AVL tree rotations in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to perform a single right rotation on a node in an AVL tree.

Data Structures Theory

def right_rotate([1]):
    y = [1].left
    T2 = y.right

    y.right = [1]
    [1].left = T2

    return y

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

Az

Bx

Cnode

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names inconsistently.

Forgetting to update the left or right child pointers.

The function takes a node as input and performs a right rotation around it. The variable node is used consistently to refer to the node being rotated.

2fill in blank

medium

Complete the code to perform a single left rotation on a node in an AVL tree.

Data Structures Theory

def left_rotate([1]):
    y = [1].right
    T2 = y.left

    y.left = [1]
    [1].right = T2

    return y

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

Aroot

Bnode

Ctemp

Dcurrent

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up left and right child pointers.

Using inconsistent variable names.

The function rotates the given node to the left by adjusting pointers accordingly.

3fill in blank

hard

Fix the error in the code that performs a left-right rotation in an AVL tree.

Data Structures Theory

def left_right_rotate([1]):
    [1].left = left_rotate([1].left)
    return right_rotate([1])

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Anode

Broot

Ctemp

Dcurrent

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names for the node parameter.

Incorrect order of rotations.

The parameter node is used consistently to perform the left-right rotation by first rotating the left child to the left, then the node to the right.

4fill in blank

hard

Fill both blanks to complete the right-left rotation function in an AVL tree.

Data Structures Theory

def right_left_rotate([1]):
    [1].right = [2]([1].right)
    return left_rotate([1])

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

Anode

Broot

Cleft_rotate

Dright_rotate

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the order of rotations.

Using incorrect function names for rotations.

The function performs a right-left rotation by first rotating the right child to the left, then rotating the node to the left.

5fill in blank

hard

Fill all three blanks to complete the balance factor calculation and rotation decision in an AVL tree node insertion.

Data Structures Theory

def insert([1], key):
    if not [1]:
        return Node(key)

    if key < [1].key:
        [1].left = insert([1].left, key)
    else:
        [1].right = insert([1].right, key)

    balance = height([1].left) - height([1].right)

    if balance > 1 and key < [1].left.key:
        return right_rotate([1])

    if balance < -1 and key > [1].right.key:
        return left_rotate([1])

    if balance > 1 and key > [1].left.key:
        [1].left = left_rotate([1].left)
        return right_rotate([1])

    if balance < -1 and key < [1].right.key:
        [1].right = right_rotate([1].right)
        return left_rotate([1])

    return [1]

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

Anode

Broot

Ccurrent

Dtemp

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names inconsistently.

Forgetting to return the updated node after rotations.

The parameter node is used consistently to refer to the current node in the AVL tree during insertion and balancing.

Practice

1. What is the main purpose of rotations in an AVL tree?

easy

A. To keep the tree balanced for faster search and update operations

B. To delete nodes from the tree

C. To increase the height of the tree

D. To sort the nodes in ascending order

Solution

1. Step 1: Understand AVL tree balance

   AVL trees maintain balance by ensuring the height difference between left and right subtrees is at most 1.

2. Step 2: Role of rotations

   Rotations adjust the tree structure to restore balance after insertions or deletions, improving operation speed.

3. Final Answer:

   To keep the tree balanced for faster search and update operations -> Option A

4. Quick Check:

   AVL rotations = balance tree = faster operations [OK]

Hint: Rotations fix balance to keep operations fast [OK]

Common Mistakes:

• Thinking rotations delete nodes
• Believing rotations sort nodes
• Assuming rotations increase tree height

2. Which of the following is the correct syntax to perform a right rotation on a node x in an AVL tree?

easy

A. rightRotate(x)

B. x.rightRotate()

C. rotateRight(x)

D. rotate(x, 'right')

Solution

1. Step 1: Identify common function naming

   In AVL tree implementations, the function to rotate right is commonly named rotateRight(node).

2. Step 2: Check options

   rotateRight(x) matches the common syntax. rightRotate(x) and x.rightRotate() are less standard, and rotate(x, 'right') is a generic call not typical in AVL code.

3. Final Answer:

   rotateRight(x) -> Option C

4. Quick Check:

   Right rotation function = rotateRight(node) [OK]

Hint: Look for 'rotateRight' as standard right rotation function name [OK]

Common Mistakes:

• Using method calls on node objects incorrectly
• Confusing rightRotate with rotateRight
• Using generic rotate function without direction

3. Given the following AVL tree insertion sequence: Insert 10, then 20, then 30. Which rotation will be performed to balance the tree?

medium

A. Left rotation

B. Right rotation

C. Left-Right rotation

D. Right-Left rotation

Solution

1. Step 1: Analyze insertion order and imbalance

   Inserting 10, then 20, then 30 creates a right-heavy chain (10 -> 20 -> 30), causing imbalance at 10.

2. Step 2: Determine rotation type

   This is a Right-Right case, fixed by a single left rotation at node 10.

3. Final Answer:

   Left rotation -> Option A

4. Quick Check:

   Right-heavy imbalance = left rotation [OK]

Hint: Right-heavy chain = left rotation to balance [OK]

Common Mistakes:

• Choosing right rotation for right-heavy imbalance
• Confusing Left-Right with Right-Right cases
• Ignoring the order of insertions

4. You implemented a left-right rotation but the AVL tree remains unbalanced after insertion. What is the most likely error?

medium

A. Performed rotations in wrong order

B. Used right rotation instead of left rotation

C. Inserted duplicate keys

D. Forgot to update node heights after rotation

Solution

1. Step 1: Understand rotation steps

   Left-right rotation requires two rotations and updating node heights to maintain AVL properties.

2. Step 2: Identify common mistake

   Not updating heights after rotations causes incorrect balance checks, leaving tree unbalanced.

3. Final Answer:

   Forgot to update node heights after rotation -> Option D

4. Quick Check:

   Update heights after rotations to keep balance [OK]

Hint: Always update heights after rotations [OK]

Common Mistakes:

• Doing rotations in wrong order
• Mixing up left and right rotations
• Ignoring height updates

5. After inserting nodes 30, 20, 25 into an empty AVL tree, which rotation(s) will balance the tree?

hard

A. Single left rotation at 20

B. Left-Right rotation at 30

C. Single right rotation at 30

D. Right-Left rotation at 20

Solution

1. Step 1: Analyze insertion sequence and imbalance

   Inserting 30, then 20, then 25 creates a left-right case: 30 has left child 20, which has right child 25.

2. Step 2: Identify correct rotation

   Left-right imbalance requires a left rotation on 20 followed by a right rotation on 30, called a left-right rotation.

3. Final Answer:

   Left-Right rotation at 30 -> Option B

4. Quick Check:

   Left-right case = left-right rotation [OK]

Hint: Left child with right-heavy subtree = left-right rotation [OK]

Common Mistakes:

• Choosing single rotations instead of double
• Confusing left-right with right-left cases
• Rotating wrong nodes