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

[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 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)

 

[lofgran]

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.