BST property and invariant in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the BST Property

Which of the following best describes the Binary Search Tree (BST) property?

A For every node, the values in the left subtree are equal to the node's value, and the right subtree contains greater values.

B For every node, all values in its left subtree are greater than the node's value, and all values in its right subtree are less.

C For every node, all values in its left subtree are less than the node's value, and all values in its right subtree are greater.

D For every node, the left and right subtrees contain equal numbers of nodes.

💡 Hint

Think about how the tree helps you find values quickly by comparing with the current node.

The BST property ensures that for each node, all values in the left subtree are smaller, and all values in the right subtree are larger. This allows efficient searching.

📋 Factual

intermediate

Invariant Maintenance in BST Operations

Which invariant must be maintained after inserting a new value into a BST?

A The tree remains balanced with equal height on both sides.

B The BST property that left subtree values are less and right subtree values are greater than the node's value.

C All leaf nodes must be at the same depth.

D The root node must always have the smallest value.

💡 Hint

Focus on what property defines a BST regardless of shape.

After insertion, the BST property must hold so that searching remains efficient. Balancing or leaf depth equality is not guaranteed in a basic BST.

🔍 Analysis

advanced

Detecting BST Property Violation

Given the following tree structure, which node violates the BST property?

      10
     /  \
    5    15
   / \     \
  2   12    20

A Node with value 12

B Node with value 5

C Node with value 15

D Node with value 20

💡 Hint

Check if all nodes in the left subtree are less than 10 and all in the right subtree are greater than 10.

The node with value 12 is in the left subtree of 10 but is greater than 10, violating the BST property.

❓ Comparison

advanced

Comparing BST and Binary Tree Properties

Which statement correctly distinguishes a Binary Search Tree (BST) from a general Binary Tree?

A A BST requires the left child to be smaller and the right child to be larger than the node, while a Binary Tree has no such ordering requirement.

B A BST requires nodes to have at most two children, while a Binary Tree can have any number of children.

C A BST must be a complete tree, while a Binary Tree can be incomplete.

D A BST stores only unique values, while a Binary Tree allows duplicates.

💡 Hint

Think about the ordering rules that make searching efficient.

A BST has a strict ordering rule for left and right children, unlike a general Binary Tree which has no ordering constraints.

❓ Reasoning

expert

Effect of Violating BST Invariant on Search

If a node in a BST violates the BST property, what is the most likely consequence when searching for a value?

A The search will convert the tree into a balanced BST automatically.

B The search will ignore the violation and continue correctly.

C The search will always find the value faster than in a balanced BST.

D The search might fail to find the value even if it exists in the tree.

💡 Hint

Consider how the search algorithm relies on the BST property to decide which subtree to explore.

If the BST property is violated, the search may go down the wrong path and miss the target value even if it is present.