What is the total number of nodes generated by Iterative Deepening depth first search and Breadth First search

Question

What is the total number of nodes generated by Iterative Deepening depth first search and Breadth First search in terms of branching factor "b" and depth of shallowest goal "d"

Answer 1

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 :

https://mhesham.wordpress.com/tag/depth-first-search/

Iterative Deepening DFS worst case # of nodes:

N(IDS) = (b)d + (d – 1)b2 + (d – 2)b3 + …. + (2)bd-1 + (1)bd = O(bd)

BFS worst case # of nodes generated:

N(BFS) = b + b2 + b3 + b4 + …. bd + (bd + 1 – b) = O(bd + 1)

Example using real numbers:

branching factor = 10 and depth of shallowest goal = 5

N(IDS) = 50 + 400 + 3000 + 20000 + 100000 = 123450

N(BFS) = 10 + 100 + 1000 + 10000 + 100000 + 999990 = 1111100

Answer 2

As seen on Wikipedia:

"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] So the total number of expansions in an iterative deepening search is IDS number of expansions

Example: For b=10 and d=5 example "

Reference: https://en.wikipedia.org/wiki/Iterative_deepening_depth-first_search#Proof