---
id: 587d8258367417b2b2512c81
title: Delete a Node with One Child in a Binary Search Tree
challengeType: 1
---

## Description
<section id='description'>
Now that we can delete leaf nodes let's move on to the second case: deleting a node with one child. For this case, say we have a tree with the following nodes 1 — 2 — 3 where 1 is the root. To delete 2, we simply need to make the right reference in 1 point to 3. More generally to delete a node with only one child, we make that node's parent reference the next node in the tree.
Instructions: We've provided some code in our <code>remove</code> method that accomplishes the tasks from the last challenge. We find the target to delete and its parent and define the number of children the target node has. Let's add the next case here for target nodes with only one child. Here, we'll have to determine if the single child is a left or right branch in the tree and then set the correct reference in the parent to point to this node. In addition, let's account for the case where the target is the root node (this means the parent node will be <code>null</code>). Feel free to replace all the starter code with your own as long as it passes the tests.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: The <code>BinarySearchTree</code> data structure exists.
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() }; return (typeof test == 'object')})(), 'The <code>BinarySearchTree</code> data structure exists.');
  - text: The binary search tree has a method called <code>remove</code>.
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.remove == 'function')})(), 'The binary search tree has a method called <code>remove</code>.');
  - text: Trying to remove an element that does not exist returns <code>null</code>.
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; return (test.remove(100) == null); })(), 'Trying to remove an element that does not exist returns <code>null</code>.');
  - text: If the root node has no children, deleting it sets the root to <code>null</code>.
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(500); test.remove(500); return (test.inorder() == null); })(), 'If the root node has no children, deleting it sets the root to <code>null</code>.');
  - text: The <code>remove</code> method removes leaf nodes from the tree
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(5); test.add(3); test.add(7); test.add(6); test.add(10); test.add(12); test.remove(3); test.remove(12); test.remove(10); return (test.inorder().join('') == '567'); })(), 'The <code>remove</code> method removes leaf nodes from the tree');
  - text: The <code>remove</code> method removes nodes with one child.
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(-1); test.add(3); test.add(7); test.add(16); test.remove(16); test.remove(7); test.remove(3); return (test.inorder().join('') == '-1'); })(), 'The <code>remove</code> method removes nodes with one child.');
  - text: Removing the root in a tree with two nodes sets the second to be the root.
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.remove !== 'function') { return false; }; test.add(15); test.add(27); test.remove(15); return (test.inorder().join('') == '27'); })(), 'Removing the root in a tree with two nodes sets the second to be the root.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
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, change code below this line
  };
}
```

</div>


### After Test
<div id='js-teardown'>

```js
BinarySearchTree.prototype = {
    add: function(value) {
        var node = this.root;
        if (node == null) {
          this.root = new Node(value);
          return;
        } else {
            function searchTree(node) {
                if (value < node.value) {
                    if (node.left == null) {
                        node.left = new Node(value);
                        return;
                    } else if (node.left != null) {
                        return searchTree(node.left)
                    };
                } else if (value > node.value) {
                    if (node.right == null) {
                        node.right = new Node(value);
                        return;
                    } else if (node.right != null) {
                        return searchTree(node.right);
                    };
                } else {
                    return null;
                };
            };
            return searchTree(node);
        };
    },
    inorder: function() {
        if (this.root == null) {
          return null;
        } else {
          var result = new Array();
          function traverseInOrder(node) {
              if (node.left != null) {
                  traverseInOrder(node.left);
              };
              result.push(node.value);
              if (node.right != null) {
                  traverseInOrder(node.right);
              };
          }
          traverseInOrder(this.root);
          return result;
        };
    },    
    isBinarySearchTree() {
        if (this.root == null) {
            return null;
        } else {
            var check = true;
            function checkTree(node) {
                if (node.left != null) {
                    var left = node.left;
                    if (left.value > node.value) {
                        check = false;
                    } else {
                        checkTree(left);
                    }
                }
                if (node.right != null) {
                    var right = node.right;
                    if (right.value < node.value) {
                        check = false;
                    } else {
                        checkTree(right);
                    };
                };
            };
            checkTree(this.root);
            return check;
        }
    }
};
```

</div>

</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
