# How to check if search problem has no solution in depth limit search?

• MHB
• shivajikobardan
In summary, the depth limit for a search problem is determined by considering the complexity of the problem and available resources. It serves to prevent the search algorithm from getting stuck or taking too much time. If a search problem has no solution within the depth limit, the algorithm reaches the limit without finding a solution. It is possible for a search problem to have no solution even with a high depth limit, in which case the approach or algorithm may need to be reconsidered. In some cases, there may be no solution at all and further modifications or help from experts may be necessary.
shivajikobardan
Depth-limited search can be terminated with two Conditions of failure:

Standard Failure: it indicates that the problem does not have any solutions.

Cutoff Failure Value: It defines no solution for the problem within a given depth limit.

https://www.analyticsvidhya.com/blog/2021/02/uninformed-search-algorithms-in-ai/
https://www.javatpoint.com/ai-uninformed-search-algorithms
I checked for cut off failure. But I don't know how to check for standard failure. Can you guide me a bit?
Python:
# Python dictionary to act as an adjacency list
graph = {
'7' : ['19','21', '14'],
'19': ['1', '12', '31'],
'21': [],
'14': ['23', '6'],
'1' : [],
'12': [],
'31': [],
'23': [],
'6' : []
}

goal='6'
visited = [] # List of visited nodes of graph.
def dls(visited, graph, node,depth):
if(depth>=0):

if node not in visited:
visited.append(node)

if(node==goal):
print("goal found")
print("path to goal=",visited)
exit()        for neighbor in graph[node]:
dls(visited, graph, neighbor,depth-1)

print(node)

# Driver Code
print("Following is the Depth-First Search")
res=dls(visited, graph, '7',1)
if(res):
print("Path to goal node available")
print("Path",path)
else:
print("No path available for the goal node in given depth limit ie cut off failure")

print("visited=",visited)

it is important to have a clear understanding of the problem and its constraints before beginning any search algorithm. In this case, we are dealing with an uninformed search algorithm, which means that we do not have any prior knowledge about the problem. Therefore, we need to carefully analyze the problem and its parameters before implementing any search algorithm.

To check for standard failure in depth-limited search, we need to consider the following:

1. The problem may have multiple solutions, but none of them can be found within the given depth limit. In this case, the algorithm will terminate with a cutoff failure value, but we cannot conclude that the problem does not have any solutions. Therefore, we need to check if there are any unvisited nodes left after the algorithm terminates. If there are unvisited nodes, it means that the problem may have solutions beyond the given depth limit.

2. The problem may have a solution, but it cannot be reached within the given depth limit due to the structure of the search space. In this case, the algorithm will also terminate with a cutoff failure value, but we cannot conclude that the problem does not have any solutions. Therefore, we need to carefully analyze the search space and consider adjusting the depth limit to see if a solution can be found.

In summary, to check for standard failure in depth-limited search, we need to carefully analyze the search space and consider adjusting the depth limit if necessary. We also need to check if there are any unvisited nodes after the algorithm terminates to ensure that the problem does not have any solutions.

## 1. How does depth limit search differ from other search methods?

Depth limit search is a search method that limits the depth of the search tree, meaning it will only search a certain number of levels deep before stopping. This is different from other search methods such as breadth-first search, which explores all possible paths before moving to the next level.

## 2. What is the purpose of setting a depth limit in a search problem?

The purpose of setting a depth limit is to prevent the search algorithm from getting stuck in an infinite loop or taking too long to find a solution. It also helps to conserve memory and computing resources by limiting the amount of space needed to store the search tree.

## 3. How do you determine the appropriate depth limit for a search problem?

The appropriate depth limit for a search problem depends on various factors such as the complexity of the problem, the available computing resources, and the desired level of accuracy. Generally, a higher depth limit will result in a more accurate solution, but it may also take longer to find. It is important to balance these factors when determining the depth limit.

## 4. What is the best way to check if a search problem has no solution using depth limit search?

The best way to check if a search problem has no solution using depth limit search is to set the depth limit to a reasonably high value and see if the algorithm is able to find a solution within that limit. If the algorithm is unable to find a solution within the set depth limit, it is likely that the problem does not have a solution.

## 5. Are there any alternatives to depth limit search for checking if a search problem has no solution?

Yes, there are other methods for checking if a search problem has no solution. One alternative is to use a heuristic search algorithm, which uses an informed approach to determine the next best step in the search process. Another alternative is to use a constraint satisfaction algorithm, which checks if a set of constraints can be satisfied or not. Both of these methods can be more efficient and accurate than depth limit search in certain situations.

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