Given a binary tree, remove all the half nodes

Given a binary tree, how do you remove all the half nodes? - GeeksforGeeks

Given A binary Tree, how do you remove all the half nodes (which has only one child)? Note leaves should not be touched as they have both children as NULL.

For example consider the below tree.

Nodes 2 and 4 are half nodes as one of their child is Null.

The idea is to use post-order traversal to solve this problem efficiently. We first process the left children, then right children, and finally the node itself. So we form the new tree bottom up, starting from the leaves towards the root. By the time we process the current node, both its left and right subtrees were already processed. Below is C implementation of this idea.


    // Removes all nodes with only one child and returns

    // new root (note that root may change)

    Node RemoveHalfNodes(Node node) 

    {

        if (node == null)

            return null;

   

        node.left = RemoveHalfNodes(node.left);

        node.right = RemoveHalfNodes(node.right);

   

        if (node.left == null && node.right == null)

            return node;

   

        /* if current nodes is a half node with left

         child NULL left, then it's right child is

         returned and replaces it in the given tree */

        if (node.left == null) 

        {

            Node new_root = node.right;

            return new_root;

        }

   

        /* if current nodes is a half node with right

           child NULL right, then it's right child is

           returned and replaces it in the given tree  */

        if (node.right == null) 

        {

            Node new_root = node.left;

            return new_root;

        }

   

        return node;

    }

Java Version:
public Node removeAllHalfNodesFromBinaryTree(Node root) {
if (root != null) {
Node leftNode = root.left = removeAllHalfNodesFromBinaryTree(root.left);
Node rightNode = root.right = removeAllHalfNodesFromBinaryTree(root.right);

if (leftNode == null && rightNode == null) {
return root;
}
if (leftNode == null) {
return root.right;
} else if (rightNode == null) {
return root.left;
}
}
return root;
}
http://ideone.com/HpMcSm

1. public void removeHalfNodes(Node root, Node parent, Boolean isLeft)
2. {
3. while (isHalfNode(root))
4. {
5. if (root.left != null && root.right == null)
6. {
7. if (isLeft)
8. {
9. parent.left = root.left;
10. }
11. else
12. {
13. parent.right = root.left;
14. }
15. root = root.left;
16. }
17. if (root.left == null && root.right != null)
18. {
19. if (isLeft)
20. {
21. parent.left = root.right;
22. }
23. else
24. {
25. parent.right = root.right;
26. }
27. root = root.right;
28. }
29. }
30. if (root == null)
31. return;
32. removeHalfNodes(root.left, root, true);
33. removeHalfNodes(root.right, root, false);
35. }

https://javamirror.wordpress.com/2015/06/06/remove-all-half-nodes-from-a-tree/

        /**

         * Method to remove Half nodes in a tree.<br/>

         * If one of its left and right child is null for a node, remove<br/>

         * this node and assign its non-null child to its parent node.

         */

        private void removeHalfNodes(BNode parent) {

            if((this.left == null && this.right != null) || (this.left != null && this.right == null)) {

                if(parent.left == this) {

                    parent.left = this.left != null ? this.left : this.right;

                    parent.left.removeHalfNodes(parent);

                }

                 

                if(parent.right == this) {

                    parent.right = this.left != null ? this.left : this.right;

                    parent.right.removeHalfNodes(parent);

                }

            } else {

                if(this.left != null)

                    this.left.removeHalfNodes(this);

                 

                if(this.right != null)

                    this.right.removeHalfNodes(this);

            }

             

        }

    }

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