Delete a node in a Binary Search Tree BST.

bst-delete-node.js

/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {TreeNode} root
 * @param {number} key
 * @return {TreeNode}
 */
var deleteNode = function(root, key) {
    // Find node to delete.
    if (root !== null) {
        var current = root;
        var stack = [];
        
        while (current) {
            stack.push(current);
            
            if (current.val === key) {
                // Found the node to delete.
                stack.pop();
                var parent = stack.pop();
    
                if (!current.left && !current.right) {
                    // No children, just remove the node.
                    if (parent && parent.left && parent.left.val === current.val) {
                        parent.left = null;
                    }
                    else if (parent) {
                        parent.right = null;
                    }
                    else {
                        // No parent, this must be the root node.
                        root = [];
                    }
                }
                else if (current.left && !current.right) {
                    // One left child node.
                    if (parent && parent.left && parent.left.val === current.val) {
                        parent.left = current.left;
                    }
                    else if (parent) {
                        parent.right = current.left;
                    }
                    else {
                        // No parent, this must be the root node.
                        root = current.left;
                    }
                }
                else if (current.right && !current.left) {
                    // One right child node.
                    if (parent && parent.left && parent.left.val === current.val) {
                        parent.left = current.right;
                    }
                    else if (parent) {
                        parent.right = current.right;
                    }
                    else {
                        // No parent, this must be the root node.
                        root = current.right;
                    }
                }
                else {
                    // Node has 2 children.
                    // First, find the minimum element in the right subtree of the node to be removed.
                    var minNode = current.right;
                    while (minNode) {
                        if (minNode.left) {
                            minNode = minNode.left;
                        }
                        else {
                            // We're at the bottom of the subtree.
                            break;
                        }
                    }
                    
                    // Delete minNode.
                    current = deleteNode(current, minNode.val);

                    // Replace value.
                    current.val = minNode.val;
                }
                break;
            }
            else if (key < current.val) {
                current = current.left;
            }
            else if (key > current.val) {
                current = current.right;
            }
        }
    }

    return root;
};

zexample.txt

Given a root node reference of a BST and a key, delete the node with the given key in the BST. Return the root node reference (possibly updated) of the BST.

Basically, the deletion can be divided into two stages:

Search for a node to remove.
If the node is found, delete the node.
Note: Time complexity should be O(height of tree).

Example:

root = [5,3,6,2,4,null,7]
key = 3

    5
   / \
  3   6
 / \   \
2   4   7

Given key to delete is 3. So we find the node with value 3 and delete it.

One valid answer is [5,4,6,2,null,null,7], shown in the following BST.

    5
   / \
  4   6
 /     \
2       7

Another valid answer is [5,2,6,null,4,null,7].

    5
   / \
  2   6
   \   \
    4   7