Question 65 : How to do boundary traversal of binary tree.

 Write a java program to do boundary traversal of binary tree as shown in below image.

If you look closely to above diagram, boundary traversals can be divided into three essential parts

• Print left edge nodes (Excluding leaf nodes)
• Print leaf nodes
• Print right edge nodes (From bottom to top)

Print left edge nodes (Excluding leaf nodes)

If you define a boundary for left part, it is nothing but left child if present, otherwise right child.

private static void printLeftEdgeNodes(TreeNode root) {
        if(root==null)
            return;
 
        // if leaf node, ignore while printing edges
        if(root.left==null && root.right==null)
            return;
 
        System.out.print(root.data+" ");
 
        // If left is null, right will be the boundary edge.
        if(root.left==null)
        {
            printLeftEdgeNodes(root.right);
        }
        else
        {
            printLeftEdgeNodes(root.left);
        }
 
    }

Print leaf nodes:

Its pretty simple operation.  Whenever you encounter leaf node, print it.

private static void printLeafNodes(TreeNode root) {
        if(root==null)
            return;
 
        if(root.left==null && root.right==null)
        {
            System.out.print(root.data+" ");
            return;
        }
        printLeafNodes(root.left);
        printLeafNodes(root.right);
    }

Print right edge nodes (From bottom to top) :

If you define boundary for right part, it is nothing but right child if present, otherwise left child. As we need to print bottom up, we will print the node while returning back from recursion stack.

private static void printRightBottomUp(TreeNode root)
    {
        if(root==null)
            return;
 
        // if leaf node, ignore while printing edges
        if(root.left==null && root.right==null)
        {
            return;
        }
 
        if(root.right!=null)
        {
            printRightBottomUp(root.right);
        }
        else if(root.left!=null)
        {
            printRightBottomUp(root.left);
        }
 
        System.out.print(root.data+" ");
}

public class BinaryTreeBoundaryTraversal {
    public static class TreeNode
    {
        int data;
        TreeNode left;
        TreeNode right;
        TreeNode(int data)
        {
            this.data=data;
        }
    }
 
    public static void boundaryLevelTraversal(TreeNode root)
    {
        System.out.print(root.data+" ");
        printLeftEdgeNodes(root.left);
        printLeafNodes(root);
        printRightBottomUp(root.right);
 
    }
 
    private static void printLeafNodes(TreeNode root) {
        if(root==null)
            return;
      if(root.left==null && root.right==null)
     {
            System.out.print(root.data+" ");
            return;
        }
        printLeafNodes(root.left);
        printLeafNodes(root.right);
    }
 
    private static void printRightBottomUp(TreeNode root)
    {
        if(root==null)
            return;
 
        // if leaf node, ignore while printing edges
        if(root.left==null && root.right==null)
        {
            return;
        }
 
        if(root.right!=null)
        {
            printRightBottomUp(root.right);
        }
        else if(root.left!=null)
        {
            printRightBottomUp(root.left);
        }
 
        System.out.print(root.data+" ");
    }
 
    private static void printLeftEdgeNodes(TreeNode root) {
        if(root==null)
            return;
 
        // if leaf node, ignore while printing edges
        if(root.left==null && root.right==null)
            return;
 
        System.out.print(root.data+" ");
 
        // If left is null, right will be the boundary edge.
        if(root.left==null)
        {
            printLeftEdgeNodes(root.right);
        }
        else
        {
            printLeftEdgeNodes(root.left);
        }
 
    }
 
    public static void main(String[] args)
    {
        // Creating a binary tree
        TreeNode rootNode=createBinaryTree();
        System.out.println("Boundary traversal of binary tree will be:");
        boundaryLevelTraversal(rootNode);
    }
 
    public static TreeNode createBinaryTree()
    {
 
        TreeNode rootNode =new TreeNode(40);
        TreeNode node20=new TreeNode(20);
        TreeNode node10=new TreeNode(10);
        TreeNode node30=new TreeNode(30);
        TreeNode node60=new TreeNode(60);
        TreeNode node50=new TreeNode(50);
        TreeNode node70=new TreeNode(70);
        TreeNode node5=new TreeNode(5);
        TreeNode node45=new TreeNode(45);
        TreeNode node55=new TreeNode(55);
 
        rootNode.left=node20;
        rootNode.right=node60;
 
        node20.left=node10;
        node20.right=node30;
 
        node60.left=node50;
        node60.right=node70;
 
        node10.right=node5;
        node5.right=node45;
 
        node50.right=node55;
        return rootNode;
    }
}

When you run the above program, you will get the below output:

Boundary traversal of binary tree will be:
40 20 10 5 45 30 55 70 60

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