---
id: 5cc0c1b32479e176caf3b422
title: Check if Tree is Binary Search Tree
challengeType: 1
---

## Description

<section id='description'>
Since you already know what a binary search tree is, this challenge will establish how it is you can tell that a tree is a binary search tree or not.
The main distinction of a binary search tree is that the nodes are ordered in an organized fashion. Nodes have at most 2 child nodes (placed to the right and/or left) based on if the child node's value is greater than or equal to (right) or less than (left) the parent node.
</section>

## Instructions

<section id='instructions'>
In this challenge, you will create a utility for your tree. Write a JavaScript method <code>isBinarySearchTree</code> which takes a tree as an input and returns a boolean value for whether the tree is a binary search tree or not. Use recursion whenever possible.
</section>

## Tests

<section id='tests'>

```yml
tests:
  - text: Your Binary Search Tree should return true when checked with <code>isBinarySearchTree()</code>.
    testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; test.push(3); test.push(4); test.push(5); return isBinarySearchTree(test) == true})(), 'Your Binary Search Tree should return true when checked with <code>isBinarySearchTree()</code>.');
```

</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;
}
function isBinarySearchTree(tree) {
  // change code below this line
  // change code above this line
}
```

</div>

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

```js
BinarySearchTree.prototype.push = function(val) {
  var root = this.root;

  if (!root) {
    this.root = new Node(val);
    return;
  }

  var currentNode = root;
  var newNode = new Node(val);

  while (currentNode) {
    if (val < currentNode.value) {
      if (!currentNode.left) {
        currentNode.left = newNode;
        break;
      } else {
        currentNode = currentNode.left;
      }
    } else {
      if (!currentNode.right) {
        currentNode.right = newNode;
        break;
      } else {
        currentNode = currentNode.right;
      }
    }
  }
};
```

</div>

</section>

## Solution

<section id='solution'>

```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;
}
function isBinarySearchTree(tree) {
  if (tree.root == null) {
    return null;
  } else {
    let isBST = true;
    function checkTree(node) {
      if (node.left != null) {
        const left = node.left;
        if (left.value > node.value) {
          isBST = false;
        } else {
          checkTree(left);
        }
      }
      if (node.right != null) {
        const right = node.right;
        if (right.value < node.value) {
          isBST = false;
        } else {
          checkTree(right);
        }
      }
    }
    checkTree(tree.root);
    return isBST;
  }
};
```

</section>