# What is the complexity of breadth-first search?

What is the complexity of breadth-first search? The time complexity of BFS if the entire tree is traversed is O(V) where V is the number of nodes. If the graph is represented as adjacency list:

## What is the complexity of breadth-first search?

The time complexity of BFS if the entire tree is traversed is O(V) where V is the number of nodes. If the graph is represented as adjacency list: Here, each node maintains a list of all its adjacent edges. Let’s assume that there are V number of nodes and E number of edges in the graph.

## What is the complexity of best first search?

Analysis : worst case time complexity for Best First Search is O(n * Log n) where n is number of nodes. In worst case, we may have to visit all nodes before we reach goal. Note that priority queue is implemented using Min(or Max) Heap, and insert and remove operations take O(log n) time.

What is the time complexity of breadth-first search in worst case?

The Time complexity of BFS is O(V + E) when Adjacency List is used and O(V^2) when Adjacency Matrix is used, where V stands for vertices and E stands for edges.

Why is BFS V E?

Thus the total running time of BFS is O(V+E). This can be viewed as a simple instance of aggregate analysis. Each vertex is visited once and each edge twice assuming implementation with an adjacency list so the running time is a constant multiple of the number of edges + number of vertices. Thus it is O(V + E).

### Why is A * better than best-first search?

Best First Search Example So in summary, both Greedy BFS and A* are Best first searches but Greedy BFS is neither complete, nor optimal whereas A* is both complete and optimal. However, A* uses more memory than Greedy BFS, but it guarantees that the path found is optimal.

### What is AO * algorithm?

AO* Algorithm basically based on problem decompositon (Breakdown problem into small pieces) When a problem can be divided into a set of sub problems, where each sub problem can be solved separately and a combination of these will be a solution, AND-OR graphs or AND – OR trees are used for representing the solution.

Why is BFS over DFS?

BFS can be used to find the shortest path, with unit weight edges, from a node (origional source) to another. Whereas, DFS can be used to exhaust all the choices because of its nature of going in depth, like discovering the longest path between two nodes in an acyclic graph.

Why BFS time complexity is V E?

## Why DFS complexity is V E?

The time complexity of DFS if the entire tree is traversed is O(V) where V is the number of nodes. So, the time complexity in this case is O(V) + O(E) = O(V + E). For an undirected graph, each edge appears twice. Once in the adjacency list of either end of the edge.