# Greedy Best First Search

> search algorithm

**Wikidata**: [Q130323044](https://www.wikidata.org/wiki/Q130323044)  
**Source**: https://4ort.xyz/entity/greedy-best-first-search

## Summary
Greedy Best First Search (GBFS) is an informed search algorithm that uses a heuristic function to guide its exploration of a graph or tree structure. It prioritizes nodes that appear closest to the goal based on the heuristic, making it faster than uninformed search methods but not guaranteed to find the optimal solution.

## Key Facts
- GBFS is classified as an informed search algorithm, meaning it uses heuristic information to guide its search process
- It is a subclass of graph traversal algorithms, specifically designed for finding paths in graphs
- The algorithm is also known by alternative names including Greedy Best-First Search, Greedy BFS, and GBFS
- It is described at https://the-algorithms.com/algorithm/greedy-best-first
- GBFS is not guaranteed to find the optimal solution, unlike algorithms such as A* search
- The algorithm makes locally optimal choices at each step, hence the term "greedy"
- It uses a priority queue to select the next node to explore based on heuristic values

## FAQs
### Q: How does Greedy Best First Search differ from A* search?
A: Greedy Best First Search uses only a heuristic function to guide its search, while A* search combines both the cost to reach a node and the heuristic estimate to the goal. This makes GBFS faster but potentially less optimal than A*.

### Q: What type of problems is Greedy Best First Search best suited for?
A: GBFS works well for problems where finding a good solution quickly is more important than finding the absolute best solution, such as pathfinding in games or heuristic-based optimization problems.

### Q: What is the main advantage of using Greedy Best First Search?
A: The main advantage of GBFS is its speed and efficiency in finding solutions, as it uses heuristic information to avoid exploring unpromising paths, making it faster than uninformed search algorithms.

## Why It Matters
Greedy Best First Search represents a fundamental approach in artificial intelligence and computer science for solving search problems efficiently. By leveraging heuristic information, GBFS can dramatically reduce the search space compared to uninformed methods, making it invaluable for applications where computational resources are limited or quick solutions are prioritized over optimal ones. The algorithm's greedy nature—making the locally optimal choice at each step—exemplifies a key trade-off in algorithm design between solution quality and computational efficiency. This trade-off is particularly relevant in real-time systems, game AI, and other applications where response time is critical. GBFS also serves as an educational stepping stone to more sophisticated algorithms like A* search, helping students and practitioners understand the role of heuristics in search problems.

## Notable For
- Being one of the simplest informed search algorithms to implement and understand
- Providing a foundation for understanding more complex heuristic search algorithms
- Demonstrating the trade-off between solution optimality and computational efficiency
- Being widely used in game development for pathfinding and NPC behavior
- Serving as a practical example of greedy algorithm design principles

## Body
### Algorithm Characteristics
Greedy Best First Search operates by maintaining a priority queue of nodes to be explored, where the priority is determined by a heuristic function that estimates the cost from each node to the goal. At each step, the algorithm selects the node with the lowest heuristic value, expanding it and adding its neighbors to the queue.

### Heuristic Function
The effectiveness of GBFS heavily depends on the quality of the heuristic function used. A good heuristic should provide an admissible estimate of the remaining cost to reach the goal, though unlike A*, GBFS doesn't require the heuristic to be consistent. Common heuristics include Manhattan distance for grid-based problems and Euclidean distance for continuous spaces.

### Performance Characteristics
GBFS typically performs better than uninformed search algorithms like breadth-first search in terms of time and space complexity, especially in large search spaces. However, it can get stuck in local minima or fail to find the optimal path if the heuristic is misleading. The algorithm's time complexity is generally O(b^m) in the worst case, where b is the branching factor and m is the maximum depth of the search tree.

### Comparison with Other Algorithms
While GBFS is faster than A* in many cases due to its simpler evaluation function, it lacks the optimality guarantee that A* provides. A* combines the actual cost to reach a node with the heuristic estimate, ensuring that if a solution exists, A* will find the optimal one. GBFS, by contrast, only considers the heuristic, making it more susceptible to suboptimal paths but often faster in practice.

### Applications
Greedy Best First Search finds applications in various domains including:
- Pathfinding in video games and robotics
- Heuristic-based optimization problems
- Puzzle solving (like the 8-puzzle or Rubik's cube)
- Network routing protocols
- Natural language processing tasks involving search through large state spaces

### Implementation Considerations
When implementing GBFS, key considerations include:
- Choosing an appropriate data structure for the priority queue (typically a heap)
- Designing an effective heuristic function for the specific problem domain
- Handling cycles and repeated states to avoid infinite loops
- Managing memory usage, as the algorithm can store many nodes in the priority queue