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Graph traversal algorithms: Breadth First Search

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• Breadth First Search:     visit all your neighbors before your neighbor's neighbors
  • What is breadth first:

    Start at some node: Visit all the neighbors first: Only then visit the neighbors' neighbors: And so on

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  • Data structure that helps in the implementation of the Breadth First Search algorithm:

    A queue Nodes will be visit in the order imposed by the FIFO queue

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  • Breadth first search:

    Put an arbitrary node x in queue Q Mark the node x as visited Repeat: h = remove the first node from queue Q Put all of h's unvisited neighbor nodes in a queue Q Mark all inserted nodes as visited

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  • Example:

    Graph: Initial state: State after processing 0 State after processing 1 State after processing 3 State after processing 8 State after processing 7 State after processing 2 State after processing 4 State after processing 5 State after processing 6 DONE (The queue has become empty)

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• Implementation in Java
  • Java code:

    public void bfs() { // BFS uses Queue data structure Queue q = new LinkedList(); q.add(rootNode); visited[rootNode] = true; printNode(rootNode); while( !q.isEmpty() ) { int n, child; n = (q.peek()).intValue(); child = getUnvisitedChildNode(n); // Returns -1 if no unvisited niode left if ( child != -1 ) { // Found an unvisted node visited[child] = true; // Mark as visited printNode(child); q.add(child); // Add to queue } else { q.remove(); // Process next node } } }

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  • Example Program: (Demo above code)                                                
    • The BFS Prog file: click here
    • A Test program: click here