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## Depth First Search

Depth First Search (DFS) searches deeper into the problem space. Breadth-first search always generates successor of the deepest unexpanded node. It uses last-in first-out stack for keeping the unexpanded nodes. More commonly, depth-first search is implemented recursively, with the recursion stack taking the place of an explicit node stack.

### Algorithm: Depth First Search

1.If the initial state is a goal state, quit and return success.
2.Otherwise, loop until success or failure is signaled.
a) Generate a state, say E, and let it be the successor of the initial state. If there is no successor, signal failure.
b) Call Depth-First Search with E as the initial state.
c) If success is returned, signal success. Otherwise continue in this loop.

• The advantage of depth-first Search is that memory requirement is only linear with respect to the search graph. This is in contrast with breadth-first search which requires more space. The reason is that the algorithm only needs to store a stack of nodes on the path from the root to the current node.

• The time complexity of a depth-first Search to depth d is O(b^d) since it generates the same set of nodes as breadth-first search, but simply in a different order. Thus practically depth-first search is time-limited rather than space-limited.

• If depth-first search finds solution without exploring much in a path then the time and space it takes will be very less.

• The disadvantage of Depth-First Search is that there is a possibility that it may go down the left-most path forever. Even a finite graph can generate an infinite tree. One solution to this problem is to impose a cutoff depth on the search. Although the ideal cutoff is the solution depth d and this value is rarely known in advance of actually solving the problem. If the chosen cutoff depth is less than d, the algorithm will fail to find a solution, whereas if the cutoff depth is greater than d, a large price is paid in execution time, and the first solution found may not be an optimal one.

• Depth-First Search is not guaranteed to find the solution.

• And there is no guarantee to find a minimal solution, if more than one solution exists.

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