Dfs presentation

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PRESETA
TION
DATA S
TRUCTU
RE
Click icon to add picture
GROUP
MEM
BERS
WAJIH
A IMTI
AZ
AMMARA SID
DIQUI
SAMIA JA
VED
HAMNA AFZ
AL
RUBAB ZAHRA
DEPTH F
IRST
SEARCH
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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.
a d
cf
e
b
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
F
A
B C G
D
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dfs(A)AF AG
Function call stack:
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DIRECTED DEPTH FIRST SEARCH
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dfs(A)AF AG
Function call stack:
visit(F)FE
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DIRECTED DEPTH FIRST SEARCH
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
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DIRECTED DEPTH FIRST SEARCH
F
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B C G
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
dfs(C)CA CD
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DIRECTED DEPTH FIRST SEARCH
F
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B C G
D
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
dfs(C)CA CD
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DIRECTED DEPTH FIRST SEARCH
F
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B C G
D
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
dfs(C)CA CD
dfs(D)DC DF
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DIRECTED DEPTH FIRST SEARCH
F
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B C G
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
dfs(C)CA CD
dfs(D)DC DF
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DIRECTED DEPTH FIRST SEARCH
F
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B C G
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dfs(A)AF AGFunction call
stack:
dfs(F)FE
dfs(E)EC ED EG
dfs(C)CA CD
dfs(D)DC DF
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DIRECTED DEPTH FIRST SEARCH
F
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B C G
D
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
dfs(C)CA CD
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DIRECTED DEPTH FIRST SEARCH
F
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
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DIRECTED DEPTH FIRST SEARCH
F
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
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DIRECTED DEPTH FIRST SEARCH
F
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
dfs(G)
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DIRECTED DEPTH FIRST SEARCH
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dfs(A)AF AG
Function call stack:
dfs(F)FE
dfs(E)EC ED EG
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DIRECTED DEPTH FIRST SEARCH
F
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dfs(A)AF AG
Function call stack:
dfs(F)FE
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DIRECTED DEPTH FIRST SEARCH
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dfs(A)AF AG
Function call stack:
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DIRECTED DEPTH FIRST SEARCH
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dfs(A)AF AG
Function call stack:
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DIRECTED DEPTH FIRST SEARCH
F
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B C G
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Nodes reachable from A: A, C, D, E, F, G
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DIRECTED DEPTH FIRST SEARCH
F
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B C 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. Depthfirst 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 depthfirst Search is that memory requirement is only linear with respect to the search graph. This is in contrast with breadthfirst 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 depthfirst Search to depth d is O(b^d) since it generates the same set of nodes as breadthfirst search, but simply in a different order. Thus practically depthfirst search is timelimited rather than spacelimited.
• If depthfirst 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 DepthFirst Search is that there is a possibility that it may go down the leftmost 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. • DepthFirst 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