The repetitive search processes of level 1 and level 2 happen in this search. The search processes continue until the solution is found. Nodes are generated until a single goal node is created. Stack of nodes is saved.

In the context of artificial intelligence, an iterative deepening depth-first search (IDDFS) algorithm is a combination of two search strategies: depth-first search (DFS) and iterative deepening.

Here’s how it works:

Depth-First Search (DFS): DFS explores as far as possible along each branch before backtracking. It starts at the root node and explores as far as possible along each branch before backtracking.
Iterative Deepening: This strategy is used to overcome some of the limitations of DFS. Instead of searching to the maximum depth of the tree in one go, iterative deepening performs multiple depth-first searches with increasing depth limits. It starts with a depth limit of 0, then gradually increases the depth limit until the goal is found.

By combining these two techniques, IDDFS ensures that the search explores deeper levels gradually, effectively balancing the benefits of DFS (space efficiency) with the advantages of breadth-first search (completeness and optimality). It is particularly useful in scenarios where the depth of the search tree is unknown and memory constraints are tight.

The key idea behind IDDFS is to reap the benefits of DFS’s memory efficiency while ensuring completeness and optimality by gradually increasing the depth limit. This allows IDDFS to find the optimal solution with minimal memory usage.