How to Find the Branching Factor of a Tree

Question

A particular search tree has 6 nodes at level 3. At the next level, there are 24 nodes. What is the branching factor at level 3?

The answer is 4, but can someone tell me why, I thought that it was 2.

Swung

Wikipedia: en.wikipedia.org/wiki/Branching_factor – Madera

Answer 1

From Wikipedia:

In computing, tree data structures, and game theory, the branching factor is the number of children at each node, the outdegree. If this value is not uniform, an average branching factor can be calculated.

You have 6 nodes at level 3, 24 nodes at level 4, so the average number of children per node at level 3 is 24/6=4.

Benita

Answer 2

On different types of trees the branching factor can be either a static value throughout the tree, which only happens in perfect binary trees or an average branching factor which is most time the case for trees.

The branching factor is one characteristic of a node next to depth and gives a clue how complex a tree gets. For example, for the GO Game on a 19x19 board, the branching factor on the first level is 361, after 4 more moves at depth 4 you end up having 10 billion nodes. (possible moves)

Source: An Introduction To Artificial Intelligence, Janet Finlay

Agata

Answer 3

You could also just draw a search tree. Start with level 3. 6 nodes have 24 successors. It means that each of the 6 nodes has 24/6= 4 children. You can check this: 6 parent nodes * 4 children = 24 nodes on level 4. The branching factor at level 3 is thus 4.

Edgebone