Rebalancing an arbitrary BST?

Question

Reference: I was asked this question @MS SDE interview, 3rd round. And it\'s not a homework problem. I also gave it a thought and mentioning my approach bel

Answer 1

This will convert your normal BST into a balanced BST with minimum possible height in O(n). First, save all your nodes sorted into a vector. Then, the root is the mid element and recursively build a tree from 0 to mid-1 as its left and build a tree from mid+1 to vector.size()-1 as its right child. After all these steps root keeps the balanced BST with the min-height.

    import java.util.Vector;

        public class ConvertBSTIntoBalanced {

            public static void main(String[] args) {
                TreeNode node1 = new TreeNode(1);
                TreeNode node2 = new TreeNode(2);
                TreeNode node3 = new TreeNode(3);
                TreeNode node4 = new TreeNode(4);
                node1.right = node2;
                node2.right = node3;
                node3.right = node4;
                ConvertBSTIntoBalanced convertBSTIntoBalanced = new ConvertBSTIntoBalanced();
                TreeNode balancedBSTRoot = convertBSTIntoBalanced.balanceBST(node1);
            }

            private void saveNodes(TreeNode node, Vector nodes) {
                if (node == null)
                    return;
                saveNodes(node.left, nodes);
                nodes.add(node);
                saveNodes(node.right, nodes);
            }

            private TreeNode buildTree(Vector nodes, int start, int end) {
                if (start > end)
                    return null;
                int mid = (start + end) / 2;
                TreeNode midNode = nodes.get(mid);
                midNode.left = buildTree(nodes, start, mid - 1);
                midNode.right = buildTree(nodes, mid + 1, end);
                return midNode;
            }

            public TreeNode balanceBST(TreeNode root) {
                Vector nodes = new Vector<>();
                saveNodes(root, nodes);
                return buildTree(nodes, 0, nodes.size() - 1);
            }

        public class TreeNode {

        public Integer val;
        public TreeNode left;
        public TreeNode right;

        public TreeNode(Integer x) {
            val = x;
        }

    }

        }

I hope it helps.