BST Property and Why It Matters in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if a value should go to the left subtree in a BST.

DSA Javascript

if (value [1] node.value) {
  // go left
}

Drag options to blanks, or click blank then click option'

A>

B<

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' causes wrong subtree choice.

Using '==' or '!=' is incorrect for BST placement.

In a BST, values less than the current node go to the left subtree.

2fill in blank

medium

Complete the code to insert a new value into the BST correctly.

DSA Javascript

if (value [1] node.value) {
  node.left = insert(node.left, value);
} else {
  node.right = insert(node.right, value);
}

Drag options to blanks, or click blank then click option'

A>

B<=

C==

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<=' causes duplicates to go left, which may be incorrect depending on BST rules.

Using '==' is not suitable for comparison here.

Values less than the node go to the left subtree; others go right.

3fill in blank

hard

Fix the error in the BST search condition to find a value.

DSA Javascript

if (node.value [1] value) {
  return search(node.left, value);
} else if (node.value === value) {
  return node;
} else {
  return search(node.right, value);
}

Drag options to blanks, or click blank then click option'

A>

B<

C<=

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' causes searching the wrong subtree.

Using '<=' or '>=' can cause incorrect search paths.

If the node's value is greater than the target, search left subtree; else right.

4fill in blank

hard

Fill both blanks to create a BST property check function.

DSA Javascript

function isBST(node) {
  if (!node) return true;
  if (node.left && node.left.value [1] node.value) return false;
  if (node.right && node.right.value [2] node.value) return false;
  return isBST(node.left) && isBST(node.right);
}

Drag options to blanks, or click blank then click option'

A>=

B<

C<=

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' for left child check causes wrong validation.

Using '>=' for right child check causes wrong validation.

Left child must be less than node (so fail if left >= node). Right child must be greater than node (fail if right <= node).

5fill in blank

hard

Fill all three blanks to create a function that collects BST values in order.

DSA Javascript

function inorderTraversal(node, result = []) {
  if (!node) return result;
  inorderTraversal(node.[1], result);
  result.push(node.[2]);
  inorderTraversal(node.[3], result);
  return result;
}

Drag options to blanks, or click blank then click option'

Aleft

Bvalue

Cright

Dparent

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'parent' instead of 'left' or 'right' causes errors.

Pushing node instead of node.value adds wrong data.

Inorder traversal visits left subtree, then node value, then right subtree.

Practice

1. What is the main property that defines a Binary Search Tree (BST)?

easy

A. Each node has exactly two children.

B. For each node, all values in the left subtree are smaller, and all values in the right subtree are larger.

C. All nodes have the same value.

D. Nodes are arranged in a circular linked list.

Solution

1. Step 1: Understand BST node value rules

   In a BST, the left subtree contains values smaller than the node, and the right subtree contains values larger than the node.

2. Step 2: Compare options with BST definition

   For each node, all values in the left subtree are smaller, and all values in the right subtree are larger. matches the BST property exactly, while others describe different structures.

3. Final Answer:

   For each node, all values in the left subtree are smaller, and all values in the right subtree are larger. -> Option B

4. Quick Check:

   BST property = left < node < right [OK]

Hint: Remember: left < node < right defines BST [OK]

Common Mistakes:

• Confusing BST with binary tree (not ordered)
• Thinking all nodes must have two children
• Assuming all values are equal

2. Which of the following is the correct way to check if a value should go to the left subtree in a BST insertion function in JavaScript?

easy

A. if (value < node.value) { insertLeft(); }

B. if (value > node.value) { insertLeft(); }

C. if (value == node.value) { insertLeft(); }

D. if (value >= node.value) { insertLeft(); }

Solution

1. Step 1: Recall BST insertion rule

   Values smaller than the current node go to the left subtree.

2. Step 2: Match condition to insertion side

   Only the condition 'value < node.value' correctly directs insertion to the left.

3. Final Answer:

   if (value < node.value) { insertLeft(); } -> Option A

4. Quick Check:

   Smaller values go left [OK]

Hint: Use < for left subtree insertion [OK]

Common Mistakes:

• Using > instead of < for left subtree
• Using == which is not for left or right
• Using >= which includes equal values incorrectly

3. What will be the in-order traversal output of the following BST?

    10
   /  \
  5   15
 / \    \
3   7    20

medium

A. [20, 15, 10, 7, 5, 3]

B. [10, 5, 3, 7, 15, 20]

C. [3, 5, 7, 10, 15, 20]

D. [5, 3, 7, 10, 15, 20]

Solution

1. Step 1: Understand in-order traversal

   In-order traversal visits left subtree, then node, then right subtree recursively.

2. Step 2: Apply in-order to given tree

   Left subtree of 10: 3, 5, 7; then 10; then right subtree: 15, 20. Combined: [3, 5, 7, 10, 15, 20]

3. Final Answer:

   [3, 5, 7, 10, 15, 20] -> Option C

4. Quick Check:

   In-order = sorted BST values [OK]

Hint: In-order traversal of BST gives sorted values [OK]

Common Mistakes:

• Confusing pre-order or post-order with in-order
• Listing nodes in insertion order
• Reversing the traversal order

4. Consider this BST insertion code snippet in JavaScript:

function insert(node, value) {
  if (!node) return { value, left: null, right: null };
  if (value <= node.value) {
    node.left = insert(node.left, value);
  } else {
    node.right = insert(node.right, value);
  }
  return node;
}

What is the main issue with this code regarding BST property?

medium

A. It inserts larger values on the left subtree incorrectly.

B. It does not handle the case when node is null.

C. It returns undefined instead of the node.

D. It allows duplicate values on the left subtree, which may break strict BST rules.

Solution

1. Step 1: Analyze duplicate handling in insertion

   The condition 'value <= node.value' inserts duplicates to the left subtree.

2. Step 2: Understand BST strictness

   Strict BSTs require left subtree values strictly less than node value; duplicates on left can break this.

3. Final Answer:

   It allows duplicate values on the left subtree, which may break strict BST rules. -> Option D

4. Quick Check:

   Duplicates on left break strict BST [OK]

Hint: Use < for left to avoid duplicates on left [OK]

Common Mistakes:

• Ignoring duplicate value placement
• Thinking null check is missing
• Confusing left and right subtree insertion

5. You have a BST where some nodes violate the BST property because their left child has a value greater than the node. Which approach best fixes the tree without rebuilding it completely?

hard

A. Swap the values of the violating nodes with their children to restore BST property locally.

B. Ignore the violations as they do not affect search operations.

C. Delete all nodes and insert them again in correct order.

D. Perform an in-order traversal, collect values, then rebuild the BST from sorted values.

Solution

1. Step 1: Understand the violation type

   Left child having greater value than node breaks BST property locally.

2. Step 2: Choose minimal fix without full rebuild

   Swapping values of violating nodes with their children can restore local BST property without full rebuild.

3. Step 3: Evaluate other options

   Perform an in-order traversal, collect values, then rebuild the BST from sorted values. rebuilds fully, Delete all nodes and insert them again in correct order. deletes all nodes (costly), Ignore the violations as they do not affect search operations. ignores problem (wrong).

4. Final Answer:

   Swap the values of the violating nodes with their children to restore BST property locally. -> Option A

5. Quick Check:

   Local swaps fix BST violations efficiently [OK]

Hint: Fix BST by swapping violating node values locally [OK]

Common Mistakes:

• Rebuilding entire tree unnecessarily
• Ignoring violations thinking no impact
• Deleting all nodes instead of fixing