Process of Breadth first search:
It's very useful to think of this search as the evolution of the given tree, and how each string of letters of word is found via the search in a breadth first time. The numbers above the boxes specify at which step and why in the search the string was found.
We see that there each node leads to three others which are connect, which according to this fact that after every step of this procedure, three further steps are may be put on this agenda. This is known as the branching rate of a search to specified, and acutely affects both how long a search is going to be take and why and how much memory it will use up.
Breadth first search is an almost complete strategy for this kind of search: given enough period and memory for store, it will find a solution if one can exists. Unfortunately, this memory is a big type of problem for breadth first search. We can think for this how big the agenda grows, but in effect we are just counting the number of states which are still 'alive' for this , i.e., there are some still steps in the agenda for involving them. As it is clear in the above diagram, that states, which are still alive are those fewer than three arrows coming from them; obviously there are 14 in all.
It's fairly easy to know that in a search with a branching rate of b, if we really want to search all the way into a depth of d, then the largest number of states will be the agent that will have to store at any one time is b^{d-1}. For example, if our professor wanted to search for all the names up to length 8, than she would have to remember (or write down) 2187 on different strings to complete a breadth in first search. This is just because she would need to remember 3^{7} strings of length 7 in order to be set and able to build all the strings of length 8 from them which are use. In searches with a higher type of branching rate, for the memory requirement can often become too large for an agent's processor as it require.