Iterative Deepening Search (IDS) is a graph traversal algorithm that builds on the Depth-First Search (DFS) algorithm. The main idea behind IDS is to perform a series of depth-limited searches, increasing the depth limit with each iteration until the goal node is found.

IDS works by first performing a depth-limited search with a depth limit of one. If the goal node is not found at this depth, the algorithm performs a depth-limited search with a depth limit of two. This process continues, with the depth limit increasing by one with each iteration, until the goal node is found.

The advantage of IDS over DFS is that it avoids the problem of DFS getting stuck in an infinite loop when searching a graph with cycles. In DFS, once a cycle is encountered, the algorithm can get trapped in an infinite loop, repeatedly visiting the same nodes. IDS, on the other hand, limits the depth of each search, ensuring that the algorithm does not get stuck in an infinite loop.

Iterative Deepening Depth First Search (IDDFS) is a variant of IDS that combines the advantages of IDS and DFS. IDDFS performs a series of DFS searches, with the depth limit increasing with each iteration, just like in IDS. However, instead of restarting the search from the root node at each iteration, IDDFS continues the search from the last node visited in the previous iteration.

The advantage of IDDFS over IDS is that it can save time and memory by avoiding recomputing the same nodes in each iteration. However, IDDFS can still get stuck in an infinite loop if the graph has cycles.

Overall, IDS and IDDFS are useful algorithms for graph traversal when the depth of the goal node is unknown, and the graph is too large to be searched exhaustively. They can also be used as a baseline algorithm for more complex search algorithms, such as A* search.

Iterative Deepening Depth First Search (IDDFS) is an extension of the Depth First Search (DFS) algorithm. It uses a similar approach to DFS, but instead of limiting the search depth to a fixed value, IDDFS incrementally increases the depth limit with each iteration until a solution is found. Here is a breakdown of how IDDFS works:

- Set the initial depth limit to 1.
- Perform a depth-first search on the graph with the current depth limit.
- If the goal node is found, return the solution.
- If the goal node is not found and the maximum depth limit has not been reached, increment the depth limit and repeat from step 2.
- If the goal node is not found and the maximum depth limit has been reached, return failure.

In IDDFS, the search starts at the root node, and the algorithm traverses the graph or tree in a depth-first manner. However, instead of stopping when the maximum depth limit is reached, IDDFS increases the limit and performs another depth-first search. This process continues until the goal is found or the maximum depth limit is reached.

IDDFS guarantees that the optimal solution will be found with the least possible depth, as the algorithm explores all nodes up to a certain depth before incrementing the depth limit. However, it also performs a lot of redundant searches as it repeats the search process for each depth limit, which can be time-consuming in large search spaces.

Iterative Deepening Depth First Search (IDDFS) is a powerful algorithm that has various applications in computer science.

**Here are some of the common applications of IDDFS:**

**Artificial Intelligence**: IDDFS is widely used in artificial intelligence applications, particularly in game-playing algorithms. In games such as chess, checkers, or Go, IDDFS is used to search through the possible moves and determine the best possible move by exploring the game tree.**Robotics**: IDDFS is also used in robotics for motion planning and navigation in complex environments. In robotics, the search space is often large and unknown, making IDDFS an ideal search algorithm.**Natural Language Processing**: IDDFS is used in natural language processing to search through large knowledge graphs, such as Wikipedia or Google's Knowledge Graph, to extract relevant information.**Information Retrieval**: IDDFS is used in information retrieval systems to search through large databases and knowledge graphs. It is used to rank the search results based on their relevance to the query.**Machine Learning**: IDDFS is used in machine learning applications to search through the space of possible models or hyperparameters. It is used to optimize the performance of the machine learning algorithm.

**Advantages:**

**Optimal solution**: IDDFS is a complete algorithm, which means that it will always find a solution if one exists. Moreover, if the depth limit is set correctly, IDDFS will always find the optimal solution.**Less memory usage**: IDDFS uses less memory than Breadth-First Search (BFS), as it only needs to store the current path being traversed instead of the entire search tree.**Efficiency**: IDDFS is more efficient than BFS when the goal node is located near the root of the tree. This is because BFS needs to explore all nodes at a certain depth before moving on to the next depth level, whereas IDDFS will only explore the nodes along the path to the goal node.

**Disadvantages:**

**Repetitive computation**: IDDFS may re-compute nodes that were already visited in previous iterations, which can result in repetitive computation.**Time-consuming**: IDDFS can be time-consuming for large search spaces, as it performs multiple depth-first searches, each with an increasing depth limit.**May not work for infinite depth**: IDDFS may not be suitable for problems with infinite depth, as it will continue to increase the depth limit until the goal node is found, which may never happen.

Overall, IDDFS is a useful algorithm for graph traversal when the depth of the goal node is unknown, and the graph is too large to be searched exhaustively. However, it may not be the best choice for all problems, and the depth limit must be set appropriately to ensure efficient and effective search.

**Conclusion **

In conclusion, Iterative Deepening Depth First Search (IDDFS) is a search algorithm that combines the advantages of both depth-first search and breadth-first search. It is a complete algorithm that will always find a solution if one exists and is more memory-efficient than BFS. However, IDDFS may be time-consuming for large search spaces, and it may not be suitable for problems with infinite depth. IDDFS is a useful algorithm for graph traversal when the depth of the goal node is unknown, and the graph is too large to be searched exhaustively. As with any algorithm, the depth limit must be set appropriately to ensure efficient and effective search. Overall, IDDFS is a valuable addition to the range of search algorithms available to computer scientists and programmers.

**References**

*Korf, R. E. (1985). Depth-first iterative-deepening: An optimal admissible tree search. Artificial Intelligence, 27(1), 97-109.**Russell, S. J., & Norvig, P. (2010). Artificial intelligence: a modern approach. Prentice Hall Press.**Moffat, A., & Turpin, A. (2015). Compression and approximate search. Information Retrieval: Implementing and Evaluating Search Engines, 195-219.**Bhattacharya, S. (2014). Iterative deepening search. In Artificial intelligence and soft computing (pp. 283-287). Springer, Cham.**Masehian, E., & Binaee, K. (2008). Iterative deepening A* algorithm. Journal of Artificial Intelligence Research, 33, 445-462.*