One Pager Cheat Sheet

• Write a function, isValidBST(node), that returns true if the given binary search tree is valid according to the defined conditions.
• The left subtree of a node in a Binary Search Tree (BST) must only contain nodes with keys LESS than the node's key, while the right subtree must contain nodes with keys GREATER than the node's key to maintain its in-order traversal which produces an increasing order of nodes.
• The In-order traversal of a Binary Search Tree follows a specific algorithm to access data in a very efficient manner, visiting each node left to right by recursively calling the Inorder() function.
• An in-order traversal of a BST processes the node keys in ascending order by beginning at the smallest key and progressively traversing rightward.
• The given recursive function will return 2 times the result of the recursive call until the if statement evaluates to True, in which case the value of n is returned, which in the example is 4 and the result of func(2) is 16.
• Running through inputs with a binary search tree can help trigger insights for a solution.
• Checking if every left child is smaller than the root, and every right child is greater than the local root is a brute force solution for determining the direction of nodes in a tree.
• We can recursively check every subtree by running through the method, but to ensure accuracy we should extend the tree by adding two more children to the root's left child.
• We can use an in-order depth-first search to check a binary search tree for validity by comparing its processed node values in sorted order.
• We can determine if a given tree is valid in O(n) time complexity and O(logn) space complexity by iterating through all n elements and checking that each successive element is greater than the previous iteration.

This is our final solution.

To visualize the solution and step through the below code, click Visualize the Solution on the right-side menu or the VISUALIZE button in Interactive Mode.

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}

var assert = require('assert');

​

function isValidBST(root) {

  const searchResults = [];

  inOrder(root, searchResults);

​

  for (let i = 1; i < searchResults.length; i++) {

    if (searchResults[i - 1] >= searchResults[i]) {

      return false;

    }

  }

​

  return true;

}

​

function inOrder(root, output) {

  if (!root) {

    return;

  }

​

  inOrder(root.left, output);

  output.push(root.val);

  inOrder(root.right, output);

}

​

function Node(val) {

  this.val = val;

  this.left = null;

  this.right = null;

}

​

// Regular binary trees

Alright, well done! Try another walk-through.

If you had any problems with this tutorial, check out the main forum thread here.