freeCodeCamp/guide/english/certifications/coding-interview-prep/data-structures/find-the-minimum-and-maximum-height-of-a-binary-search-tree/index.md

---
title: Find the Minimum and Maximum Height of a Binary Search Tree
---
# Find the Minimum and Maximum Height of a Binary Search Tree


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## Solutions

<details><summary>Solution 1 (Click to Show/Hide)</summary>

```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;
  // change code below this line
  // change code above this line
  this.findMinHeight = function(root = this.root) {
    // empty tree.
    if (root === null) {
      return -1;
    }
    // leaf node.
    if (root.left === null && root.right === null) {
      return 0;
    }
    if (root.left === null) {
      return this.findMinHeight(root.right) + 1;
    }
    if (root.right === null) {
      return this.findMinHeight(root.left) + 1;
    }
    const lHeight = this.findMinHeight(root.left);
    const rHeight = this.findMinHeight(root.right);
    return Math.min(lHeight, rHeight) + 1;
  };
  this.findMaxHeight = function(root = this.root) {
    // empty tree.
    if (root === null) {
      return -1;
    }
    // leaf node.
    if (root.left === null && root.right === null) {
      return 0;
    }
    if (root.left === null) {
      return this.findMaxHeight(root.right) + 1;
    }
    if (root.right === null) {
      return this.findMaxHeight(root.left) + 1;
    }
    const lHeight = this.findMaxHeight(root.left);
    const rHeight = this.findMaxHeight(root.right);
    return Math.max(lHeight, rHeight) + 1;
  };
  this.isBalanced = function(root = this.root) {
    if (root === null) {
      return true;
    }

    if (root.left === null && root.right === null) {
      return true;
    }

    if (root.left === null) {
      return this.findMaxHeight(root.right) <= 0;
    }

    if (root.right === null) {
      return this.findMaxHeight(root.left) <= 0;
    }

    const lHeight = this.findMaxHeight(root.left);
    const rHeight = this.findMaxHeight(root.right);
    if (Math.abs(lHeight - rHeight) > 1) {
      return false;
    }
    return this.isBalanced(root.left) && this.isBalanced(root.right);
  };
}
```
</details>