Lecture09

Tree traversals

• Tree Traversal: a process to visit all nodes in a tree is called a tree traversal. Typically used to find a key or process all or some keys.
• Traversal always starts at the root of the tree.

Binary Tree Traversal involves three "visits":

• The node is visited(the root)
• The node's left child is traversed
• The node's right child is traversed

Binary Tree Traversals

• The sequence in which those three "visits" are executed determins what kind of traversal it si.
  • Typical traversals:
  • Pre-order Traversal(Node, Left Child, Right Child)
  • In-order Traversal(Left Child, Node, Right Child)
  • Post-order Traversal(Left Child, Right Child, Node)

Pre-order(Node, Left, Right)

• Pre-order Traversal(Node, Left Child, Right Child)
  • See parent first, then look at left and right branches

image-20210326214120936.png

In-order(Left Child,Node, Right Child)

• In-order(Left Child,Node, Right Child)
  • See left branch first, then look at the parent, and finally look at the right branch

image-20210326214247275.png

Post-order Traversal(Left Child, Right Child, Node)

• Post-order Traversal(Left Child, Right Child, Node)
  • Look at left and right branches first, and then see parent

image-20210326214334788.png

Level-order(Level-first|Left-Right)

image-20210326214438559.png

Binary Tree: Recursive Structure

image-20210326214554687.png

Traversals: Algorithms

• Pre-order Traversal(recursive)

void preOrder(Node node){
    if(node != null){
        System.out.print(node.getKey());
        preOrder(node.getLeftChild);
        preOrder(node.getRightChild);
    }else{
        return;
    }
}

• In-order Traversal(recursive)

void inOrder(Node node){
    if(node != null){
        inOrder(node.getLeftChild);
        System.out.print(node.getKey());
        inOrder(node.getRightChild);
    }else{
        return;
    }
}

• Post-order Traversal(recursive)

void postOrder(Node node){
    if(node != null){
    postOrder(node.getLeftChild);
    postOrder(node.getRightChild);
    System.out.print(node.getKey());
    }
}

• Level-order Traversal

void levelOrder(Node node){
    if(node !=null){
        queue.add(node);
        while(queue.isEmpty()==null)
            current = queue.dequeue();
            System.out.println(current);
            queue.enqueue(current children)
    }
}

Traversals: Selected Applications

• Depth first search(DFS)

• Pre-order Traversal

  • binary tree duplicaiton

• In-order Traversal

  • binary search tree in order processing("show sorted")

• Post-order Traversal Traversal

  • deleting sub-trees

• Level-order(Level-by-level | left-to-right)

  • Breadth first search(BFS)
  • finding shortest paths
  • calculating maximum flow algorithms

Binary Search Tree: getMin()

image-20210326221100543.png

Binary Search Tree: getMax()

image-20210326221148574.png