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DEPTH F

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

Definition:The aim of the DFS algorithm is travers the graph in such a way that is try to go

for from the root node. Stack is use in the implementation of the depth first search. Lets see how depth first search work with

respect to the following graph.

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Un Directed graph

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

ProcessAs stated before in DFS nodes are visited by going through the depth of the tree from the starting node if we do the depth first traversal of the above graph and print the visited node it will be “ A B C D E F CD “ DFS visited the root node then its children nodes until it reach the end node E and F them moves up to the parents nodes

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

Algorithm stepsStep:1 Push the root node in stack.Step:2 Loop until stack is empty.Step:3 Peek the node of the stack.Step:4 If the node has unvisited child nodes get the unvisited child node mark it has travers and push it on stack.

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

Directed graph

Example

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DIRECTED DEPTH FIRST SEARCH

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dfs(A)A-F A-G

Function call stack:

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dfs(A)A-F A-G

Function call stack:

visit(F)F-E

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

dfs(C)C-A C-D

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

dfs(C)C-A C-D

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

dfs(C)C-A C-D

dfs(D)D-C D-F

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

dfs(C)C-A C-D

dfs(D)D-C D-F

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dfs(A)A-F A-GFunction call

stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

dfs(C)C-A C-D

dfs(D)D-C D-F

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

dfs(C)C-A C-D

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

dfs(G)

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

dfs(E)E-C E-D E-G

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dfs(A)A-F A-G

Function call stack:

dfs(F)F-E

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dfs(A)A-F A-G

Function call stack:

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dfs(A)A-F A-G

Function call stack:

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Nodes reachable from A: A, C, D, E, F, G

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Nodes reachable from A: A, C, D, E, F, G

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

Assume that graph is connected. Depth-first search visits every vertex in the graph and checks every edge its edge. Therefore, DFS complexity is O(V + E). As it was mentioned before, if an adjacency matrix is used for a graph representation, then all edges, adjacent to a vertex can't be found efficiently, that results in O(V2) complexity.

Time Complexity

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

Advantage of depth first search

• 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.

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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages

Disadvantages • 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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DefinitionProcess Algorithmic stepsExampleCodeTime ComplexityAdvantagesDisadvantages