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# What is the maximum number of nodes expanded by breadth first tree search?

## What is the maximum number of nodes expanded by breadth first tree search?

What is the maximum number of nodes expanded by breadth-first tree search? (without dy- namic programming) Answer It’s bd (branching factor to the depth of the solution), which in this case is 4x+y.

A breadth-first search graph divides into layers, one for each depth. As in A*, a lower-bound estimate of the cost of an optimal path through node n is given by a node evaluation function f(g) = g(n) + h(n), where h is an admissible heuristic.

## What is node expansion?

Each application of a successor function to a node is called expanding the node. The start and goal nodes are labeled, and the order of node expansions is shown by a numeral next to each node. Nodes of the same depth are expanded according to some fixed order.

Breadth-first search (BFS) is a method for exploring a tree or graph. In a BFS, you first explore all the nodes one step away, then all the nodes two steps away, etc. A BFS will find the shortest path between the starting point and any other reachable node.

## Is the maximum number of successors of the node?

If there is no limit on the number of successors that a node can have, the tree is called a general tree. If there is an maximum number N of successors for a node, then the tree is called an N-ary tree. In a binary tree the two children are called the left and right.

## WHY A * algorithm is better than BFS?

The advantage of A* is that it normally expands far fewer nodes than BFS, but if that isn’t the case, BFS will be faster. That can happen if the heuristic used is poor, or if the graph is very sparse or small, or if the heuristic fails for a given graph. Keep in mind that BFS is only useful for unweighted graphs.

## HOW DOES a * search work?

A* is an informed search algorithm, or a best-first search, meaning that it is formulated in terms of weighted graphs: starting from a specific starting node of a graph, it aims to find a path to the given goal node having the smallest cost (least distance travelled, shortest time, etc.).

## Which search method will expand the node that is closest to the goal?

In the best first search algorithm, we expand the node which is closest to the goal node and the closest cost is estimated by heuristic function, i.e.

## Why is BFS better for the shortest path?

We say that BFS is the algorithm to use if we want to find the shortest path in an undirected, unweighted graph. The claim for BFS is that the first time a node is discovered during the traversal, that distance from the source would give us the shortest path. The same cannot be said for a weighted graph.

## Where is Breadth First Search used?

Breadth-first search can be used to solve many problems in graph theory, for example: Copying garbage collection, Cheney’s algorithm. Finding the shortest path between two nodes u and v, with path length measured by number of edges (an advantage over depth-first search)

## Which is the best definition of breadth first search?

Breadth-first search ( BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a ‘search key’ ), and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level.

## How is the time complexity of breadth first search calculated?

For each node, we discover all its neighbors by traversing its adjacency list just once in linear time. For a directed graph, the sum of the sizes of the adjacency lists of all the nodes is E. So, the time complexity in this case is O (V) + O (E) = O (V + E). For an undirected graph, each edge appears twice.

## Is there a breadth first search for a graph?

Breadth First Traversal (or Search) for a graph is similar to Breadth First Traversal of a tree (See method 2 of this post ). The only catch here is, unlike trees, graphs may contain cycles, so we may come to the same node again. To avoid processing a node more than once, we use a boolean visited array.

## What is the total number of nodes generated by iterative search?

Here i found this on this website, it might help what you are looking for, the number really depends on the values for d and b : “In an iterative deepening search, the nodes at depth d are expanded once, those at depth d-1 are expanded twice, and so on up to the root of the search tree, which is expanded d+1 times. [5]