# Possible solution for Delete a Node with Two Children in a Binary Search Tree

What is your hint or solution suggestion?
Hint: apply recursion to second tree to remove replacement node until it reach a node with no right or left

Solution
``````var displayTree = tree => console.log(JSON.stringify(tree, null, 2));
function Node(value) {
this.value = value;
this.left = null;
this.right = null;
}

function BinarySearchTree() {
this.root = null;
this.remove = function(value) {
if (this.root === null) {
return null;
}
var target;
var parent = null;
// Find the target value and its parent
(function findValue(node = this.root) {
if (value == node.value) {
target = node;
} else if (value < node.value && node.left !== null) {
parent = node;
return findValue(node.left);
} else if (value < node.value && node.left === null) {
return null;
} else if (value > node.value && node.right !== null) {
parent = node;
return findValue(node.right);
} else {
return null;
}
}.bind(this)());
if (target === null) {
return null;
}
// Count the children of the target to delete
var children =
(target.left !== null ? 1 : 0) + (target.right !== null ? 1 : 0);
// Case 1: Target has no children
if (children === 0) {
if (target == this.root) {
this.root = null;
} else {
if (parent.left == target) {
parent.left = null;
} else {
parent.right = null;
}
}
}
// Case 2: Target has one child
else if (children == 1) {
var newChild = target.left !== null ? target.left : target.right;
if (parent === null) {
target.value = newChild.value;
target.left = null;
target.right = null;
} else if (newChild.value < parent.value) {
parent.left = newChild;
} else {
parent.right = newChild;
}
target = null;
}
// Case 3: Target has two children
// Only change code below this line
else if(children == 2){
this.findReplacement = (type, root = targe, value = null)=>{
if(root){
if(value == null) value = root;
if(type == 'small'){
if(value.value > root.value) value = root;
}else{
if(value.value < root.value) value = root;
}
}
if(root.left) value = this.findReplacement(type, root.left,value);
if(root.right) value = this.findReplacement(type, root.right,value);
return value;
}
if(parent == null || value == parent.right.value){
let replacement = this.findReplacement('small',target.right);
this.remove(replacement.value);
target.value = replacement.value;
}else{
let replacement = this.findReplacement('large',target.left);
this.remove(replacement.value);
target.value = replacement.value;
}
}
};
}
``````

Challenge: Delete a Node with Two Children in a Binary Search Tree