In this article, you will learn to implement Depth First Search (DFS) algorithm on a graph by using Java with iterative and recursive approaches

Depth First Search (DFS) is an algorithm for traversing or searching for a graph. The algorithm starts at an arbitrary node and explores as far as possible along each branch before backtracking

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Problem

  • Give an undirected/directed graph G(V, E)

  • Write a Depth-First search algorithm to print out each vertex value exactly once

Example

For the above graph with 0 as the starting vertex, assuming that the left edges are chosen before the right edges, the DFS traversal order will be 0 -> 1 -> 3 -> 2 -> 4

Approach 1: Iterative

  • Use an array to track visited nodes to avoid processing a node more than once

  • Use a stack to track which nodes to visit next


GraphUndirectedByAdjacencyList is defined in Graph Data Structure

  • Output
0 1 3 2 4  
  • Time complexity: O(V+E)

  • Space complexity: O(V)

Approach 2: Iterative with Color

  • Use a color array to track vertex states. Each vertex can have 3 states marked by color

    • White represents unvisited

    • Gray represents a visit in progress

    • Black represents visited

  • Use a stack to track which nodes to visit next


GraphUndirectedByAdjacencyList is defined in Graph Data Structure

  • Output
0 1 3 2 4  
  • Time complexity: O(V+E)

  • Space complexity: O(V)

Approach 3: Recursive

  • Use an array to track visited nodes to avoid processing a node more than once

  • Instead of using a stack, the DFS algorithm calls to itself to explore unvisited vertices


GraphUndirectedByAdjacencyList is defined in Graph Data Structure

  • Output
0 2 1 3 4  
  • Time complexity: O(V+E)

  • Space complexity: O(V)

Approach 4: Recursive with Color

  • Use a color array to track vertex states. Each vertex can have 3 states marked by color

    • White represents unvisited

    • Gray represents a visit in progress

    • Black represents visited

  • Instead of using a stack, the DFS algorithm calls to itself to explore White vertices


GraphUndirectedByAdjacencyList is defined in Graph Data Structure

  • Output
0 2 1 3 4  
  • Time complexity: O(V+E)

  • Space complexity: O(V)

Applications

  • Detect Cycle in a Directed Graph

    You can use DFS to detect a cycle in a directed graph. When visiting a vertex v and its adjacency vertices, if there is a back edge (w, v) which directs to v then that graph has a cycle

    Learn more

  • Implement Topological Sort with Directed Acyclic Graph

    Topological sort is an algorithm which takes a directed acyclic graph and returns a list of vertices in the linear ordering where each vertex has to precede all vertices it directs to

    Learn more