Data Structures and Algorithms The Complete Masterclass - Binary Search Tree

This video tutorial covers binary search trees (BSTs), explaining their structure, types, and operations. It discusses the differences between balanced and unbalanced BSTs, focusing on their complexity and logarithmic dependence. The tutorial also details operations like searching, insertion, and deletion, including handling cases with zero, one, or two children. The importance of maintaining a balanced tree for optimal performance is emphasized.

What is a key characteristic of a Binary Search Tree?

• Left subtree nodes are greater than the root.

• All nodes have exactly two children.

• Right subtree nodes are less than the root.

• Left subtree nodes are less than the root, and right subtree nodes are greater.

What defines a balanced Binary Search Tree?

• The tree is perfectly symmetrical.

• All nodes have two children.

• The height difference between left and right subtrees is not more than one.

• The tree has an equal number of nodes on the left and right.

What is the primary advantage of a balanced BST over an unbalanced one?

• Consistent time complexity for operations.

• Faster insertion times.

• More nodes can be stored.

• Simpler structure.

How does the height of a balanced BST typically relate to the number of nodes?

• It is directly proportional to the number of nodes.

• It is constant regardless of the number of nodes.

• It is logarithmic in relation to the number of nodes.

• It is quadratic in relation to the number of nodes.

What is the average time complexity for searching in a balanced BST?

• O(log n)

• O(n^2)

• O(n)

• O(1)

Which operation in a BST can be the most complex due to multiple cases?

• Traversal

• Deletion

• Searching

• Insertion

What is the worst-case time complexity for insertion in an unbalanced BST?

• O(n^2)

• O(1)

• O(n)

• O(log n)

What is the average time complexity for deletion in a balanced BST?

• O(n)

• O(n^2)

• O(log n)

• O(1)

In a BST, what happens when a node with two children is deleted?

• The node is replaced by its right child.

• The node is replaced by the highest value in the left subtree or the lowest in the right subtree.

• The node is replaced by its left child.

• The node is simply removed.

How can repeated insertions affect a BST?

• They have no effect on the tree's structure.

• They can cause the tree to become unbalanced.

• They make the tree perfectly balanced.

• They always maintain the tree's balance.