Algorithms, rated Advanced. It follows Floyd-Warshall Algorithm. The next topic is Minimum Spanning Tree.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Algorithms quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is A* Search?
Heuristic-guided shortest path search. It belongs to Algorithms and is an advanced-level topic.
Where do people use A* Search?
Pathfinding in video games and robotics, route planning, puzzle solving such as the 8-puzzle and natural language parsing use A*.
What is the most common mistake with A* Search?
An overestimating heuristic can return suboptimal paths, and a weak one makes A* behave like Dijkstra.
What should I learn before this topic?
Start with Floyd-Warshall Algorithm, the topic just before it in Algorithms.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Algorithms quiz. You can also explore Graph Traversal in the Visual Lab.
Is A* Search hard to learn?
It is an Advanced topic. Expect to read the explanation more than once and to connect it with earlier topics. Working through a small example by hand helps most.
How long does it take to learn A* Search?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to A* Search?
Floyd-Warshall Algorithm, Minimum Spanning Tree, Bellman-Ford Algorithm are closely connected. The full list is in the related topics section of this page.
What should I study after A* Search?
Continue with Minimum Spanning Tree, the next topic in Algorithms.

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