## Introduction to Depth First Iterative Deepening Search (DFID)

Have you ever searched for something and found yourself lost in an endless number of possibilities? This can happen when searching for the optimal solution to a problem using search algorithms.

There are many types of search algorithms such as Depth First Search (DFS) and Breadth First Search (BFS), each with their own advantages and disadvantages. But have you heard of Depth First Iterative Deepening Search (DFID)?

DFID is an algorithm used to search for the optimal solution using less space and time complexity than BFS and DFS. In this article, we will explore DFID, its advantages over BFS and DFS, and how it works.

## Advantages of DFID over BFS and DFS

DFID combines the advantages of BFS and DFS. BFS is guaranteed to find the optimal solution with the least number of steps, but it requires more space complexity than DFS.

DFS, on the other hand, uses less space complexity but may not find the optimal solution. DFID solves the issues of BFS and DFS by finding the shortest path to the goal state using a depth-first search while limiting the depth of the search.

DFID begins with a depth limit of one for the first iteration, followed by an increase in the limit each iteration until the goal state is reached.

## Working of DFID algorithm

The working of DFID is based on the depth of the search. It begins with a depth limit of one and performs a DFS search.

If the goal state is not found, it increases the depth limit by one and performs another DFS search. This process is repeated until the goal state is found.

DFID keeps the current limit in memory and discards the nodes beyond the limit, reducing space complexity.

## Implementation of DFID in Python

The implementation of DFID in Python requires the creation of a graph class containing nodes. Each node represents a state in the state space of the problem.

The dfids() function is responsible for searching the graph for the optimal solution. It takes in the search parameters (node, depth, limit) and returns the optimal solution.

```
class Graph:
def __init__(self, graph_dict=None):
if graph_dict is None:
graph_dict = {}
self.graph_dict = graph_dict
def add_edge(self, node1, node2):
if node1 not in self.graph_dict:
self.graph_dict[node1] = [node2]
else:
self.graph_dict[node1].append(node2)
def get_nodes(self):
return list(self.graph_dict.keys())
def get_edges(self):
return self.graph_dict.items()
def dfids(graph, start, goal, limit):
for depth in range(limit):
visited = {}
stack = [start]
while stack:
node = stack.pop()
if node not in visited:
visited[node] = True
if node == goal:
return True
for neighbor in graph.graph_dict[node]:
if neighbor not in visited:
stack.append(neighbor)
if len(visited) == len(graph.get_nodes()):
return False
return False
# Example graph
graph = Graph()
graph.add_edge("A", "B")
graph.add_edge("A", "C")
graph.add_edge("B", "D")
graph.add_edge("B", "E")
graph.add_edge("C", "F")
graph.add_edge("C", "G")
graph.add_edge("D", "H")
graph.add_edge("E", "I")
graph.add_edge("F", "J")
graph.add_edge("G", "K")
# Find the shortest path from A to K
start = "A"
goal = "K"
limit = 6
if dfids(graph, start, goal, limit):
print("Goal state found!")
else:
print("Goal state not found!")
```

## Example application using DFID

Consider a problem where you need to find the shortest path to a destination in a city. The roads connecting the destinations are represented as a graph of nodes, where each node represents an intersection, and each edge represents a connecting road.

The optimal solution for this problem is finding the path with the least number of intersections. DFID is an ideal search algorithm for this problem since it is guaranteed to find the optimal solution while using less space complexity than BFS.

## Conclusion

Depth First Iterative Deepening Search (DFID) is a powerful search algorithm that combines the advantages of BFS and DFS. It is used to find the optimal solution to a problem while using less space and time complexity than BFS and DFS.

DFID employs a depth-first search algorithm while limiting the depth of the search, ensuring that only nodes within the limit are kept in memory. DFID is an ideal search algorithm for problems that require finding the optimal solution while using limited space resources.

Next time you find yourself lost in search possibilities, try using DFID to find the optimal solution.

## Applications of DFID

Depth First Iterative Deepening search (DFID) is a powerful algorithm used to find the optimal solution to problems in various fields. In this section, we will discuss some applications of DFID in artificial intelligence (AI), data science, puzzle-solving, graph analysis, sorting a directed acyclic graph (DAG), and solving the N-Queens problem.

### Use of DFID in AI and Data Science

DFID is widely used in AI and data science for network analysis. Network analysis aims to understand the relationships between different data points in a network or graph.

DFID can be used to analyze networks with millions of nodes by searching for the shortest path to a goal state. It can also be used for heuristic searches in machine learning algorithms to optimize decision-making.

### Puzzle-solving with DFID

DFID is a popular algorithm for solving puzzles such as sudoku. Sudoku is a number-placement puzzle that requires placing numbers in a 9×9 grid with some given constraints.

DFID can be used to solve this puzzle by representing the different possible solutions as nodes in a graph and searching for the shortest path to the goal state. The search begins with a depth limit of 1, and the depth is increased in each iteration until the goal state is found.

### Detecting cycle in a graph using DFID

Detecting a cycle in a graph is an important application of DFID. A cycle in a graph refers to a path in which the first and last vertices are the same.

To detect a cycle, DFID can perform a depth-first search while keeping track of the visited nodes. If a visited node is visited again, then it means that there is a cycle in the graph.

This algorithm is efficient and can detect cycles in large graphs within a reasonable amount of time.

### Sorting Directed Acyclic Graph (DAG) with DFID

DFID can be used to sort a directed acyclic graph (DAG) efficiently. DAG is a graph that contains no cycles.

It is used in several applications such as flow networks, scheduling, and classification problems. To sort a DAG, DFID can perform a topological sort algorithm by searching for the nodes in the graph with no incoming edges.

These nodes are added to a queue and then removed from the graph. This process is repeated until all nodes have been removed from the graph.

### N-Queens problem and DFID

DFID can be used to solve the N-Queens problem. The N-Queens problem is a classic problem where a player must place N queens on a chessboard such that no two queens attack each other.

DFID can represent the different possible solutions as nodes in a graph and search for the optimal solution. The search begins with a depth limit of 1 and increases the depth in each iteration until the optimal solution is found.

## Conclusion

DFID is a powerful algorithm that can be applied to many problems in various fields, including AI, data science, puzzle-solving, graph analysis, sorting a directed acyclic graph, and problem-solving. By combining the advantages of DFS and BFS, DFID guarantees to find the optimal solution while using less space and time complexity than BFS and DFS.

Its ability to work with large graphs and its efficiency in finding optimal solutions make DFID an important algorithm in several applications. In conclusion, Depth First Iterative Deepening (DFID) is a powerful algorithm with various applications in different fields.

Its ability to find the optimal solution through a combination of DFS and BFS makes it a preferred algorithm over the others. DFID finds its use in AI and Data Science, puzzle-solving, cycle detection of a graph, sorting DAG, and even solving the N-Queens problem.

Its efficiency and ability to work with large graphs make it an ideal algorithm to find optimal solutions. DFID is an important algorithm whose use continues to grow in importance, with the potential to provide faster and optimal solutions to complex problems.